polars-online
Online model fitting for Polars — linear models, streaming moments, clustering and regime detection — for data that can never fit in memory all at once. When the data has a time order, a fit can also be local: a rolling fit that follows the recent rows, without refitting a window at every step. Rust core, Python API, and a standalone command line (docs/RUNNER.md).
A note on Polars versions. Both of the ways this library plugs into Polars carry no stability promise from Polars, so
polars>=1.34.0,<3is measured rather than guaranteed: a weekly job runs the whole test suite on the newest Polars, every release runs it again before publishing, and the response to a failure is decided in advance (Versioning and the Polars pin).
Contents. Introduction · The models · Install · How a bank sees a stream · Running a bank · Saving, loading and serving · Preparing a stream · Reading the fit · Diagnostics, selection and evaluation · Models · Performance · Against scikit-learn · What this is not · Versioning and the Polars pin · Testing · Development
Introduction
The idea. You describe one or more models — a ridge regression of a stock's return on two signals, say, with a separate regression for every stock. polars-online fits all of them in a single pass over your rows. Each row is predicted first, from what the models have learned so far, and learned from second; that order is what makes every prediction honest, because no row's own outcome is in the number predicted for it. The models keep only what they have learned, never the rows, which is what lets the whole thing run on far more rows than fit in memory. The order of the rows matters only when a model forgets: with a decay, older rows count less, so the rows must come in time order; without a decay, a model that solves or accumulates gives the same answer in any order.
Four words this README uses throughout.
| word | meaning |
|---|---|
| spec | the description of one model: which model, which columns it reads, how it should treat time. po.spec.ewridge(...) builds one |
| model bank — "the bank" | a set of specs fitted together over the same rows, and the Python object that holds them, ModelBank. Wherever this README says the bank, it means a model bank |
| stream, chunk | the rows, in the order the bank reads them — time order, when a model forgets — and the pieces they arrive in. The bank takes one chunk at a time and its results never depend on where one chunk ended and the next began |
| state | everything a bank has learned. Its size depends on the models, not on how many rows have gone past, which is why the stream can be any length |
One fit over every row. Turn forgetting off and a model that solves converges to the batch fit over every row it has seen, in any row order (Without a decay). The state is then a complete summary of those rows, which is what makes it a model worth saving and serving: fit it over a folder of parquet files that never has to fit in memory, save it at the last row, then score new rows against it without learning from them.
import polars as pl
import polars_online as po
ols = po.spec.ewridge(
"ridge", # the spec's name; its output column is named after it
targets=["ret"], features=["signal_a", "signal_b"],
halflife=float("inf"), # no forgetting: every row counts the same, so this is
# ridge regression over the whole stream, in bounded memory
group="stock_id", # one separate regression per stock
)
(
pl.scan_parquet("ticks/*.parquet") # a Polars query over the files; nothing is read yet
.online.fit_predict([ols], save_state="bank.state") # the bank, inside the query
.filter(pl.col("ridge").struct.field("n_eff") > 20) # ordinary Polars on what comes out
.sink_parquet("fitted.parquet") # runs the query, writing the result a chunk at a time
)
scored = pl.scan_parquet("today.parquet").online.predict("bank.state").collect() # score; learn nothing
flat = scored.online.unnest([ols]) # pred_ret, resid_ret, n_eff, coef_ret_intercept, coef_ret_signal_a, ...
# Each spec adds one column, named after it, whose value in each row is a record of named fields:
# the prediction pred_<target>, the residual resid_<target>, the effective number of observations
# n_eff, the coefficients coef, and the diagnostics you switch on. unnest spreads them into columns.
One fit that follows the recent rows. Give the same spec a clock and a
halflife and each row's weight halves every 600 seconds of ts. The fit
is now local: it describes the recent past rather than the whole history,
and it moves from row to row. So the thing to read is not the state it
happens to end on but the path the coefficients took, which coef_every=1
writes on every row.
local = po.spec.ewridge(
"local", targets=["ret"], features=["signal_a", "signal_b"],
clock="ts", halflife=600.0, max_dclock=300.0, # a row's weight halves every 600 s of ts, and a gap
# longer than 300 s decays as though it were 300 s
group="stock_id",
coef_every=1, # write the coefficients on every row, not once a chunk
)
betas = (
pl.scan_parquet("ticks/*.parquet")
.online.fit_predict([local])
.online.unnest([local]) # coef_ret_intercept, coef_ret_signal_a, coef_ret_signal_b
.select("ts", "stock_id", "^coef_.*$")
.collect()
)
# One row per input row: each stock's exposure to each signal, as it stood before that row.
# That is a time series -- plot it, difference it, or compare two stocks' exposures over a day.
path = betas.filter(pl.col("stock_id") == "b0").select("ts", "coef_ret_signal_a")
# null until the fit exists, then one value per row: how b0's return loaded on signal_a, over time.
The two examples answer different questions, and the difference is the decay. Without one, every row counts forever and the saved state is the model. With one, the state is only the last few hundred seconds, so the coefficients are the output and serving from the final state means predicting with the most recent fit alone.
Mistakes are named: every keyword is checked against its type, and a missing column is reported by which spec wanted it and in what role.
Three ways to run a model bank, same numbers from each. Inside a Polars
query, as above: lf.online.fit_predict(specs)
returns a LazyFrame, and running the query runs the bank. In your own
Python loop: make a ModelBank
and call fit_predict on each chunk yourself. Or with no live Python at
all: the standalone online command line runs the same specs from a file
to a file. Running a bank shows each.
Time, decay and convergence. The rows of a stream are not all equally
relevant, so a model can forget: each row's weight halves every halflife
units of a clock, a column you name that says how far apart two rows are
— in seconds, in cumulative traded volume, or simply by counting rows.
Streams from markets bring their own shape, and the bank handles it: a
session boundary (the row that opens a new trading day), a gap in the
clock (an hour with no rows), and a clock that resets between sessions. Put
the same decay on one of the frame's own feature columns, with the rows
sorted by it, and the fit becomes local in that feature — a curve rather
than a line — in one pass. How a bank sees a
stream explains each of these.
Two guarantees. Every row is predicted before its own outcome is learned. One chunk or a thousand gives the same output, to the last bit. Both are tests in the suite, not intentions.
And the rest. What a bank has learned can be saved to a file and loaded back, to keep learning or to score new rows without learning (Saving, loading and serving). Coefficients come back as a table or as columns; residual spread and z-scores, break detection, a choice or an average among several settings, running R², correlation and hit rate, residual quantiles and autocorrelation are all computed from what the models have already learned, so none of them see the row they describe, in memory that does not grow with the stream (Diagnostics, selection and evaluation). Each (spec, group) pair is fitted on its own thread, and the number of threads changes the speed and nothing else: with 64 groups, 14 threads process 8× the rows per second of one (Parallelism). About 650 Rust tests and 2,200 Python test cases — against numpy, against an independent implementation, on adversarial streams, with fixed reference numbers on every OS — run on macOS, Windows and Linux on every push (Testing).
The models
Twenty model families, one set of stream semantics: a spec's clock, decay, grouping and warm-up mean the same thing whichever model it names. Each row links to the model's builder in the API reference, which has every parameter, and to the section of this README that states its update rule.
Learns by says how a model takes in a row. A model that solves keeps running sums and computes its coefficients from them; one that accumulates keeps running sums and reports them. Both converge to the ordinary batch answer when decay is off, in any row order. A model that steps moves its coefficients a little on each row, one that filters carries a belief forward from row to row, and one that tests counts evidence as it goes; those three depend on the order the rows came in, with or without decay (Without a decay).
| model | learns by | what it is |
|---|---|---|
ewridge · math |
solve | exponentially weighted ridge regression — the workhorse; several ridge values, feature sets and halflives can be fitted from the same running sums at almost no extra cost |
rls · math |
solve | recursive least squares, in the numerically safe square-root form |
lasso · math |
solve | lasso / elastic-net path with the penalty chosen as the stream runs |
kalman · math |
filter | Kalman filter with coefficients that drift as random walks |
huber · quantile · math |
solve | robust and quantile regression |
sgd · math |
step | stochastic gradient descent with squared, Huber, quantile, ε-insensitive, Poisson and logistic losses |
pa · math |
step | passive-aggressive regression — no learning rate to tune |
ftrl · math |
step | FTRL-proximal logistic regression, with an L1 penalty that zeroes coefficients |
ew_cov · math |
accumulate | running mean, variance, covariance, correlation, partial correlation, Mahalanobis distance and principal components |
holt · math |
step | Holt's linear trend — the baseline that uses no features |
kmeans · math |
step | exponentially weighted k-means — cluster labels assigned before the row is learned from, with a split–merge move that finds a cluster born after seeding |
micro · math |
step | density-based clustering — DenStream micro-clusters linked into clusters of any shape and number; flags the rows that belong to none |
ew_class · math |
accumulate | Gaussian classification — QDA, LDA or naive Bayes, one set of running moments per class; a label column in, class probabilities out |
seqtest · math |
test | a sequential test of a sign by betting — evidence you can read at any row; on its own a column's sign, with a/b whether one spec of the bank predicts closer than another |
marginal · math |
accumulate | every (feature, target) pair's running mean, variance, covariance, correlation, slope and t — for a wide set of columns, kept in the state and read back as a table; optionally at a set of lags, and with binned target moments for the relations a correlation cannot see |
deco · math |
accumulate | one correlation for the whole matrix — Engle & Kelly's equicorrelation, or one per block and per pair of blocks |
rcov · math |
accumulate | a block's realised covariance, robust to microstructure noise — the Barndorff-Nielsen–Hansen–Lunde–Shephard kernel or Christensen–Kinnebrock–Podolskij pre-averaging, reported when a group closes |
hmm · math |
filter | a Gaussian hidden Markov model, filtered as the stream runs — ew_class without the labels, with a transition matrix that can be learned |
corrchange · math |
test | has the correlation structure changed — the Wied–Krämer–Dehling constancy test span by span, or the size of a change between two windows against a permutation null |
bocpd · math |
filter | how long has this regime lasted — Adams & MacKay's run-length posterior, so the answer is the age of the regime and not a flag |
Install
pip install polars-online # or: uv add polars-online
Wheels for macOS (arm64, x86_64), Windows x64 and Linux (x64 glibc and musl,
aarch64 glibc) are on PyPI; those and the command-line binaries are attached
to each GitHub release. Python 3.12+. The wheel is about 19 MB to download
and 59 MB installed: it carries its own copy of the Rust half of Polars, so
nothing beyond polars itself has to be present at run time. numpy is an
optional extra: only ModelBank.gram() and the po.gram / po.corr /
po.sim helpers need it.
From a checkout:
uv sync
uv run maturin develop --release -m crates/online-py/Cargo.toml
How a bank sees a stream
A model bank reads a stream of rows one chunk at a time. The parameters in
this section are shared by every model and say how the rows are to be
read: which columns, how time and forgetting work, which rows belong to
which model, how much each row counts, and when a model has seen enough to
report. The polars_online.spec
reference states each one with its units and its default.
What a spec names
spec = po.spec.ewridge(
"ridge",
targets=["y"], # at least one; the targets of one spec share the features' running sums
features=["x0", "x1", "x2"], # numeric columns of any width, Decimal and Boolean included; read as 64-bit floats
add_intercept=True, # the default: the fit has a level of its own
clock="t", halflife=600.0, max_dclock=300.0,
)
# A text column in either list is refused rather than silently read as nulls.
# Columns the spec does not name pass through to the output untouched.
Two more parameters describe the output rather than the input, and are
explained where they matter: coef_every under
Coefficients, and label_delay under Labels that arrive
late.
Time and decay
A model forgets. Each row's weight in the fit is halved every halflife
units of a clock: a column of the frame that says how far apart two rows
are, in seconds, in cumulative traded volume, in any number that only goes
up. Row by row, the weight of everything learned so far is multiplied by
λ = 0.5 ** (Δclock / halflife), where Δclock is the clock's step from
the previous row. With no clock column, the row count is the clock, and a
halflife of 100 means a row 100 rows back counts half as much as the latest.
A stream from a market brings its own shape. A session is a span of rows whose clock measures time continuously — a trading day, say; at the boundary between two sessions the previous session's clock no longer measures time, so the bank applies a step you choose instead of the raw jump. A gap in the clock — an hour with no rows — should not decay the fit as though an hour of rows had gone by, so the clock's step is capped. And a clock that resets or runs backwards between sessions has a policy. Every one of those is a parameter of the spec:
timed = po.spec.ewridge(
"timed", targets=["y"], features=["x0", "x1"],
clock="t", # a numeric column that only goes up; None means the row count
halflife=600.0, # a row's weight halves every 600 clock units (or lam=, the weight kept per unit)
max_dclock=300.0, # the most the clock may step between two rows a model learns from; required with a clock
on_clock_reset="max", # a backwards clock: "max" (the step is max_dclock), "zero", "reset_state", or "error"
session="session", # a column whose value changes at a session boundary ...
session_gap=60.0, # ... and the clock step to apply there, at most max_dclock; "reset" starts the model over
)
# halflife=inf (or lam=1.0) turns forgetting off. A list of halflives fits one model per value.
# max_dclock=0 turns forgetting off; max_dclock=inf removes the cap. The cap also bounds the step
# a run of skipped rows hands the row after them, however long the run.
# ewridge only: session_shrink= and long_halflife= pull the fit partway back, at a session
# boundary, toward a twin that forgets more slowly.
Date and time columns are refused as the clock; convert first
(pl.col("ts").dt.epoch("s")), so that the units of halflife,
max_dclock and session_gap are the units you chose. A huge finite
halflife is not inf: halflife=1e12 still forgets, and the model
schedules that key off the halflife scale with it. Say inf for no
forgetting.
With a decay: a local fit along any feature
The clock does not have to be a time. Sort the frame by one of its own
feature columns and name that column as the clock. halflife is then a
bandwidth in that feature's units: every row is fit on the rows before it,
each weighted by 0.5 ** (Δx / halflife), an exponential kernel. The fit
is a local regression, computed in one pass from running sums that do not
grow, where the usual way of getting one refits a window of rows at every
point.
curve = df.sort("x0")
local = po.spec.ewridge(
"local",
targets=["y"],
features=["x0"],
clock="x0", # the clock is a feature: the decay is a kernel in it
halflife=0.5, # the bandwidth, in x0's own units
max_dclock=1.0, # a wider gap decays as if it were this wide
max_rows_between_solves=1, # refit at every row
min_periods=10.0,
)
fitted = po.ModelBank([local]).fit_predict(curve).unnest("local")
# pred_y is the fitted curve, read at each row's own x0
# coef is the line through that row's neighbourhood
They are the numbers a batch fit would give: against a kernel-weighted least squares recomputed from scratch at every row they agree to 1e-12.
The kernel is one-sided — a row is fit on the rows before it, never after —
so the fit follows a curve with a lag, and the bandwidth trades that lag
against noise. On sin(x) with a bandwidth of 0.25 the fit sits 0.08 from
the truth where the best straight line sits 0.39; at a bandwidth of 1.0 the
same stream gives 0.29, most of the way back to the line. features need
not include the clock column: with other features the same fit is a
regression whose coefficients move along the clock. The clock belongs to
every model, not only to ewridge.
Without a decay: convergence in bounded memory
With decay off — halflife=inf, or lam=1.0 — a model that solves or
accumulates (the model table says which) converges to the
batch fit it defines over every row it has seen, and the order of the rows
does not reach the fit at all: forwards, backwards or shuffled gives the
same coefficients. A model that steps or filters depends on the order
whether or not decay is on. Each model's own section says what it
converges to.
Either way, memory is proportional to the model's state — the running sums
it keeps — and not to the number of rows that have passed: the frame never
has to fit in memory, and a stream of any length fits in the same state.
solve_every makes a solving model compute its coefficients less often
than every row when the exact-at-every-row fit is not needed; they are then
at most that many rows out of date.
Groups
group names a column, and the bank keeps one separate model per distinct
value of it — one per stock, per symbol, per anything — all fitted in the
same pass over the stream. Every other parameter, the clock included,
applies within the group.
per_stock = po.spec.ewridge(
"per_stock", targets=["y"], features=["x0", "x1"], clock="t", halflife=600.0, max_dclock=300.0,
group="stock_id", # one model per distinct value of this column
group_close="monotone", # or "session": when a group is finished, write its running sums out as
) # one row and free its memory -- read them with bank.closed_groups()
group_close is what keeps a bank's memory bounded when new group values
never stop appearing (One row per finished
group). Groups otherwise live for the life of
the bank; a long-running bank can drop the ones that have gone quiet (In a
loop).
Weights
weighted = po.spec.ewridge(
"weighted", targets=["y"], features=["x0", "x1"], clock="t", halflife=600.0, max_dclock=300.0,
weight="w", # a column of row weights: a row of weight w counts as w observations would
) # weight 0 is legal: the row is scored, the clock advances, nothing is learned
n_eff, below, counts weight rather than rows. Nulls, and three ways to
hold a row back says when weight
0 is the right one of the three.
Warm-up
min_periods lets a model report only once it has seen enough data to
have converged, so it never reports a number it is not yet informed
enough to give.
warm = po.spec.ewridge(
"warm", targets=["y"], features=["x0", "x1"], clock="t", halflife=600.0, max_dclock=300.0,
min_periods=50.0, # in n_eff units, not rows: every output is null until n_eff reaches it
) # a list gives one threshold per target; the model learns from every row either way
n_eff is the effective number of observations: the total weight behind
the state that produced this row's prediction, after forgetting, and
measured before the row's own update. So it is 0 on a stream's first row,
runs one behind the row count while nothing is forgotten, settles at
1 / (1 − λ) once forgetting balances arrival, and means the same thing in
every model — which is what makes one min_periods mean the same thing
across a bank. A model that keeps a weight per target checks each target's
threshold against its own, which is the weight of the rows that target was
present on, so a target that is often null reports later than the others;
the n_eff field is the shared weight either way. Which models keep one is
in polars_online.spec.
Nulls, and three ways to hold a row back
A null in any feature, or in the weight, skips the row: outputs are null, no
update happens, the clock still advances. A null in one target still emits
that target's pred, leaves its resid null, and skips only that target's
update. NaN, ±inf and any magnitude above 1e100 count as null, so sentinels
never reach a model.
Three ways to keep a row from teaching a model differ, and it matters which you use.
- Weight
0— the row is scored, the clock advances, nothing is learned: the coefficients do not move at all. Use it to keep a row's place in the stream. Since the clock advances,n_effkeeps decaying and can fall belowmin_periodsif you score for a long stretch this way. - A null target — the row is scored, and each model decides what the
missing label means for its fit; its section says. In
ewridgeandlassounder the defaulttarget_gaps="own_rows", the target's fit does not move: its sums cover only the rows it is present on, and a row without it only ages them.n_effstill counts the row, so unlike weight0it does not decay towardmin_periods. Undertarget_gaps="pairwise"the feature sums take the row and the target's sums do not, so the coefficients wander with feature noise. predict— scores every row against the bank exactly as it stands and touches nothing: no clock advance, no decay,n_efffrozen. Use it to serve. It is also the fast path:ewridgescores at 1.8–2.9× its learning throughput.
Two guarantees
- Predictions are out-of-sample. Every row is predicted from the state as it stood before the row's own target was learned. Nothing here can leak a row's outcome into its own prediction.
- Chunk invariance. One chunk or a thousand, with or without a save and
resume in the middle, the output is bit-identical. The one exception is
coef, which is a reporting cadence: it is written everycoef_everyrows and on each chunk's last row, so smaller chunks report it more often.
Both rest on one thing the caller supplies: a fixed row order. An online
model learns in row order, so a plan whose order polars does not guarantee
is a different model each time it runs. A LazyFrame handed to a bank runs
through polars' streaming engine, and a join, group_by or unique without
an order guarantee delivers a different stream there than lf.collect()
gives — measured: collect() kept the input order, collect_batches() did
not. Give a join maintain_order="left", a group_by maintain_order=True,
sort after a unique, or sort before the bank. A plan with such a node
raises OrderNotGuaranteedWarning when it is handed over, naming the node.
Running a bank
As a query: lf.online.fit_predict
A Polars LazyFrame is a query that runs only when you ask for its result.
lf.online.fit_predict(specs) puts a model bank inside such a query. When
the query runs — collect() for the result as one frame, sink_parquet()
to write it to a file without holding it all, collect_batches() to get it
a chunk at a time — the rows go through a bank that starts with nothing
learned, chunk_rows rows at a time, and whatever comes after the bank in
the query is ordinary Polars:
(
pl.scan_parquet("ticks/*.parquet")
.online.fit_predict([spec], chunk_rows=100_000) # a bank with nothing learned yet; every run starts from the same place
.filter(pl.col("ridge").struct.field("n_eff") > 100) # after the bank: filters what comes out, never what the bank learns from
.select("ts", "stock_id", "ridge") # Polars reads only these columns (and the specs') from the files
.sink_parquet("fitted.parquet") # runs the query; memory is state + one chunk, however long the files
)
# "ridge" is one column whose value per row is a record of named fields:
# {pred_y__r0.000001, resid_y__r0.000001, pred_y__r0.1, resid_y__r0.1, n_eff, coef}
lf.online.fit_predict([spec]).head(5).collect() # learns from the first 5 rows and no more
lf.online.predict(bank).collect() # score against an existing bank; learn nothing
lf.online.fit_predict(load_state="bank.state", save_state="bank.state") # continue from a saved state; save again at the last row
Two things the comments cannot carry. save_state writes when the run
reaches the last row, whole or not at all, and the same bytes a
ModelBank would write. A run abandoned early, or ended by an error inside
the bank, leaves the file untouched. An error after the bank — in a later
step of the query — does not stop the bank, so the state is written although
the query failed (docs/STATE-WORKFLOW.md has the
measurements). Filter after the bank, not before, unless the model must
skip those rows. A filter after the bank never changes what the bank
learns from, and the query still runs a chunk at a time. A filter before
the bank makes Polars hold several blocks of each parquet file in memory
per thread — 2.5 GB at 12M rows, against 0.78 GB for the same filter
after (docs/PERFORMANCE.md §11).
If the model must not learn from some rows, give them weight 0 instead of
filtering them out: they still flow through, still come out scored, and no
gap opens in the clock.
(
lf.with_columns(pl.when(pl.col("venue") == "X").then(1.0).otherwise(0.0).alias("w"))
.online.fit_predict([po.spec.ewridge("ridge", targets=["y"], features=["x0", "x1"],
clock="t", halflife=600.0, max_dclock=300.0,
weight="w")])
.sink_parquet("fitted.parquet")
)
df.online.fit_predict(specs) does the same for a DataFrame already in
memory. po.fit_predict(frame, ...),
po.predict(frame, bank) and po.unnest(frame, specs) are the same calls as
plain functions, for a type checker, which cannot see a registered namespace.
In a loop: ModelBank
spec = po.spec.ewridge(
"ridge",
targets=["y"], features=["x0", "x1", "x2"],
clock="t", halflife=600.0, max_dclock=300.0,
group="stock_id", ridge=[1e-6, 0.1], standardize=True,
)
bank = po.ModelBank([spec]) # nothing learned yet
for chunk in lf.collect_batches(): # the files, one chunk at a time; the whole stream is never in memory
out = bank.fit_predict(chunk) # the chunk's columns, plus one column per spec
...
bank.save("bank.state") # written whole or not at all: a temporary file, then a rename
repr(bank) # ModelBank(['ridge'], groups=4, rows_seen=400)
bank.specs # the spec dicts back, as their builders made them -- a copy, read-only
bank.groups() # one row per (spec, group):
# ┌───────┬───────┬────────────────┬────────────┐
# │ spec ┆ group ┆ rows_processed ┆ last_clock │
# │ ridge ┆ b0 ┆ 100 ┆ 396.0 │
# │ ridge ┆ b1 ┆ 100 ┆ 397.0 │
# └───────┴───────┴────────────────┴────────────┘
# Groups live until dropped -- a long-running bank forgets the ones that have gone quiet:
stale = bank.groups().filter(pl.col("last_clock") < now - 30 * 86400)
bank.drop_groups(stale["group"]) # they start over if they reappear
A bank is one ordered stream, so it is not for two threads at once; a
call that finds it busy on another thread raises RuntimeError rather
than interleave. predict learns nothing and may run from any number of
threads.
The same output as Arrow, for a consumer that is not Polars:
structs = po.ModelBank([spec]).fit_predict_arrow(df) # one per spec, as Arrow
out = df.with_columns([pl.Series(s) for s in structs]) # or hand them straight to pyarrow or duckdb
Each struct is what that spec produced, exposing __arrow_c_array__. The
values are fit_predict's exactly — field for field, null for null — and only
the way out differs. A Polars Series crosses on py-polars' private methods,
which is why this package measures a Polars range rather than promising one;
the capsule interface is an Arrow specification instead, so anything that
speaks Arrow can read the result. Exporting hands the buffers to the consumer,
so each struct is read once and says so if asked twice. predict_arrow is the
same for predict.
Outside a live Python process
A scheduled job, or a deployment with no Python at all, runs the same bank
from a file to a file: docs/RUNNER.md has the standalone
online command line. Same specs, same state file, same numbers.
Saving, loading and serving
What a bank has learned — the running sums of every (spec, group) — can be
saved to one file, written whole or not at all, and loaded back. The same
two words, save_state and load_state, work from a bank object, from a
query, and from the file-to-file runner, and the bytes are the same
whichever wrote them:
# From a bank object
bank.fit_predict(df)
bank.save("bank.state") # written whole or not at all: a temporary file, then a rename
bank = po.ModelBank.load("bank.state", specs=[spec]) # specs= checks the file holds this model, not another
bank.fit_predict(today) # keep learning: the state moves
scored = bank.predict(today) # serve: score the rows, learn nothing
# From a query
lf.online.fit_predict([spec], save_state="bank.state").sink_parquet("fitted.parquet") # fit, then save at the last row
lf.online.fit_predict(load_state="bank.state", save_state="bank.state").sink_parquet("more.parquet") # continue, then save again
served = lf.online.predict("bank.state").collect() # serve from the file
# The same file, in memory rather than on disk -- for a checkpoint that lives somewhere else:
blob = bank.save_bytes()
bank = po.ModelBank.load_bytes(blob, specs=[spec])
Loading names the problem it hits: FileNotFoundError when there is no
file yet, ValueError for a file that is not a bank, was written by a
newer version, or holds a different model.
scored = bank.predict(today)
# Row i of `scored` carries what fit_predict would have reported had it been the next row
# of the stream -- pred, n_eff, sigma, resid_z, selection, metrics, field for field -- and
# every row is scored from the same state: nothing moves.
# - the target column may be absent; resid is then null
# - the weight column is not read
# - a group the bank has never seen scores null
# - the stream's session and clock rules still hold
docs/STATE-WORKFLOW.md walks the whole workflow — fit, save, serve, learn on — with what each step guarantees.
A state file describes itself
A saved bank can be read by something that knows nothing about it. No specs, no configuration, no data — the file carries what it needs:
bank = po.ModelBank.load("bank.state") # no specs=: the file is enough
bank.specs # every spec back, as the dict its builder made -- a copy, read-only:
# the bank runs the state it was built from, so a list edited on the
# Python side would only ever mislabel what coef() reports
bank.groups() # spec, group, rows_processed, last_clock
bank.output_fields() # {'ridge': ['pred_y', 'resid_y', 'n_eff', 'coef'], ...}
bank.rows_seen() # rows fed, over every chunk and group
bank.solve_failures() # per spec, per group: solves that needed jitter or kept the previous fit
# Four more tables: how the fit is doing, and what it was trained on.
# Each returns every spec by default with `spec` as the first column, and the columns are the
# same for every spec, so banks from different runs stack with a plain concat.
bank.last_row() # the output row of the last row each group learned from
bank.coef() # one row per coefficient, with the term it belongs to (Coefficients, below)
bank.summary() # per group: rows fed, learned, skipped, and the clock's range
bank.describe() # per input column per group: count, nulls, mean, std, min, max
The last row and the two feeding tables, in more detail:
bank = po.ModelBank.load("bank.state", specs=[spec])
last = bank.last_row("ridge") # one row per group: spec, group, pred_y__r0.000001, ..., n_eff, coef
# -- the fit_predict row field for field: pred, sigma, the metrics and the
# interval when the spec asks for them, n_eff, and coef when that row carried it
# Fit many models, save each, and comparing them is one concat over the files:
from pathlib import Path
table = pl.concat(
[po.ModelBank.load(f).last_row() for f in sorted(Path(".").glob("*.state"))],
how="diagonal_relaxed", # specs with different fields stack with nulls
)
fed = bank.summary("ridge") # one row per group:
# rows_fed routed to the group
# rows_processed the model accepted
# rows_skipped it did not (a feature or the weight was missing)
# rows_learned moved the fit (a weight above zero and a target present)
# rows_zero_weight advanced the clock and nothing else
# weight_sum, clock_min, clock_max, last_clock
# session_changes, clock_backwards, resets what the clock rules met
cols = bank.describe("ridge") # one row per input column per group: column, role, count, null_count, mean, std, min, max
# -- counting as the models count: a null, a NaN, an infinity or a magnitude
# beyond 1e100 is a null_count, not a value
Neither feeding table forgets: they are plain counts over the whole stream,
computed in row order, so they are the same whatever the chunking, and
predict does not move them. A group that has not learned from a row yet
gives a last row of nulls.
Reading a state without this library
text = bank.to_json() # everything save() writes, as JSON: look at a state, compare two, hand one to a non-Python program
bank.save_json("bank.json") # the same, to a file
It is an export, not a second format — load reads the binary form only —
and it is faithful, including the values JSON has no way to write: NaN
and ±inf are written as the strings "nan", "inf" and "-inf", the same
spelling a spec's halflife uses. That matters: halflife=inf means no
forgetting, so an ordinary state carries an infinity, and a plain JSON
encoder writes it as null without saying so. Every export is read back
and checked against the state before you get it, so a state that could not
be carried is an error rather than a file that is quietly wrong.
Preparing a stream
Two things a stream may need before a bank sees it: a target that is not known at the row it sits on, and several series that do not tick at the same moments.
Labels that arrive late
A target that is a forward quantity — the next five minutes' return, the
next day's fill rate — is not known at the row it sits on. A stream that
learns it there hands the model that much of the future before it predicts
the rows in between. Every "out-of-sample" number after that is
contaminated, and with a feature that is correlated with itself over time
even a pure-noise column starts to look predictive. label_delay is the
fix, and it is one parameter:
spec = po.spec.ewridge("fwd", targets=["ret_5m"], features=["x0", "x1"],
clock="ts", max_dclock=3600.0, halflife=1800.0,
label_delay=300.0) # the return takes 5 minutes to be known
# Each row is scored where it sits and learned from 300 clock units later. Everything
# downstream of the label moves with it -- the prediction, sigma, resid_z, the metrics,
# break detection, the conformal interval, n_eff and min_periods all see only labels
# that had really arrived.
# - the clock is the model's own (capped by max_dclock, skipped rows' time included),
# which is what makes the release depend on the clock alone and survive any chunking
# - with no clock column, one unit is one accepted row: label_delay=20 is twenty rows
# - a reset drops the rows still waiting; a session change releases them in order
# - rows still waiting when the stream ends are never learned from
# - the waiting rows live in the state and are saved with it: one row's values per
# row inside the delay, per group
po.prep.embargo writes the same thing out as data, for when the delay
has to be visible in the frame, or for an engine other than this one:
doubled = po.prep.embargo(lf, clock="t", delay=300.0) # every row twice: a zero-weight copy to score at t,
# and a copy to learn from at t + delay, in clock order
The built-in path agrees with the doubled stream field by field, to the
bit, with three exceptions: resid_quantiles, emit_autocorr and
emit_drift. Those three take no row weight, so a zero-weight row feeds
them as much as its learning copy does; in a doubled stream every residual
therefore lands twice, where label_delay feeds them once.
Series that tick at their own times
Two series observed at different instants cannot be correlated directly. A
fine common grid pushes the correlation towards zero (the Epps effect), and
filling forward invents observations that were never made.
po.prep.refresh_time puts them on the grid Barndorff-Nielsen, Hansen, Lunde
and Shephard defined: a point wherever every series has ticked at least
once since the last point, each carrying its last observed value.
from polars_online import prep
grid = prep.refresh_time(ticks, # long input: one row per tick, the series named in a column
series="symbol", names=["AAA", "BBB", "CCC"],
time="t", value="px").collect()
# one row per grid point:
# time_refresh the grid point
# AAA_value, ... each series' last observed value at that point
# n_obs_AAA, ... ticks of that series since the previous point: the staleness of its value
# retained_fraction how much of the data survived -- read this before trusting a correlation
The grid runs at the pace of the slowest series, so a fast one loses most
of its ticks; retained_fraction says how much. pairs=True runs an
independent two-series grid per pair instead, which keeps far more when one
series is slow. Rows must be in time order; a backwards time is an error
naming the row, and nothing is interpolated. The output looks synchronous
and is not: each value is up to one of its own inter-tick intervals old,
and the series with the largest n_obs is the one holding the grid up.
Reading the fit
What a bank can tell you about its fit with no data at hand, and how to reach a field of its output without building its name.
Coefficients
Two ways, and they agree row for row:
ols = po.spec.ewridge("ols", targets=["y"], features=["x0", "x1"], clock="t",
halflife=600.0, max_dclock=300.0, group="stock_id",
coef_every=1) # write coef on every row (default 0: on each chunk's last row only)
# 1. From a bank -- live, or loaded from a state file with no data at hand.
bank = po.ModelBank([ols])
bank.fit_predict(df)
betas = bank.coef() # one row per coefficient: spec, group, instance, n_eff, ..., term, coef
# -- the fit as of the last row each group learned from
wide = betas.pivot("term", index=["group", "instance"], values="coef")
# 2. From the output, as columns: the fit as it moved, one row per row.
path = (
lf.online.fit_predict([ols])
.online.unnest([ols]) # pred_y, resid_y, n_eff, coef_y_intercept, coef_y_x0, coef_y_x1
.select("t", "stock_id", "^coef_.*$")
.collect()
)
The output's coef is written after each row's update; the row's own
pred comes from the fit before it. With coef_every=1 that is a list
of k floats on every row of the output. Under a grid — several ridge
values, feature_sets, a lasso_path, several targets — the list holds
one block per (target × grid point). unnest names each block's columns
the way the pred fields are named (coef_y_x0__r0.5@h500 beside
pred_y__r0.5@h500), bank.coef() carries the same columns to tell blocks
apart (add them to the pivot's index), and unnest reads a saved output
the same way: pl.scan_parquet("fitted.parquet").online.unnest([ols]). It
takes the specs, a bank, or the path of a saved state.
Output field names
You index the result column by field names, so the names are a contract. The grammar:
pred_{target}{combo}{instance} combo = "" single ridge, no feature sets
resid_{target}{combo}{instance} | __r{ridge} ridge grid
sigma_{target}{combo}{instance} | __{set} feature sets, single ridge
absresid_q{level}_{target}... | __{set}_r{ridge}
n_eff{instance} instance = "" single halflife
coef{instance} | @h{halflife} halflife grid
Numbers render as plain decimals in [1e-6, 1e7) and as compact scientific
outside it. Every name, default and signature is pinned against a checked-in
snapshot, so a change is a reviewable diff and a version bump, never a silent
rename of your columns. You never have to build these strings:
grid = po.spec.ewridge("m", targets=["y"], features=["x0", "x1"], clock="t",
max_dclock=300.0, halflife=[100.0, 500.0], ridge=[1e-6, 0.5])
idx = po.spec.output_index(grid) # every field, with the values its name encodes, and its dtype
name = idx.filter((pl.col("kind") == "pred") & (pl.col("target") == "y")
& (pl.col("ridge") == 0.5) & (pl.col("halflife") == 500.0))["field"].item()
out["m"].struct.field(name) # "pred_y__r0.5@h500"
row = po.spec.coef_fields(grid).filter( # one row per coefficient: its list, position, and unnest column
(pl.col("term") == "x1") & (pl.col("ridge") == 0.5) & (pl.col("halflife") == 500.0)
).row(0, named=True)
out["m"].struct.field(row["field"]).list.get(row["position"]) # field "coef@h500", position 5
Both tables come from the same Rust code that renders the names, so they
cannot drift from the strings, and the index carries each field's dtype,
the column types the bank declares to Polars before the first row is read.
One sharp edge: avoid __ and @ in target names and feature-set labels
if you parse field names downstream, since a target named y__r0.5
renders like a ridge grid on y. Every field of every model is listed in
docs/OUTPUTS.md.
The running sums behind a fit
bank.gram(spec) hands back the matrices the model itself solves against —
its Gram, in least-squares terms — per group and per halflife. They are
a complete summary of the rows the model has seen (a sufficient statistic,
in the statistical sense), so a saved state answers questions the run never
asked:
ols = po.spec.ewridge("ols", targets=["y"], features=["x0", "x1", "x2"],
halflife=500.0, ridge=1e-9, standardize=False)
fitted = po.ModelBank([ols])
fitted.fit_predict(df)
g = fitted.gram("ols")[0] # one dict per (group, halflife, Gram); needs numpy, an optional extra
g["targets"] # the targets fitted from this Gram
g["means"], g["comoments"] # the feature means, and the centred k x k co-moment matrix
g["cross_moments"], g["target_weights"] # per target: the uncentred E[z*y], and the weight behind it
g["means_by_target"] # per target: the column means over the rows it was present on
g["cross_centred"] # per target: E[(z - m)(y - ybar)] at those means, what the fit is solved from
g["target_means"], g["target_vars"] # per target: the target's own mean and centred variance
g["n_eff"], g["n_kish"], g["target_n_kish"] # the accumulated weight, and Kish's effective sample size (features, and per target)
# The algebra the model runs, done by hand: the centred system, which a level costs nothing.
slopes = np.linalg.solve(g["comoments"][1:, 1:], g["cross_centred"][0][1:]) # column 0 is the intercept
intercept = g["cross_moments"][0][0] - g["means_by_target"][0][1:] @ slopes
resid_var = g["target_vars"][0] - slopes @ g["comoments"][1:, 1:] @ slopes
r2 = 1 - resid_var / g["target_vars"][0]
# po.gram is the toolkit for these, so the same algebra is one call:
r2 = po.gram.coef_stats(g, po.gram.solve(g, ridge=1e-9))["r2"] # residual variance, R², standard errors and t
ridges = po.gram.solve(g, ridge=[0.0, 0.01, 0.1, 1.0], standardize=True) # the model's own ridge, in original units; a list of ridges is one eigendecomposition
worst = po.gram.condition(g)["kappa"] # Belsley's condition indexes and variance-decomposition proportions
po.gram.correlation(g) # the correlation matrix
po.gram.vif(g) # variance inflation factors
po.gram.subset(g, ["x0", "x1"]) # the Gram of some of the columns: a sub-block, not a recomputation
po.gram.merge([g, g]) # pools the Grams of disjoint row sets into the Gram of their union, exactly
po.gram.lasso_path(g, [0.1, 0.01]) # the lasso model's coordinate descent, offline
Three things to know before reading the numbers. n_eff counts weight, not
rows; n_kish = n_eff² / Σw² is the number of equally weighted rows the
moments are worth, which is what a standard error divides by, and it does
not fall when a stream goes quiet (n_eff does). A spec has more than one
Gram when targets go missing on different rows: under the default
target_gaps="own_rows" such a target is fitted from a Gram of its own,
and gram() returns one dict per Gram, each naming its targets. And
bank.coef() is as of the model's last solve, which its solve_every
schedule decides, while gram() is as of the last row, so the two can
disagree by the rows since. The ModelBank.gram
reference states every array and the identities that relate them.
One row per finished group
A bank keeps one state per group key, for the life of the bank. On a stream
whose key space keeps growing — a day id, a session id, a block number — that
is unbounded memory for state nobody will read again. group_close says
when a group is finished; the bank then writes its running sums out as one
row and frees the group's memory.
blocks = po.spec.ew_cov("cov", features=["x0", "x1"], lam=1.0,
group="block", group_close="monotone") # "monotone": the key never goes backwards, so
by_block = df.with_columns(block=pl.int_range(pl.len()) // 100) # a key below the largest seen is finished
bank = po.ModelBank([blocks])
bank.fit_predict(by_block)
closed = bank.closed_groups() # one row per finished block: the gram() a driver would have read at that
# moment, bit for bit, plus the span's own rows_fed, rows_learned,
# clock_min, clock_max; coef for a model that has one; the
# eigendecomposition for an ew_cov with pca; a marginal's pairs
first = po.gram.from_row(closed.head(1))
corr = po.gram.correlation(first) # everything in po.gram works on it
"monotone" refuses a chunk whose keys are out of order, naming the row.
An integer key column is ordered as numbers; anything else is ordered as
text, so "9" comes after "10": sort by the same rule the bank reads, or
the chunk is refused (a Categorical column sorts by the order its
categories were first seen, so cast it to pl.String first). "session"
closes a group where its session value changes. Either way the last group
never closes, since nothing proves it is finished, and stays readable
through gram().
A run writes the same rows to a sidecar file, which with no other output at all is the whole shape of an accumulate-only pass: read a stream that does not fit in memory, write one row per block.
for _ in by_block.lazy().online.fit_predict([blocks], closed_groups="blocks.parquet").collect_batches():
pass # the per-row output is not wanted; only the sidecar file is
(by_block and blocks are from the block above.) The command line writes
it too (docs/RUNNER.md). What has closed and
not been read is saved with the state, so a driver that saves between chunks
does not lose rows silently.
Reading a correlation matrix
po.gram solves and diagnoses a design matrix. po.corr is its
complement: the arithmetic that comes after a correlation matrix, in the
same style — numpy only, pure functions, each held against the paper it
comes from.
r = po.corr.matrix(closed.head(1)) # an array, a gram() dict, or a closed row -> a correlation matrix
fixed, dist, iters = po.corr.nearest(r) # Higham (2002): the nearest correlation matrix, by alternating projections
shrunk, alpha = po.corr.shrink(r, alpha=0.2) # Ledoit-Wolf shrinkage toward a constant-correlation (or identity) target
z = po.corr.to_z(r); back = po.corr.from_z(z) # Fisher's transform, clipped so a degenerate +-1 is finite
rho = po.corr.equicorr(r) # deco's one number for the whole matrix, offline
vals, vecs = po.corr.spectral(r, 1) # the top eigenpairs ...
po.corr.from_spectral(vals, vecs) # ... and the completion back to a correlation matrix
po.corr.absorption(r, 1) # the absorption ratio: how much of the variance the top k eigenpairs carry
lo, hi = po.corr.mp_edge(n=2000, m=50) # the Marchenko-Pastur edges: eigenvalues inside them are what pure noise gives
po.corr.fisher_se(n=2000, rho=0.3) # the standard error of a correlation, with the AR(1) inflation and its caveats
The rest of the module — block_means / from_blocks (mean correlation
within and between labelled blocks, and back), mp_density,
signal_share (how much of a correlation's movement across blocks is not
the sampling floor), loss (qlike, z_mse or Engle–Colacito minvar),
epps_invert (the correlation at a coarser scale from ew_cov's lagged
co-moments), shift and equicorr_loglik — is in the API
reference.
Diagnostics, selection and evaluation
Outputs you switch on. All are computed from what the models have already learned and read before each row, so none of them see the row they describe — they are as out-of-sample as the predictions — and all live in memory that does not grow with the stream:
diag = po.spec.ewridge(
"diag", targets=["y"], features=["x0", "x1"], clock="t", max_dclock=300.0, halflife=500.0,
ridge=[1e-6, 0.1], # a grid, so there is something to select among
emit_sigma=True, # sigma_<slot>: EW standard deviation of that slot's out-of-sample residuals
emit_resid_z=True, # resid_z_<slot>: resid / sigma -- how surprising the row was, in units of recent error
emit_selected=True, # selected_<t>, pred_<t>__selected: the ridge value, feature set or halflife with the
# lowest EW out-of-sample error so far
emit_averaged=True, # pred_<t>__averaged: softmax(-eta * EW error / the best's) blend over the same
# choices -- hedges where emit_selected commits
emit_drift=True, # drift_<slot>: Page-Hinkley break detection on the residuals;
# drift_action="reset" also starts the model over
emit_metrics=True, # ic_, r2_, hit_rate_<slot>: what po.eval computes, kept beside the model
resid_quantiles=[0.5, 0.9], # absresid_q<p>_<slot>: running quantiles of |resid| (the P² algorithm) --
# an interval that assumes no distribution
emit_autocorr=True, # autocorr_<slot>: EW correlation of each residual with the previous one;
# non-zero means the model is missing something
conformal=0.9, # lo_, hi_, coverage_<slot>: an interval at that coverage, assuming no
# distribution, and the coverage it has actually delivered
)
band = po.ModelBank([diag]).fit_predict(df).unnest("diag")
emit_metrics on a sgd or ftrl fit with loss="logistic" reads
differently, because pred is a probability and y a 0/1 label rather than
a signed target: hit_rate is accuracy at a 0.5 threshold, r2 the Brier
skill score against the running base rate, and ic the point-biserial
correlation between the probability and the label, under their usual names.
There is no streaming log loss; po.eval.metrics(..., binary=True) adds it
over a collected frame instead.
conformal is the interval to use when the residuals are not Gaussian. It
tracks the coverage quantile of |resid| directly — the radius grows on a
miss and shrinks on a hit — so its long-run coverage is the number you asked
for, whatever the residuals do. sigma gives a Gaussian interval instead;
on fat-tailed or heteroskedastic residuals the Gaussian interval over-covers
by several points where this one lands on target.
ci = po.spec.ewridge("ci", targets=["y"], features=["x0", "x1"], clock="t",
max_dclock=300.0, halflife=500.0, conformal=0.9)
band = po.ModelBank([ci]).fit_predict(df).unnest("ci")
held = band.select(((pl.col("lo_y") <= df["y"]) & (df["y"] <= pl.col("hi_y"))).mean()) # the realized coverage
After the fact, po.eval reads the output frame:
po.eval.metrics(out, "ridge", by=["stock_id"]) # R², IC, hit rate, MSE
po.eval.rolling_metrics(out, "ridge", clock="t", window=3600.0) # the same, per clock window
po.eval.compare_specs(out, ["ridge", "kalman"]) # one table, many specs: which had the lower error
po.eval.seqtest(out, a="kalman", b="ridge", by=["stock_id"]) # is kalman closer? evidence per row -- the same test
# the seqtest model runs inside a bank
Those four all need the whole frame. When the output is never held in one place — fifty slots over a billion rows — reduce each chunk instead and keep ten numbers per key:
ridge = po.spec.ewridge("ridge", targets=["y"], features=["x0", "x1"],
clock="t", max_dclock=300.0, halflife=500.0, group="stock_id")
scoring = po.ModelBank([ridge])
running = None
for chunk in df.iter_slices(100):
part = po.eval.sums(scoring.fit_predict(chunk), "ridge", by=["stock_id"]) # ten numbers per key
running = part if running is None else po.eval.merge_sums(running, part) # exact, whatever the split
po.eval.from_sums(running, min_obs=10) # R², IC, hit rate, MSE and RMSE -- the same numbers metrics() gives
The sums are centred (weighted means and centred second moments, merged
with a parallel-axis term) rather than raw Σy and Σy²: a target sitting
around 1e8 with unit spread destroys the raw form's variance entirely, and
this one does not notice. weight= names a column to weight the rows by.
Data whose truth is known
The regime detectors — deco, hmm, corrchange, bocpd — are claims
about streams whose correlation structure changes, and a claim like that is
measured against data whose truth is known.
po.sim.regimes
generates such a stream from one seed and hands back the truth beside it:
out = po.sim.regimes(4, states=[0.2, 0.7], # four series; two regimes, at these equicorrelations
transition=[[0.98, 0.02], [0.02, 0.98]], # how the regimes switch
n_blocks=8, rows_per_block=500,
phi=0.3, noise=0.01, # returns correlated with their own past; observation noise
async_rates=[1.0, 1.0, 0.4, 0.4], # two series tick less often: a bar with no tick is null
seed=0) # two calls with the same seed are byte-identical
rows, truth = out["rows"], out["truth_blocks"]
# rows: what a consumer sees -- levels x_1 .. x_m (so refresh_time then .diff() apply),
# a clock, a session and an optional volume
# truth_rows: per bar, the block, state, volatility multiplier and interpolation fraction
# truth_blocks: each block's true correlation matrix
What each detector finds on such streams, and what it misses, is measured
in docs/REGIMES.md. durations makes each state last
exactly as long as it says; design="smooth" interpolates the matrix
across a boundary instead of stepping.
Models
One section per model: what it is for, its update rule, the parameters that are its own, and what it writes. The parameters every model shares — the clock, decay, groups, weights and warm-up — are in How a bank sees a stream and are not repeated here; each builder's docstring lists every keyword with its default, and every field of every model is in docs/OUTPUTS.md.
The running sums a model keeps are its accumulators. All of them are
exponentially weighted means, not sums, so they stay bounded over a
stream of any length; second moments are kept centred (a weighted
Welford update), so a variance is right even when a feature sits far from
zero. In the update rules, z is [1, x] when there is an intercept, w
the row's weight, λ the row's decay, and W the total weight so far.
ewridge — EW ridge on sufficient statistics
API: po.spec.ewridge — Rust: ewridge.rs — Outputs: fields
Ridge regression on running sums. Each target's sums are updated on the rows it is present on; the coefficients are solved from them on a schedule.
W' = λW + w n_eff, over every row
W_j' = λW_j + w on the rows where y_j is present, λW_j on the others
S_j' = (λW_j·S_j + w·z zᵀ) / W_j' r_j' = (λW_j·r_j + w·z·y_j) / W_j'
solve: (S_j + ridge·D) β_j = r_j D = I minus the intercept slot
rr = po.spec.ewridge(
"rr", targets=["y"], features=["x0", "x1", "x2"], clock="t", max_dclock=300.0, halflife=600.0,
ridge=[1e-6, 0.1], # one value, or a list: every value is solved from the same sums, so a grid is nearly free
feature_sets={"mkt": ["x0"], "all": ["x0", "x1", "x2"]}, # named subsets, likewise solved from one set of sums
solve_every=12.0, # solve every 12 clock units (default halflife/50; every row when halflife=inf or lam= is given)
max_rows_between_solves=100, # ... and at least every 100 rows, whatever the clock does
standardize=True, # solve on the correlation matrix and undo afterwards; a feature with almost no
# variance is dropped rather than allowed to blow the solve up
ridge_decay=False, # True: the ridge is a fading warm start ("start at yesterday's fit"), not a
# permanent per-observation penalty -- because S is a mean, a plain ridge is permanent
coef_prior=None, # shrink toward a stated belief instead of toward zero
target_gaps="own_rows", # a target null on some rows is fitted on its own rows; "pairwise": one S over every row
)
Each row costs O(k²) for k features, to update S; the solve is a
Cholesky factorization. With decay off and ridge=0 this is ordinary least
squares over every row seen, in any row order: the coefficients match
numpy.linalg.lstsq to 2e-13 forwards, backwards or shuffled, and 6M rows
× 20 features from a parquet stream peak at 1.4 GB against 3.97 GB for
lstsq on the same rows. One trap in that setting: the solve schedule
defaults to halflife/50, so halflife=1e12 solves once, at
min_periods, and never again — say inf, or set solve_every.
solve_every=1000 on that stream takes 1.4 s instead of 11 s, with
coefficients at most 1000 rows out of date.
target_gaps says which rows a target's S_j covers when the target is
null on some of them. "own_rows", the default, uses exactly the rows the
target is present on, so its fit is the fit of the frame with its nulls
dropped: targets present on the same rows share one S, and a target that
goes missing on a row where the others are present takes a copy and keeps
its own from then on, so a bank of targets costs one k × k matrix per
pattern of missing rows. "pairwise" keeps one S over every row, the way
pandas' DataFrame.cov takes a pairwise-complete covariance, and centres
each target's r_j at its own rows' means. The two agree when the gaps
have nothing to do with the features; where they do — a target present only
on trade rows between market-data rows — "pairwise" scales each slope by
the feature's variance on the target's rows over its variance on every row.
Both are held to independent libraries in tests/test_second_opinion.py.
At a thousand features the O(k²) update of S is most of the cost:
wide = po.spec.ewridge(
"wide", targets=["y"], features=["x0", "x1", "x2"], halflife=float("inf"), solve_every=1e9,
max_rows_between_solves=1000,
gram_block_rows=256, # hold 256 rows back and add them to S with one matrix product instead of
) # 256 single-row updates; refused with window=, and where a solve happens every row
Measured on one thread, that is 5.1× the rows per second at 256 features,
6.6× at 1,000 and 5.9× at 2,000; a solve every 512 rows brings each down to
about 4×, because the solve costs the same either way. n_eff, the timing
of every prediction and chunk invariance do not change; the coefficients
agree with the row-by-row fit to rounding, since the blocked sum is the
same sum in a different order. The held rows travel in the state file, so
a save mid-block resumes on the same block (docs/PERFORMANCE.md §18).
rls — recursive least squares
API: po.spec.rls — Rust: rls.rs — Outputs: fields
The coefficients move on every row: there is no solve schedule, so nothing is ever out of date.
A ← λA + w zzᵀ b_j ← λb_j + w y_j z β_j = A⁻¹ b_j
A₀ = ridge·I b₀ = ridge·coef_prior
rls = po.spec.rls(
"rls", targets=["y"], features=["x0", "x1"], clock="t", max_dclock=300.0, halflife=600.0,
ridge=1e-3, # A starts at ridge * I -- unlike ewridge, this penalizes the intercept too
) # a row with any null target is scored but not learned from, for every target,
# because the factor is shared between them
What the model stores is the Cholesky factor of A, updated row by row
with Givens rotations — the square-root form of the recursion. That costs
O(k²) per row, the same as the textbook recursion on the inverse P, and
avoids both of that form's failures: P loses symmetry to rounding by a
factor of 1/λ per row, and one extreme row can cancel it and freeze a
coefficient for good. The result is the same as ewridge(ridge_decay=True)
solved on every row, to better than 1e-9.
lasso — lasso path with free λ selection
API: po.spec.lasso — Rust: lasso.rs — Outputs: fields
Coordinate descent on the standardized running sums, started from the previous solution both along the path of penalties and from one solve to the next:
ρ_i = c_i − Σ_{j≠i} C_ij β_j
β_i = soft(ρ_i, λ·l1_ratio) / (C_ii + λ(1 − l1_ratio))
las = po.spec.lasso(
"las", targets=["y"], features=["x0", "x1", "x2"], clock="t", max_dclock=300.0, halflife=600.0,
lasso_path=[0.1, 0.01, 0.001], # the penalties; predictions for every one are computed anyway, so
# lam_selected_<target> -- the one with the lowest EW out-of-sample squared
# error so far, as it stood before the row -- adds no work of its own
l1_ratio=1.0, # below 1: an elastic net
target_gaps="own_rows", # which rows a target null on some is fitted from, as for ewridge
)
It reads the running sums ewridge keeps, centred the same way, so a
feature and a target far from zero cost the path nothing, and target_gaps
means what it means there. The path is checked against the KKT conditions
of its objective, and a penalized path point against statsmodels' elastic
net on the target's own rows.
kalman — random-walk-β dynamic linear model
API: po.spec.kalman — Rust: kalman.rs — Outputs: fields
A regression whose coefficients are allowed to drift, tracked by a Kalman filter.
β_j ← Φβ_j P_j ← ΦP_jΦ + Q·Δclock Φ = diag(2^(−Δclock/r_i))
s = zᵀP_j z + R_j/w k = P_j z / s
β_j ← β_j + k(y_j − zᵀβ_j) P_j ← P_j − k zᵀP_j
revert = po.spec.kalman(
"k", targets=["y"], features=["signal_a", "signal_b"], clock="t", max_dclock=10.0,
halflife=200.0, # the observation-noise estimate (the EW residual variance) forgets at this rate
coef_halflife=100.0, # how fast a coefficient may drift, on standardized features: q_i = σ²(ln2 / h_i)²,
# matching EW-RLS's steady state; one number, or one per slot; inf pins a coefficient
revert_halflife=[float("inf"), 50.0, 50.0], # by default a coefficient is a random walk and keeps its last value;
# with this, a slope halves toward zero every 50 clock units while nothing is observed
# -- a mean-reverting (AR(1)) prior; inf in the first slot leaves the intercept alone
standardize=True, # the default; with standardize=False, q=0 and a fixed obs_var= this is exactly
# Bayesian linear regression (river's BayesianLinearRegression to 3.6e-15)
)
out = po.ModelBank([revert]).fit_predict(df)
Why revert: a regressor that is only occasionally active is then forgotten
between its bursts rather than kept at its last value, and a stale effect
cannot persist through a run of null targets. The reversion acts in the
standardized coordinates, so "zero" means "no effect" for a slope and "the
target averages zero" for the intercept, and the long-run prior variance of
a reverting slot is q_i·Δclock/(1−φ_i²) instead of growing without bound.
predict moves the coefficients by the same Φ over the distance from the
last learned row (capped by max_dclock), so a prediction far past the
data is the intercept alone.
huber / quantile — robust regression
API: po.spec.huber and po.spec.quantile — Rust: robust.rs — Outputs: huber, quantile
Two regressions that do not let one wild target move the fit. Both read
each row's residual r against the fit before the row is learned, so
both stay out-of-sample, and both keep their running sums per target,
because the weights are per target.
huber: the ridge update at weight w · min(1, δσ / |r|)
quantile: one Newton step on the check loss, smoothed by a uniform kernel of half-width h = quantile_eps · σ
|r| ≤ h: a least-squares row with target y + 2h(τ − ½)
|r| > h: adds 2h · ψ_τ(r) · z to the cross-moment and nothing to the Gram, ψ_τ(r) = τ − 1{r < 0}
h is never narrower than (k/n)^{2/5} · σ, for the target's effective sample n
hub = po.spec.huber("hub", targets=["y"], features=["x0", "x1"], clock="t", max_dclock=300.0, halflife=600.0,
huber_delta=1.5) # a residual beyond huber_delta * sigma is down-weighted
med = po.spec.quantile("med", targets=["y"], features=["x0", "x1"], clock="t", max_dclock=300.0, halflife=600.0,
quantile=0.5, # the level: 0.5 is a median regression
quantile_eps=0.2) # the band the Newton step leans on, in units of sigma (default 0.2)
The band's floor is what keeps a short halflife from leaving the step nothing to lean on. A band holding under one row per coefficient takes least-squares rows until it holds rows again, which rebuilds a fit that a row at the input bound has moved. Both models are held to numpy references to about 1e-13.
sgd — stochastic gradient descent
API: po.spec.sgd — Rust: sgd.rs — Outputs: fields
One gradient step per row, no solves. O(k) per row — the cheap baseline,
and the only model here that takes count targets (loss="poisson").
eta = zᵀβ p = link(eta) gᵢ = (dL/d eta)·zᵢ·w + l2·βᵢ βᵢ -= lrᵢ·gᵢ
| loss | link | dL/d eta |
|---|---|---|
squared |
identity | p − y |
huber |
identity | clamp(p − y, ±delta) |
quantile |
identity | 1{y < p} − τ |
epsilon_insensitive |
identity | 0 inside the tube, else sign(p − y) |
poisson |
log | p − y |
logistic |
sigmoid | p − y |
weights = po.spec.sgd(
"w", targets=["y"], features=["signal_a", "signal_b", "x0"], halflife=200.0,
loss="squared", # or huber, quantile, epsilon_insensitive, poisson (count targets), logistic (0/1 targets)
learning_rate=0.01,
schedule="constant", # or inv_scaling (lr / (1 + n_eff)^power), or adagrad, whose running sum of squared
# gradients decays on the clock so an adapted rate opens up again after a long gap
clip_gradient=1e3, # the default; with a log link one large count would make the next gradient
# exponentially bigger. Never binds for the identity-link losses
coef_min=0.0, # bound each slope from below (one number, or one per feature; inf for none) ...
coef_sum=1.0, # ... and fix their total: after every step the slopes are moved to the nearest point
# that satisfies all bounds (the Euclidean projection). The intercept is never constrained.
# coef_min=0, coef_sum=1 is a long-only, fully invested portfolio;
# coef_min=0 alone is a sign the model must respect;
# coef_min equal to coef_max pins a slope at a known value
coef_every=1,
)
fit = po.ModelBank([weights]).fit_predict(df)
last = fit["w"].struct.field("coef").drop_nulls()[-1]
assert min(last[1:]) >= 0.0 and abs(sum(last[1:]) - 1.0) < 1e-12 # the fit starts from the projected zero: uniform weights
coef reports what the projection returned, in the caller's units even
under scale_features=True.
pa — passive-aggressive regression
API: po.spec.pa — Rust: pa.rs — Outputs: fields
Each row asks the fit to come within eps of its target, and the update is
the smallest change that does so — there is no learning rate to tune.
loss = max(0, |y − p| − eps) s = ‖z‖²
pa τ = loss / s pa1 τ = min(c, loss/s) pa2 τ = loss / (s + 1/(2c))
β += τ · sign(y − p) · z
pa = po.spec.pa(
"pa", targets=["y"], features=["x0", "x1"], halflife=200.0,
mode="pa1", # the default: the step is capped at c. Plain "pa" moves the fit as far as one bad
c=0.1, # row demands; "pa2" damps the step by c instead of capping it
eps=0.05, # the row is "close enough" inside this margin, and nothing moves
) # a row weight below 1 scales the step; above 1 it counts as 1
PA keeps no running sums, so its coefficients have no halflife; the clock
only drives n_eff. It takes the same coef_min, coef_max and
coef_sum as sgd, with the projection applied after each update. The
step then no longer meets the row's margin exactly, and a truth outside the
allowed set is never reached, so keep c small: each row moves the fit
only as far as c allows and the projection takes the rest back.
ew_cov — exponentially weighted moments
API: po.spec.ew_cov — Rust: ewcov.rs — Outputs: fields
Running moments of the columns you name, on the same clock as every model
here — one O(k²) update per row, where computing every pairwise
exponentially weighted correlation with Polars expressions alone takes
O(k²) passes over the data. Values are read from the state before each
row, so an ew_cov output can be a feature for that same row without
leaking it.
W' = λW + w m'ᵢ = (λW·mᵢ + w·xᵢ) / W' S'ᵢⱼ = (λW·Sᵢⱼ + w·xᵢxⱼ) / W'
varᵢ = Sᵢᵢ − mᵢ² covᵢⱼ = Sᵢⱼ − mᵢmⱼ corrᵢⱼ = covᵢⱼ / √(varᵢ·varⱼ)
mv = po.spec.ew_cov(
"mv", features=["x0", "x1", "x2"], clock="t", max_dclock=300.0, halflife=500.0,
stats=["mean", "std", "corr", "partial_corr", "mahal"], # any of mean, var, std, cov, corr, partial_corr, mahal;
# default mean + std + corr. [] is legal: learn the moments, write nothing but n_eff,
# and read them back with bank.gram("mv") -- the form for a wide set of columns
precision_prior=1e-6, # needed by partial_corr (the correlation of two columns with all the others held fixed,
# read off (C + s*prior*I)^-1, O(k³), paid only when asked) and by mahal; fades as data arrives
mahal_quantiles=[0.99], # mahal_q0.99: a running quantile of the Mahalanobis scores, so mahal > mahal_q0.99 is
# "one row in a hundred" without assuming a distribution
pca=1, pca_every=20, # pc0_var, pc0_share (of the trace), pc0_<feature> (the loading), pc0_score (this row's);
# the eigendecomposition is O(k³), so refresh it every 20 rows and score the rows between on
# the last loadings; each refresh keeps the previous sign, so a loading never flips
)
scores = po.ModelBank([mv]).fit_predict(df).unnest("mv")
odd = scores.filter(pl.col("mahal") > pl.col("mahal_q0.99")) # the joint outliers: every column in range, the combination not
first = scores.select("pc0_share", "pc0_x0", "pc0_x1", "pc0_x2", "pc0_score")
mahal is √(δᵀ (C + s·prior·I)⁻¹ δ) with δ = x − m — how far the row
is from what the columns have been doing together, in standard
deviations; on Gaussian columns mahal² is χ² with k degrees of freedom,
and with one column it is |z|.
window — a hard cutoff, not a softer decay. A halflife of h never
forgets entirely: three halflives back still carries 12.5% of the weight.
window=w makes that exactly zero — a row older than w clock units
contributes nothing:
weight(age) = 0.5 ** (age / halflife) if age <= window
= 0 otherwise
cut = po.spec.ew_cov(
"cut", features=["x0", "x1"], clock="t", max_dclock=300.0, halflife=500.0,
window=1500.0, # a row older than this many clock units contributes exactly nothing
window_every=10, # snapshot every 10 rows: the boundary is the oldest snapshot still inside the window,
) # so a coarse cadence discards a little more than asked, never less
Inside the window the weights are still exponential, so this is not a flat
rolling mean and the newest row still dominates. It is exact, because an
exponentially weighted sum contains its own past: everything at or before
a time u is λ^(t−u) times the running sum as it stood then, so
subtracting that leaves precisely the rest. The model keeps a ring of past
snapshots to do it, which is the one place here where memory grows with a
window rather than with the state: about 3 MB per group for a 1,000-row
window over 20 columns, divided by window_every. window_budget caps
that memory per ring, in MiB: with {"refuse": 64} a chunk that takes a
ring past 64 MiB is refused, the error names the ring's size and
window_every, and the bank refuses every later call rather than go on
from a chunk it has half learned — rebuild it from its last save. With
{"thin": 64} the ring drops every other snapshot and doubles its spacing
instead, which, like window_every, only ever shortens the window. A
window with no budget refuses past 256 MiB.
Four things to know before reading the numbers. The clock is the
decayed one, after max_dclock and any session_gap. The edge is a
discontinuity — a row ageing out drops its whole weight at once, so the
series has small steps a plain exponential average does not. It is a
subtraction, so precision falls with the fraction discarded: negligible
at window = 3h, worse as the window shortens toward the halflife. And
n_eff becomes the weight inside the window, so min_periods gates on
something that stops growing, and a clock gap longer than window empties
it and reports nulls rather than stale numbers. If the data fits in memory
and only the moments are wanted, Polars already does this:
df.rolling("t", period="3h").agg(...) with an exponential weight is the
same number to 1e-14. The reason to reach for the spec is a stream, a saved
state, or the time: the rolling window recomputes each window at O(n·W)
where this is O(n) — 15.8 s against 14 ms at 200k rows and a 4,680-row
window.
lags — how a column moves with another ℓ rows ago. The same
co-moments, kept one step further out; with W and m the weight and mean
before the row, and both deviations taken against that mean,
C_ℓ' = a·C_ℓ + a·b·(x_t − m)(x_{t−ℓ} − m)'
with the same a and b the co-moments use — so lag 0 would be
comoments exactly.
lagged = po.spec.ew_cov(
"lagged", features=["x0", "x1"], halflife=500.0,
lags=[1, 5], # in learned rows within the group, not clock units; strictly increasing, >= 1
stats=["corr", "lagcorr"], # lagcorr_<a>_<b>_l<l> per lag and *ordered* pair -- both orders, because a
) # lagged matrix is not symmetric: a leading b is not b leading a
lead = po.ModelBank([lagged]).fit_predict(df).unnest("lagged")
# the same numbers from the state: bank.gram("lagged")[0]["lags"], ["lag_comoments"] (an (L, k, k) array)
The ring of past rows is emptied on a session change and on a clock gap
beyond max_dclock — the two events after which "the row ℓ back" no
longer means a row ℓ ago — and a zero-weight row ages the matrices without
entering it. Nothing else moves: clearing the ring is not a reset.
ftrl — online logistic regression
API: po.spec.ftrl — Rust: ftrl.rs — Outputs: fields
FTRL-proximal (McMahan et al. 2013) for binary targets, with its running sums decayed on the same clock as everything else:
β_i = 0 if |z_i| ≤ l1 else −(z_i − sgn(z_i)l1) / ((β + √n_i)/α + l2)
p = sigmoid(zᵀβ) g_i = (p − y)·z_i·w
z_i += g_i − ((√(n_i + g_i²) − √n_i)/α)·β_i n_i += g_i²
click = po.spec.ftrl(
"click", targets=["y"], features=["x0", "x1"], halflife=500.0,
loss="logistic", # the default: pred is a probability and resid = y - p. "squared": the linear
# prediction -- a sparse linear regression with no solves and an L1 penalty
alpha=0.1, beta=1.0, # the learning-rate scale and its smoothing
l1=0.01, l2=0.0, # l1 zeroes a coefficient whose evidence is below it
)
The recursion agrees with river's FTRL to 1e-12 row for row.
holt — Holt's linear trend
API: po.spec.holt — Rust: holt.rs — Outputs: fields
The one model that takes no features: it extrapolates the target's own level and trend.
pred = l + b·Δt
l' = (λ_l·W·pred + w·y)/(λ_l·W + w) b' = (λ_b·V·b + w·(l' − l)/Δt)/(λ_b·V + w)
baseline = po.spec.holt(
"baseline", targets=["y"], clock="t", max_dclock=600.0,
level_halflife=200.0, # how fast the level forgets, in clock units
trend_halflife=2000.0, # how fast the trend forgets; inf is the whole history's drift
) # coef is [level, trend] per target
Level and trend are weighted means of what each row observes and what the
model forecast, W and V the weight each has gathered; a row at weight
w counts w times. The trend is per clock unit, so an irregular clock
extrapolates the right distance. There is no seasonal term, because a
seasonal index is a group on the phase, which the bank already does. Run
it in the same bank as the real model to answer "how much is the regression
actually adding?" — compare sigma, or let emit_selected choose.
kmeans — exponentially weighted k-means
API: po.spec.kmeans — Rust: cluster/kmeans.rs — Outputs: fields
The one model with no target: it labels each row with the nearest of k
centres, read before the row is learned from, so the label is out-of-sample
like every prediction here. Each centre is the exponentially weighted mean
of the rows assigned to it — ew_cov's mean recursion, per cluster.
j* = argmin_j ‖x − c_j‖² distances in units of each feature's EW sd
n'_j = λn_j + w c'_j = c_j + (w/n'_j)(x − c_j) for j = j*
km = po.spec.kmeans(
"km", features=["x0", "x1", "x2"], clock="t", halflife=2000.0, max_dclock=300.0,
k=3,
warm_rows=100, # seeding waits for this many rows (default 500), places the centres, replays the rows
seed_rule="lloyd", # the best of ten k-means++ starts, by inertia: one start lands in the wrong partition
# a third of the time on five blobs in four dimensions
split_merge=0.5, # every split_merge_every rows, if the two closest centres are nearer than this times the
split_merge_every=200, # sum of their radii -- two centres in one blob -- one is freed and placed on the rows
# far from every centre. 0: plain sequential k-means
dead_frac=0.05, # a centre whose blob vanished fades; under this share of an equal share it is re-placed.
) # that takes log2(1/dead_frac) halflives: 4.3 at 0.05, 2 at 0.25
out = po.ModelBank([km]).fit_predict(df).unnest("km")
# cluster the nearest centre's label, before the row is learned from
# dist the distance to it; dist2 the distance to the second-nearest
# n_eff, coef = the centres, k rows of len(features)
po.spec.coef_index(km) # target = "cluster0".., term = the feature
A row far outside its cluster (about four standard deviations of dist²
above the typical radius) is scored but not learned from: it is set aside
for the split–merge move. Raise dead_frac when regimes change faster
than the fade allows; the price is that a cluster lighter than
dead_frac/k of the stream loses its centre whenever any row is far. What
the move cannot see is one centre owning two blobs, whose rows are all
within its own radius — seeding with lloyd is what prevents it.
micro — density-based clustering, any shape
API: po.spec.micro — Rust: cluster/micro.rs — Outputs: fields
kmeans needs k and finds round clusters. micro finds clusters of any
shape, does not need their number, flags the rows that belong to none, and
follows clusters that appear and vanish. It is DenStream's micro-clusters
with a linking step over them. A summary is a small cluster: a decayed
weight n, a centre c and a radius r, the exponentially weighted
root-mean-square distance of its rows from the centre. Each row goes to
the nearest summary that can take it without its radius passing eps, in
units of each feature's exponentially weighted standard deviation; if none
can, the row opens one.
n_j ← λ n_j every summary
j* = nearest summary that keeps a r²_j + a b ‖x − c_j‖² ≤ eps² p,
a = n_j/(n_j + 1), b = 1/(n_j + 1); else a new one at x
n_j* ← n_j* + w c_j* ← c_j* + (w/n_j*)(x − c_j*) r²_j* ← min(·, eps² p)
mc = po.spec.micro(
"mc", features=["x0", "x1"], clock="t", halflife=2000.0, max_dclock=300.0, min_periods=50.0,
eps=0.1, # the spread the model reads as *one* cluster, per standardized coordinate:
# about 0.07 for two-dimensional shapes, 0.3 for well-separated Gaussians in 20 dimensions
beta_mu=5.0, # a summary with at least this much weight is established
prune_every=100, # every this many rows: drop the light summaries, link the established ones -- centres
macro_link=None, # within L of each other share a label. L is read from the spacing the summaries show
) # unless macro_link sets it (2 = link only summaries that touch)
out = po.ModelBank([mc]).fit_predict(df).unnest("mc")
out.select("cluster", "outlier", "n_clusters", "n_micro").tail(3)
# cluster the label of the nearest established summary; null while there is none
# dist the distance to that summary's centre
# micro the id of the summary this row goes to; ids only go up and are never reused
# outlier no established summary takes the row
# n_clusters, n_micro how many of each the state holds
# coef the established summaries, one [id, label, n, radius, c_1 .. c_p] row each
All are read before the row is learned from. A label is the smallest id in its chain, so it outlives everything but that summary.
Both ways to get eps wrong show in the outputs. If nearly every row
is an outlier and cluster stays null, eps is too small: no summary
reaches beta_mu before it is pruned. If n_micro is about the number of
clusters, eps is too coarse: each cluster is one summary, so the derived
L reads the spacing between clusters and bridges them into one. Lower
eps, or set macro_link=2. Measured at 20k rows with the eps above:
moons, rings and five Gaussians in twenty dimensions all score ARI 1.000
against the truth, where kmeans cannot follow the first two; noise drawn
uniformly over the box is flagged outlier 94% of the time, real rows
0.3%. A cluster born mid-stream has a label within 200 rows; one whose
rows stop lingers halflife · log2(n / beta_mu), with n the weight it
had.
ew_class — Gaussian classification on ew_cov moments
API: po.spec.ew_class — Rust: ewclass.rs — Outputs: fields
A label column in place of a numeric target. The model keeps one ew_cov
state per class — a weight n_c, a mean μ_c and a centred covariance
C_c — and scores a row by Bayes' rule over Gaussian classes.
π_c = n_c / Σ n r_c = precision_prior · s_c (s_c: the prior's fade)
M_c = C_c + r_c I (full) M = Σ π_c M_c (shared) diag(C_c) + r_c (diagonal)
ℓ_c = ln π_c − ½ ln det M_c − ½ (x − μ_c)ᵀ M_c⁻¹ (x − μ_c)
p_c = exp(ℓ_c − max ℓ) / Σ exp(ℓ − max ℓ) class = argmax ℓ
n_c ← λ n_c + w·[y = c] μ_c, C_c ← weighted Welford on the row's own class
labelled = df.with_columns(
pl.when(pl.col("y") > 0).then(pl.lit("up")).otherwise(pl.lit("down")).alias("dir")
)
cl = po.spec.ew_class(
"cl", features=["x0", "x1", "x2"], clock="t", halflife=200.0, max_dclock=300.0, min_periods=20.0,
label="dir", # the label column; a null label scores the row and learns nothing from it
classes=["down", "up"], # declared up front: a label not in the list is an error naming the row.
# integer and boolean columns work through their text: ["0", "1"], ["true", "false"]
covariance="shared", # "full": each class its own covariance (QDA); "shared": pooled by class weight (LDA);
# "diagonal": variances only (Gaussian naive Bayes)
precision_prior=0.1, # the ridge that makes a class scoreable from its first row; fades as ew_cov's does
)
out = po.ModelBank([cl]).fit_predict(labelled).unnest("cl")
out.select("dir", "class", "p_up", "n_eff").tail(3)
# class the most probable class, as a string
# p_<class> one per declared class; exactly 0 for a class no row has carried yet
# coef the class means, in the order of classes (coef_up_x0 after unnest)
All are read before the row is learned from, so a row's probabilities never saw its own label — which is also how a stream whose labels arrive late is scored: null the label, keep the features.
Choosing the shape. "full" is the general case and costs one k×k
Cholesky per class per row. "shared" factorizes once per row, and is the
right model when the classes differ in location but not in spread — it then
matches "full" to a fraction of a percent on the test data, with fewer
parameters to learn. "diagonal" is the cheapest and cannot see a
correlation: two classes with the same marginals and opposite correlations
are one class to it. Measured at 400k rows, six features and three classes:
0.9M rows/s full, 1.8M shared, 5M diagonal. On three Gaussian classes with
their own covariances the accuracy sits within 0.001 of the best any
classifier could do given the generating parameters, and the probabilities
are calibrated to about 0.01.
seqtest — a sequential test of a sign, by betting
API: po.spec.seqtest — Rust: seqtest.rs — Outputs: fields
Not a regression. A seqtest asks whether a column tends to be positive;
with a and b, it asks instead whether one spec of the bank predicts
closer than another. Either way the answer is evidence you can read at any
row, as often as you like, and act on the first time it is enough. A
p-value cannot be used that way, because checking it repeatedly inflates
its error rate. An e-process can, and that is the whole reason to reach
for it. Per target it keeps the wealth of two gamblers, one betting that
the next sign is positive and one that it is negative. Each stakes the
Krichevsky–Trofimov fraction set by the counts so far, and never bets
against its own lead:
s = sign(y) n⁺, n⁻: the signs counted before this row, n = n⁺ + n⁻
λ⁺ = max(0, (n⁺ − n⁻) / (n + 1)) λ⁻ = max(0, (n⁻ − n⁺) / (n + 1))
ln E⁺ ← ln E⁺ + ln(1 + λ⁺ s) ln E⁻ ← ln E⁻ + ln(1 − λ⁻ s)
common = dict(targets=["y"], features=["x0", "x1"], clock="t", max_dclock=300.0, group="stock_id")
ridge = po.spec.ewridge("ridge", halflife=500.0, **common)
kalman = po.spec.kalman("kalman", halflife=500.0, coef_halflife=100.0, **common)
sign = po.spec.seqtest("sign", targets=["y"], group="stock_id") # does y tend to be positive?
# log_e_pos_y, log_e_neg_y the two gamblers' log wealth, as they stood before the row
# n_pos_y, n_neg_y the signs counted so far; a zero, null or NaN is a tie: bets nothing, counts nothing
closer = po.spec.seqtest("closer", targets=["y"], a="kalman", b="ridge", group="stock_id") # does kalman predict closer?
# log_e_a_y, log_e_b_y, wins_a_y, wins_b_y the sign tested is |resid_b| - |resid_a|, positive when a came closer,
# on the out-of-sample residuals the two specs' output records report;
# a row where either side is null (warm-up, a skipped row) is no trial
out = po.ModelBank([ridge, kalman, closer]).fit_predict(df)
verdict = out.group_by("stock_id").agg(pl.col("closer").struct.field("log_e_a_y").max())
# log_e_a_y >= ln(20): on that stock, kalman beat ridge at the 5% level, read at any row
Under the null — given everything so far, the next sign is no more likely
positive than negative — E⁺ is a nonnegative supermartingale, and Ville's
inequality gives P(E⁺ ever reaches 1/α) ≤ α. So log_e_pos ≥ ln 20
rejects at the 5% level however many times you looked, and however the
rows depend on each other. No distribution is assumed and the size of the
values is invisible: 60% small gains and 40% huge losses is "positive". Where
the clip never binds the wealth has the closed form 2ⁿ B(n⁺+½, n⁻+½) / π,
the Beta(½, ½) mixture, and the bank is held to it; the two sides' average
is an e-value for the two-sided question.
A trial is a row, so there is no weight and no halflife — a spec that
gives them is refused — and session or on_clock_reset="reset_state"
restarts the test. a_suffix and b_suffix pick a grid instance
("@h500", "__r0.5@h500"). A comparison inside a bank is chunk-invariant,
saved with the state and works a chunk at a time like everything else;
po.eval.seqtest is the same computation over a frame you already
have.
marginal — every pair's moments, kept in the state
API: po.spec.marginal — Rust: marginal.rs — Outputs: fields
A marginal is not a regression and not a joint fit. It keeps the
exponentially weighted moments of each (feature, target) pair on its own,
as if every pair were a two-column ew_cov. For p features and T
targets that is O(p·T) per row; one ew_cov over all the columns would be
O((p + T)²). Per target t, on a row where y_t is present, with W_t
the weight behind that target before the row:
W'_t = λW_t + w a = λW_t / W'_t b = w / W'_t Q'_t = λ²Q_t + w²
S'_yy = a·S_yy + a·b·(y_t − m_y)² S'_xx = a·S_xx + a·b·(x_j − m_x)²
S'_xy = a·S_xy + a·b·(x_j − m_x)(y_t − m_y) m' = m + b·(value − m)
pairs = po.spec.marginal("pairs", targets=["y", "ret"],
features=["x0", "x1", "x2", "signal_a", "signal_b"],
clock="t", max_dclock=300.0, halflife=500.0, group="stock_id")
bank = po.ModelBank([pairs])
bank.fit_predict(df) # the output record holds n_eff alone
table = bank.marginal("pairs") # one row per (group, instance, feature, target):
one_stock = bank.marginal("pairs", group="b0") # 10 rows here: five features by two targets
# n_eff the target's W_t, the weight behind its pairs
# n_kish W_t² / Q_t: the count of equally weighted rows that carry the same information
# ((1 + λ)/(1 − λ) in the limit for unit weights)
# mean_x, var_x, mean_y, var_y, cov the pair's moments, population form
# corr cov / sqrt(var_x * var_y)
# beta cov / var_x: the slope of the target on that feature alone
# t corr * sqrt((n_kish - 2) / (1 - corr²)): the t-statistic at the Kish sample size --
# a scale for comparing pairs, not a p-value; the rows are neither independent nor Gaussian
That is ew_cov's arithmetic: a pair's correlation is the one an ew_cov
over the two columns would report, to the bit. A null target ages its own
pairs (W_t ← λW_t) and learns nothing for them; a null feature skips the
row, as everywhere. Nothing is written per row but n_eff: the pairs are
the state, read back as a table. corr, beta and t are null until the
target's W_t reaches min_periods (default 3; two rows give ±1 whatever
the data), and where they are undefined — a constant feature, or
n_kish ≤ 2 for t. A bank loaded from a file reports the pairs the bank
that saved it would, and one chunk or a thousand gives the same table to
the bit.
Two views sit on top of that, both off unless asked for.
lags — is t telling the truth? t is built on n_kish, which is
the right count for unequal weights and says nothing about rows that
resemble their neighbours. On a smooth stream consecutive rows are nearly
the same observation, so t claims evidence that is not there. Lags fix
that: the pair's moments are kept at each lag too — the same statistic
ew_cov(lags=) computes, to the bit — and serial_rule turns them into
Bartlett's correction. Two independent AR(1) series with φ = 0.9 and
0.8 come out at t = 2.39 and t_serial = 1.03. The first is a finding;
the second is the truth.
bins — what a correlation cannot see. Everything above is linear. A
feature can be strongly related to a target with corr at zero: a
threshold, a V, a saturation. Bin the feature and keep the target's moments
inside each bin, and all three become visible.
honest = po.spec.marginal(
"pairs", targets=["y"], features=["x0", "x1"], halflife=500.0,
lags=[1, 2, 3, 5, 8], # the pair's moments at each lag, in learned rows within the group
serial_rule="geometric", # how the lagged correlations become a count correction
bins=16, # bin each feature and keep the target's moments inside each bin
bin_rule="quantile", # edges learned from the first bin_warm_rows rows (default 1,000), by weighted quantile or
bin_warm_rows=200, # equal width; or give bin_edges= outright (a list per feature, or a dict by name), which is
) # exact and comparable across runs, and refuses bins, bin_rule and bin_warm_rows beside it
# added columns of bank.marginal("pairs"):
# lagcorr_xx, lagcorr_yy each series' own autocorrelation, one entry per lag
# lagcorr_xy, lagcorr_yx the feature now against the target l rows back, and the reverse -- a feature whose
# lagcorr_yx[0] beats its corr *leads* its target; one whose lagcorr_xy[0] does *follows* it
# n_serial n_kish divided by 1 + 2 * sum(rho_x(l) * rho_y(l)) (Bartlett 1935)
# t_serial the same statistic as t, against that count
# phi_x, phi_y the fitted per-row decays, under serial_rule="geometric"
# bin_edges the feature's edges, fixed once and never moved
# bin_n, bin_mean_y, bin_var_y the target's weight, mean and variance in each bin: the response curve
# split_gain the fraction of the target's variance removed by the best single cut -- a regression
# stump's R², so it compares directly with corr² and the difference is the nonlinear surplus
# split_at where that cut falls, in the feature's units
# split_gain_t the t a corr would need to match that gain: a ranking, not a p-value -- the cut was
# chosen by maximising over the candidates, and the statistic does not know that
The lagged lists are ew_cov's lagcorr numbers exactly — the lagged
covariance over the two standard deviations, not clamped to [−1, 1],
since a lagged correlation is not bounded by one in a finite sample. A row
where the target is missing ages its weight and holds the lag moments, as
it holds the pair's.
Binning costs O(bins) of state per pair and one binary search per pair
per row, which is why it can run across ten thousand columns in the pass
that gives them corr. A value that carries more than a bin's share — an
indicator's zero — fills a bin of its own and the rest share what is left,
so the 5% of rows that carry the signal are not lost among the zeros. The
warm-up rows are held and replayed, not spent: the histogram is what it
would have been had the edges been known before the first row. A feature
keeps only the bins it can support, so a binary feature has two and a
constant one has a single bin and no split. Each bin's moments are kept the
way every accumulator here is kept, so a target at 1e7 keeps its
variance. Both views ride into bank.closed_groups() as pair_* columns:
pair_split_gain as a list over the pairs, pair_lagcorr_xx and
pair_bin_n as lists of lists.
corrchange — has the correlation structure changed?
API: po.spec.corrchange — Rust: corrchange.rs — Outputs: fields
Two tests, because there are two questions: has the correlation been constant, and how big is the change.
kind="monitor" is the closed-sample constancy test of Wied, Krämer and
Dehling (2012), run over consecutive spans of span_rows rows. At the last
row of a span, per pair:
Q = max_{2≤j≤T} (j/√T)·|ρ̂_j − ρ̂_T| / D̂
with ρ̂_j the correlation of the span's first j rows and D̂ the
delta-method long-run standard deviation of ρ̂. Under the null Q
converges to sup|B|, a Brownian bridge, so the critical value is the
Kolmogorov quantile — computed from the series, not pinned, and it
reproduces the published 1.3581 at 5%. The test's size and power are held
to the paper's own tables (.035 at ρ = 0 and T = 500, .587 power on
a 0.5 → 0.7 break).
c = po.spec.corrchange(
"break", features=["x0", "x1"],
kind="monitor", # the constancy test above, or "window": how *big* the change is, below
span_rows=500, # nothing is reported until a span closes: a delay of at most this many rows
scalar=False, # True: run the test on the equicorrelation of the standardised row (deco's u) --
) # one statistic however many columns, and a test of its level rather than of a pair
out = df.online.fit_predict([c]).unnest("break") # stat, crit, flag, since_flag
w = po.spec.corrchange(
"size", features=["x0", "x1"],
kind="window", # ||vech(R_pre - R_post)|| over two adjacent windows of span_rows rows each ...
span_rows=100,
n_perm=200, permute_every=500, # ... against a permutation quantile: n_perm shuffles of the pooled rows between the
perm_block=10, # windows, in blocks of perm_block so rows that resemble their neighbours do not make the
) # null too liberal; or give crit= as a number and skip the permutations entirely
The window kind's null is a permutation and not a sign flip, because
negating a whole row leaves every correlation exactly where it was. Its
flag rate per row is not alpha: two windows that slide by one row are
almost the same windows, so a statistic above the quantile stays above it
for a run of rows.
hmm — which regime are we in
API: po.spec.hmm — Rust: hmm.rs — Outputs: fields
ew_class classifies a row against labelled Gaussians. An hmm does the
same arithmetic with no labels: the state is hidden, and a transition
matrix carries information from one row to the next. That is the
difference between "which regime does this row look like" and "which
regime are we in", and the second is usually the question. Hamilton's
filter, one row at a time, from the filtered p the previous row left:
p1_l = Σ_k p_k·Π_kl the predicted state
f_l = N(x | μ_l, Σ_l + r_l·I) the state's density
loglik = ln Σ_l p1_l·f_l the row's surprise
p_l ← p1_l·f_l / Σ the filtered state
h = po.spec.hmm(
"regime", features=["x0", "x1"], halflife=500.0,
k=2, # the number of hidden states
precision_prior=1e-2, # required: a state's centred co-moments start at zero, and a zero matrix has no density
warm_rows=400, # seeds the states from this many learned rows with kmeans' rule; every output is null
# until then. Should span more than one regime, or the seeds are two halves of one
means=None, covs=None, # or give the states outright, and learn=False to freeze them
) # exog_tvtp= drives the transition matrix from a column, through fixed tvtp_coef=
out = df.online.fit_predict([h]).unnest("regime")
# p_0, p_1 the filtered state, before the row; p1_0, p1_1 the predicted state
# state the most probable one; loglik the row's surprise
Everything reported is read before the row is learned from. Each state's
running sums then take the row at weight w·p_l. The responsibilities sum
to w, so n_eff is the shared recursion untouched — a row splits across
the states rather than counting more than once. The transition matrix is
learned from the filtered joint of consecutive states,
ξ_kl = p_k(t−1)·Π_kl·f_l / Σ, with a Dirichlet pseudo-count keeping a
never-visited row a distribution. What the chain adds, measured: on
two-dimensional blobs 1.5 apart, a memoryless nearest-centre rule given
the true centres is 85% right and the filter is 99%.
One limitation worth knowing: a single extreme row can be captured by one
state, and in mean form a state with zero responsibility keeps its moments —
so a state that stops winning never forgets, and the mixture is left short
one state. A larger precision_prior, given states, or cleaning upstream
are the mitigations.
rcov — a block's realised covariance, robust to noise
API: po.spec.rcov — Rust: rcov.rs — Outputs: fields
A realised covariance over ticks is the sum of outer products of returns.
Over real tick data it is wrong twice: each price is the efficient one plus
a measurement error, and the error's variance accumulates with every tick;
and if the series are not observed together, the correlation is pulled
towards zero. Both are estimated away by published estimators that are sums
over lags — which is exactly what a stream can accumulate. rcov has no
decay and no per-row output but n_eff. Its value is the block, written
when the group closes, so it needs group and group_close and the
estimate rides in that row.
r = po.spec.rcov(
"rk", features=["x0", "x1"], # rows are *returns*: difference upstream
group="block", group_close="monotone",
kind="kernel", # "plain": sum(x x'), equal to n * an ew_cov(lam=1)'s uncentred second moment at close, to the
# bit -- the cross-check, and the reference the other two are measured against
# "kernel": the multivariate realised kernel (Barndorff-Nielsen, Hansen, Lunde & Shephard
# 2011), sum_h k(h/(H+1)) Gamma_h with Parzen weights and jittered end points
# "preavg": the modulated realised covariance (Christensen, Kinnebrock & Podolskij 2010):
# returns pre-averaged over k_n = floor(theta sqrt(n)), less the residual bias
block_rows=2000, # a sizing hint for the ring, needed when bandwidth= is left out: a longer block runs,
# clipped, and reports bandwidth_used
bandwidth=None, # a fixed H; left out, H = ceil(c* xi^(4/5) n^(3/5)) with c* = 3.5134
)
bank = po.ModelBank([r])
bank.fit_predict(by_block.select("x0", "x1", "block"))
blocks = bank.closed_groups()
# rcov, rcorr vech of the upper triangle
# rcov_n, rcov_kind, bandwidth_used
# omega2, iv_sparse the noise variance and sparse integrated variance behind the bandwidth
# iq a realised-quarticity proxy, labelled one
# psd_repaired whether the estimate had to be made positive semi-definite
Parzen is the only kernel: the Bartlett kernel is not consistent for this
estimator, and Parzen's 0.97 efficiency beats the quadratic spectral's
0.93. A block too short to estimate from gives nulls, not an error.
Nothing reads a future row: the jittered end point is formed at close
from observations already in state, and a product enters Γ̂_h only once
both legs are final. weight is taken as 0 or 1 only — a sum over returns
has no fractional row.
deco — one correlation for the whole matrix
API: po.spec.deco — Rust: deco.rs — Outputs: fields
A correlation matrix of m series has m(m−1)/2 free entries. A stream
cannot keep them all moving without O(m²) work a row, and most of them are
estimated from too little data to be worth moving. deco (Engle & Kelly
2012) replaces them with their average and estimates that, in O(m) a row.
The row is standardised against the means and variances as they stood
before it, r_i = (x_i − m_i)/√v_i. With S₁ = Σ r_i and S₂ = Σ r_i²
over n features, the row's estimate is their Lemma 2.3, and the level
follows one of two dynamics, on the model's own clock:
u = (S₁² − S₂) / ((n − 1)·S₂) = mean of r_i·r_j over i ≠ j, over mean r_i²
"ew": W' = λW + w, b = w/W' ρ' = ρ + b·(u − ρ)
"linear": ρ' = (1 − α − β)·ρ̄' + α·u + β·ρ (ρ̄ the "ew" level)
eq = po.spec.deco(
"eq", features=["x0", "x1", "x2"], clock="t", max_dclock=300.0, halflife=500.0,
dynamics="ew", # the exponentially weighted mean of u: rho is exactly what an ew_cov(stats=["mean"]) over
) # the u sequence would report. "linear": the paper's eq. 21 with correlation targeting,
# which needs alpha= and beta= with alpha + beta < 1
blocked = po.spec.deco(
"blocks", features=["x0", "x1", "x2", "signal_a"], halflife=500.0,
blocks={"fast": ["x0", "x1"], "slow": ["x2", "signal_a"]}, # one number per block and one per pair of blocks --
) # the useful middle between one correlation and all of them. Every feature in exactly
# one block, and a block needs at least two
out = df.online.fit_predict([eq, blocked])
# u this row's own estimate, read before the row is learned from
# rho the level as it stood before the row
# loglik the row's Gaussian log-density in standardised coordinates under that level
# with blocks: u_fast, u_slow, u_fast_slow and their rho_* twins, and one loglik over all of them
Two things to know. u is a downward biased estimate of the
equicorrelation — the paper says so, and it is a ratio of two averages, so
E[u] is about 0.20 for a true 0.30 at six columns. Use it as a signal that
moves with the market's correlation, not as the correlation. And rho is
not the same thing as an ew_cov's corr over the columns; the mean of a
ratio is not the ratio of means, and the gap is large.
bocpd — how long has this regime lasted?
API: po.spec.bocpd — Rust: bocpd.rs — Outputs: fields
Every other detector here answers "has something changed?" with a
statistic. bocpd (Adams & MacKay 2007) keeps a probability distribution
over the run length — how many rows since the last break — so the
answer carries the age of the regime with it. "We are forty rows into a
regime" is different information from "something broke". Their Algorithm
1, with H = 1/hazard and π_r run r's posterior predictive for this
row:
growth: P(r_t = r+1, x_1:t) = P(r_t-1 = r, x_1:t-1)·π_r·(1 − H)
changepoint: P(r_t = 0, x_1:t) = Σ_r P(r_t-1 = r, x_1:t-1)·π_r·H
Each run keeps its own conjugate sufficient statistics, so slot r holds
exactly the r rows that hypothesis says came before this one in the run —
and slot 0 holds none, so its predictive is the prior's. That is what makes
"a new run starts here" a hypothesis the data can vote on.
b = po.spec.bocpd(
"regime", features=["ret"], group="stock_id",
hazard=250.0, # the expected run length: H = 1/hazard is the per-row chance of a break
prior_nu=2.0, # the prior on the variance, as 2a and 2b in the gamma parametrisation -- how Adams and
prior_scale=[2e-4], # MacKay give their own finance example (a = 1, b = 1e-4, hazard = 250). prior_scale is the
# one parameter you must set from your data: too large and no row is ever surprising
emission="diag", # a normal-inverse-gamma per feature; "gaussian": a normal-inverse-Wishart over all of them,
# O(runs d²) a row and the one that can see a break in the *correlation* alone;
# "robust": each row's contribution weighted by (pi(x)/pi(mode))**robust_beta, so one 20-sigma
# row moves nothing (without it, that row is a changepoint at p_change 0.91)
prune_below=1e-6, # drop the runs holding less than this share of the mass: what makes the model finite
max_run=None, # fold every longer run into the last kept one: caps how much history any run holds
hazard_col=None, # read the hazard per row from a column, declared in the target slot the way a weight is
)
out = df.online.fit_predict([b]).unnest("regime")
run_started_at = pl.int_range(pl.len()) - pl.col("run_mode")
# p_change P(r_t <= 1) given this row: the alarm
# run_mode the most likely run length, before the row -- so t - run_mode is the row the run began on
# run_mean the posterior mean run length, before the row
# pred_<f> the pre-row predictive mean of each feature, mixed over runs
# logscore the row's log predictive density under that mixture
run_mode is the answer; p_change is the alarm. The two are not the
same quality of signal. p_change is a per-row likelihood ratio, so it is
spiky, and its height depends on the size of the break against the prior
scale. A ten-fold variance step takes it to 0.83 on the row itself. A
four-sigma mean shift with a diffuse prior barely lifts it. A change in
correlation alone never moves it at all. The run length finds all three, one
to three rows later, and dates them to the right row. It is P(r ≤ 1) and
not P(r = 0) because the changepoint branch and the growth branch share
the same predictive, which makes the normalised mass at r = 0 exactly
H on every row whatever the data. Row one of a group reports nothing at
all: P(r ≤ 1) is 1 there however the row looks.
robust_beta is a trade: a whole new regime is a run of individually
forgiven rows, so above about 0.2 nothing is ever detected again. The
default of 0.1 ignores the outlier and still dates a four-sigma shift to
the right row.
Performance
Throughput
Apple M-series, single process, best of 3, 200k rows per run
(uv run python scripts/benchmark.py --markdown):
| configuration | notes | rows/sec |
|---|---|---|
ewridge k=5 |
1 target, 1 halflife | 10,306,024 |
ewridge k=20 |
1 target, 1 halflife | 4,122,355 |
ewridge k=50 |
1 target, 1 halflife | 1,040,742 |
ewridge k=20 |
10 targets | 2,340,621 |
ewridge k=20 |
5 halflives | 2,355,548 |
rls |
k=20, 1 target | 1,843,129 |
kalman |
k=20, 1 target | 2,122,805 |
lasso |
k=20, 1 target (3-point path) | 2,060,329 |
huber |
k=20, 1 target | 4,175,881 |
ftrl |
k=20, 1 target | 6,006,156 |
Targets share one set of feature sums, so 10 targets cost far less than
10× one. Each halflife in a grid is its own set of sums, but they run in
parallel, so a 5-halflife grid costs about 2× one rather than 5×. rls
pays 1.3–2.1× for the square-root form that keeps it from dying of
cancellation on one extreme row.
The other families, and the options that add a pass, on the same machine and rows:
| configuration | notes | rows/sec |
|---|---|---|
ewridge + conformal |
k=20, 90% interval | 4,097,559 |
sgd |
k=20, squared loss | 8,961,276 |
sgd |
k=20, coef_min=0, coef_sum=1 |
2,481,671 |
pa |
k=20 | 11,150,059 |
kalman |
k=20, revert_halflife |
1,844,755 |
ew_cov |
k=20: mean, std, corr (230 statistics) | 2,117,751 |
ew_cov |
k=20: mean, mahal, mahal_q0.99 |
750,903 |
ew_class |
k=20, 3 classes, full covariance | 495,968 |
ew_class |
k=20, 3 classes, shared covariance | 577,082 |
ew_class |
k=20, 3 classes, diagonal | 2,824,922 |
kmeans |
4 features, K=8 | 6,118,711 |
kmeans |
k=20, K=8 | 3,103,963 |
micro |
4 features, eps=1 |
15,060,666 |
seqtest |
sign of one column | 22,436,196 |
A conformal interval is free: it reads the residual the model already has.
A simplex constraint sorts 2k breakpoints per row, so it costs sgd
about 4×. The Mahalanobis distance and the full-covariance ew_class each
pay for a Cholesky factor of a k × k matrix, one per row for mahal and
one per learned row for ew_class. kmeans and micro cost a distance
to each centre; seqtest a handful of operations.
The correlation families, on the same machine and rows:
| configuration | notes | rows/sec |
|---|---|---|
deco |
k=20, one equicorrelation | 2,666,809 |
deco |
k=20 in 4 blocks | 1,892,836 |
rcov |
4 features, kernel, blocks of 1000 | 3,864,849 |
ew_cov |
k=20: mean, cov, lags 1–5 | 1,148,104 |
hmm |
4 features, K=2 | 1,343,086 |
hmm |
k=20, K=2 | 353,258 |
bocpd |
4 features, diagonal | 1,009,075 |
bocpd |
4 features, full covariance | 585,180 |
corrchange |
4 features, monitor, span_rows=500 |
388,557 |
corrchange |
4 features, window 100, permute every 500 | 187,407 |
deco is one number for the whole matrix and costs O(m) a row, which is
why it runs at ew_cov's speed and not at a covariance matrix's. rcov
accumulates per row and pays for its kernel only when the block closes.
hmm factorizes a k × k covariance per state per row, which is
ew_class's cost with the classes hidden. bocpd costs O(runs · d²),
and prune_below is what makes it finite: with prune_below=0 the run
vector grows by one entry every row and the model is O(rows²); at the
default 1e-6 it is flat in the length of the stream, and the knob is a
direct dial on throughput (204k, 324k and 687k rows/s at 1e-8, 1e-6
and 1e-4 on i.i.d. Gaussian rows). bocpd is faster on data that
breaks, because a changepoint collapses the distribution onto a short run.
corrchange's window kind is the slowest model here, and deliberately:
the permutation null re-draws n_perm statistics every permute_every
rows; crit given as a number skips it entirely. Where the time goes, and
what to reach for, is in docs/PERFORMANCE.md.
Memory: which calls stream
Every way of running a bank works a chunk at a time. Measured as the most
memory the process ever held, on one file of ewridge with 20 features,
parquet in and parquet out:
| what you write | 3M rows | 12M rows | |
|---|---|---|---|
lf.online.fit_predict([spec]) |
0.90 GB | 1.35 GB | the bank inside a query |
for chunk in lf.collect_batches(): bank.fit_predict(chunk) |
0.80 GB | 1.24 GB | your own loop |
docs/RUNNER.md has the same row for the command line: flat too, at 0.95 / 0.73 GB and 1.41 / 0.75 GB.
Memory is three things: the state, the chunks in flight, and whatever
Polars' reader has read ahead. The first two rows of the table do not grow
with the file; what growth they show is the memory allocator keeping pages
it has freed, and nearly all of the rest is Polars reading ahead in the
parquet file. The read-ahead is sized from Polars' thread count, so
POLARS_MAX_THREADS shrinks it (Parallelism, below), and
the settings below tune it directly. Everything
after the bank in a query — filters, joins, group-bys, writing the result —
runs a chunk at a time as Polars itself does. That is Polars' rule for the
steps around the bank too: a rolling window over groups (.over("group")
or group_by=) makes Polars hold every row (6.5 GB and 1.7 GB on the same
rows, against 0.25–0.28 GB without groups), whereas a bank's group= keeps
one set of running sums per group and grows with the number of groups, not
the number of rows.
Tuning memory with Polars' own settings
A bank's own memory is its state plus the chunks in flight, and neither grows with the stream. What does grow is Polars' read-ahead: the streaming engine prefetches row groups ahead of whatever consumes them, sized from the thread count, and while a bank is the bottleneck a local disk needs none of it.
Three environment variables move it. All are Polars' own, all are read at run time rather than at import, and all can be set from Python:
import os
os.environ["POLARS_ROW_GROUP_PREFETCH_SIZE"] = "1" # row groups read ahead: the lever that matters
os.environ["POLARS_MAX_THREADS"] = "4" # scales the same term, since the prefetch is sized from it
os.environ["POLARS_ROW_GROUP_PREFETCH_KBYTES_BUDGET"] = "65536" # a byte cap on the same read-ahead
Measured on 8M rows by 12 columns in 80 row groups, peak resident memory, with the allocator's page retention off so the figure is live data rather than the high-water mark of everything ever allocated:
| what runs | default | prefetch 1 |
|---|---|---|
lf.online.fit_predict(...).sink_parquet(...) |
1.63 GB | 1.12 GB |
bank.fit_predict_batches(lf) |
1.41 GB | 1.07 GB |
The prefetch is read per scan, not once at import, so unlike
POLARS_MAX_THREADS it can be set at any point before the scan that should use
it, and a scan that has already run does not lock it in. Setting it in the
shell, before the import and after the import all give the same number.
Two things to know before reading across to other measurements. docs/PERFORMANCE.md reports a larger reduction on a file whose row groups hold 262,000 rows, where pinning the prefetch takes a run from 1.86 GB to 0.51 GB. The gain depends on how much data one row group holds, so measure on your own files rather than carrying either ratio across. And the byte budget counts compressed bytes, which for a memory-mapped local file cost almost nothing, so it rarely binds.
Chunk size. chunk_rows is how many rows the bank takes at a time: a
keyword on lf.online.fit_predict, lf.online.predict and
ModelBank.fit_predict_batches, 100,000 by default; with
ModelBank.fit_predict(df) the chunk is whatever frame you pass. It never changes the numbers — one chunk or a thousand
gives the same output, and only where coef lands moves, since each
stream reports its coefficients on its last row of every chunk. It does
change the speed and the memory. The fixed cost of a chunk (handing the
frame across from Polars, gathering the columns, assembling the output) is
paid once per chunk, so tall chunks amortize it: on wide frames that
hand-off is about 8 ms per call at 10,000 columns, and chunks of 20,000
rows run 2.4× faster than chunks of 2,000. Three chunks are in flight at
once, so chunk_rows is also the size of the middle one.
Parallelism
The unit of work is a stream: one spec on one group (with no group, one
stream per spec). On every chunk, each stream in the bank becomes one task
on the bank's own thread pool — a pool separate from Polars' own — one flat
pool across all specs and all groups, longest stream first so a few big
groups do not leave cores idle at the end. Within a stream the rows go one
at a time, because each row's update depends on the last. That is what
makes the numbers independent of how the work is split. It also means a
bank with one spec and one group is one thread's work per chunk; Polars'
own reading and writing still run in parallel around it. So a bank fills
the pool with groups, with specs, or with both.
A search over factor sets is a list of specs, one per set. Each spec is its own set of running sums, with its own standardization and its own grid inside, and each is one task. The list runs as one query in one pass, with the thread counts set before anything is built:
import os
os.environ["POLARS_ONLINE_MAX_THREADS"] = "8" # the bank's pool: read at the first bank call
os.environ["POLARS_MAX_THREADS"] = "8" # polars' readers and writers: read at import
import polars as pl
import polars_online as po
from itertools import product
factors = {"mkt": ["x0"], "mkt-sz": ["x0", "x1"], "mkt-sz-val": ["x0", "x1", "x2"]}
def spec(name, features, standardize):
return po.spec.ewridge(f"{name}-std{standardize:d}",
targets=["y"], features=features, clock="t", max_dclock=300.0,
group="stock_id", session="session", session_gap=60.0,
halflife=[100.0, 1000.0], ridge=[1e-3, 0.1], # gridded inside the spec
standardize=standardize)
specs = [spec(n, f, s) for (n, f), s in product(factors.items(), [False, True])]
(pl.scan_parquet("ticks.parquet")
.online.fit_predict(specs, chunk_rows=200_000, save_state="grid.state")
.sink_parquet("grid.parquet"))
scores = po.eval.compare_specs(pl.read_parquet("grid.parquet"),
[s["name"] for s in specs]).sort("r2", descending=True)
Every chunk puts 6 × 64 stream tasks on the pool. On 2.56M rows over 64
groups that query takes 12.3 s at one thread and 2.2 s at fourteen. The
output is one column per spec, which is what compare_specs reads, and one
state file holds them all. Where the parallelism comes from:
| source | measured |
|---|---|
| groups | k=20 over 64 groups: 1.02M, 1.91M, 3.52M, 6.44M and 8.20M rows/s at 1, 2, 4, 8 and 14 threads — 8.0× on a 14-core machine |
| specs | eight single-group specs in one bank run in 130 ms against 515 ms one at a time |
| halflives | each halflife in a grid is its own set of running sums, and the instances of a stream run alongside each other; ridge and feature-set grids share one set of sums and are expanded at solve time, so they need no thread |
| Python | Python's global lock is released while a chunk is in the bank, so a Python reader thread can run ahead of ModelBank.fit_predict |
Thread count is POLARS_ONLINE_MAX_THREADS for the bank's pool and
POLARS_MAX_THREADS for Polars' readers and writers; unset, each is one
thread per core. The bank builds its pool at the first bank call, and Polars
builds its own at import, so each must be set before that point — as above,
or in the shell (POLARS_ONLINE_MAX_THREADS=8 python fit.py), which is the
form that always works. Set later, the variable is ignored, and
po.thread_pool_size() says what took (pl.thread_pool_size() for
Polars'). A value that is not a count is refused by name at the first bank
call. Threads change the speed and nothing else: the same stream at 1 and 8
threads, in separate processes, gives identical output. Everything is one
process; there is no distributed execution, by design (What this is
not).
The two counts do different things. Polars' count also sizes how much of a parquet file its reader holds in flight, so more threads is a bigger pile of decoded rows, while the bank's count buys speed and nothing else. A run that has to fit in a smaller box keeps Polars small and gives the bank every core:
import os
os.environ["POLARS_MAX_THREADS"] = "4" # the reader's read-ahead is sized from this
os.environ["POLARS_ONLINE_MAX_THREADS"] = "14" # the bank still has every core
import polars as pl
import polars_online as po
(pl.scan_parquet("ticks.parquet")
.online.fit_predict([spec], chunk_rows=200_000)
.sink_parquet("fit.parquet"))
On 12M rows over 64 groups, one spec: 14 and 14 takes 2.6 s at a peak of 1.1 GB; 4 and 14 takes the same 2.6 s at 0.8 GB, a third less memory at the same speed. The pools never wait on each other, because a bank task never calls back into Polars' pool, so giving both more threads than there are cores costs no time either.
Against scikit-learn
The model most people compare this to is
SGDRegressor.partial_fit,
and the honest comparison starts by naming what each side is. SGDRegressor
is a first-order stochastic optimiser: its answer depends on the learning
rate, the schedule, the feature scaling and the row order. The primary
regression here is a different algorithm class — ewridge, rls, lasso,
huber and quantile accumulate sufficient statistics and solve, so there
is no learning rate, and with decay off ewridge is ordinary least squares
to 2e-13 of numpy.linalg.lstsq in any row order. The counterpart to
SGDRegressor here is sgd, the cheap
O(k) baseline.
Measured on one generated stream, 100,000 rows, k = 20, each contender at
its best over a sweep of its own settings (scripts/sklearn_comparison.py,
scikit-learn 1.9.0, docs/PERFORMANCE.md §19 for the full tables and the
sweeps). The noise ceiling is the R² of the generating signal itself:
| contender | R² stationary | R² drifting | rows/sec | what a prediction saw |
|---|---|---|---|---|
| noise ceiling | 0.9831 | 0.9923 | ||
SGDRegressor, row by row |
0.9829 | 0.9899 | 3,400 | every row before it |
SGDRegressor, batches of 1,000 |
0.9830 | 0.9820 | 2,200,000 | every row before its batch |
po.spec.sgd |
0.9826 | 0.9906 | 6,000,000 | every row before it |
po.spec.ewridge |
0.9831 | 0.9907 | 575,000 | every row before it |
Three things to take from it. Accuracy is not the difference. Everything
reaches the ceiling on the stationary stream, and the row-by-row contenders
are within 0.001 of each other on the drifting one; SGDRegressor and
po.spec.sgd at the same constant step give the same number to four
places, because they are the same recursion. The one gap in the table, the
batched 0.9820, is staleness: a prediction made up to 999 rows before its
update. The speed difference is a difference in semantics: sklearn's fast
form updates once per 1,000-row batch, while every prediction here is made
from the state as it stands. Asked for that same guarantee, partial_fit
per row, SGDRegressor runs at 3,400 rows/second, and the cost is Python's
per-row overhead rather than the algorithm. And a halflife is not the
advantage here: a constant learning rate forgets too, at about 1/eta
rows, and on evenly spaced rows that is a halflife. The clock matters when
the rows are not evenly spaced, which this stream is not.
Where the Gram wins: the first hundred rows of every group. An exact
solve is right as soon as its X'X is full rank, about k rows in; a
first-order method needs about 1/eta rows per direction. 500 groups of 200
rows, each group its own coefficients, k = 20, R² by position in the group
— sklearn as one estimator and one scaler per group in a dict, row by row,
the bank as group="g":
| contender | rows 25–50 | rows 50–100 | rows 100–200 | rows/sec |
|---|---|---|---|---|
| noise ceiling | 0.9896 | 0.9903 | 0.9900 | |
SGDRegressor per group, at its best |
0.7277 | 0.9242 | 0.9789 | 3,342 |
po.spec.sgd, scale_features=True, the same step |
0.7182 | 0.9213 | 0.9788 | 18,519,660 |
po.spec.ewridge |
0.9693 | 0.9860 | 0.9882 | 5,130,803 |
The sgd row is sklearn's step. The 0.01 of R² between the two sgd rows
is where the prediction is standardised: sklearn's loop standardises the
row it predicts against the moments before it and the row it learns from
against the moments including it, while here one standardised row serves
both, so a prediction is on the same footing as every row the coefficients
were learned from; the gap closes as the fit converges. What else is
different: a grid of six penalties is 3.8× the work for sklearn (six
estimators) and 1.6× here (one accumulator, six solves); multiple targets
share one X'X; group= is one state per key rather than a dict of
estimators; standardisation is streaming and cannot leak the way a
StandardScaler fitted on the whole frame does; chunk invariance is a
test; and the state is a versioned cross-OS file rather than a pickle.
Where sklearn wins: a wide row against ewridge, by batching.
ewridge keeps a (k+1)² matrix, so at k = 10,000 it carries 860 MB of
state and runs at 53 rows/second, against 0.31 MB and 20,007 for
SGDRegressor in batches of 1,000. That cost is the matrix itself: a
rank-1 update moves all 800 MB of it every row, at 85 GB/s, near this
machine's memory bandwidth. gram_block_rows=1024 touches the matrix once
per 1,024 rows instead and buys 7.2× of the throughput (379 rows/second)
and none of the memory. sgd is the O(k) answer here — 0.89 MB and
33,271 rows/second at the same width — and it is faster than sklearn's
batch with every prediction made from the state as it stands;
SGDRegressor asked for the same, row by row, runs at 2,206 rows/second at
that width, and the two agree (correlation 0.999997 with
scale_features=True, sklearn's own recipe of a scaler in front of the
step). Both are run at learning_rate = 0.2 / k: an LMS step is stable
only while eta · |z|² < 2, and a standardised row has |z|² ≈ k. And the
ecosystem is sklearn's: pipelines, GridSearchCV, calibration, and far
more use. What this has is the stream.
What this is not
A model layer, not a stream-processing framework. It expects a frame that is
already aligned — and, when a spec names a clock, each group's rows in
clock order — and it keeps a fixed amount of memory per stream. It
deliberately does not provide:
- connectors or ingestion — feed it whatever Polars can read;
- event-time windowing, asof or interval joins — build features with Polars expressions upstream, or with a streaming framework such as Pathway;
- watermarks or late-arrival policy —
clock,max_dclock,on_clock_resetandsessiondescribe time within a stream, not pipeline lateness. Under aclock, a row that arrives out of order is a data error, andon_clock_reset="error"will say so; - distributed execution — one process, a thread pool across (spec × group).
Those boundaries make the two compose:
examples/pathway_integration.py runs a
ModelBank as a stateful operator inside a Pathway pipeline — Pathway does
ingestion, event-time alignment and windowing; we do the model. Chunk
invariance means the engine's batching cannot change the numbers, and
save_bytes/load_bytes let a pipeline checkpoint carry the model state.
Pathway is not a dependency; the example imports it lazily.
Versioning and the Polars pin
What is pinned
| py-polars | rust polars | pyo3-polars | pyo3 | Python |
|---|---|---|---|---|
| >= 1.34.0, < 3 (built and tested against 1.44.1) | 0.55.2 | 0.28 | 0.29 | ≥ 3.12 (abi3-py312) |
The Rust polars is pinned exactly and built into the wheel; the runtime
requirement is a range, because the two copies never meet. The floor is
LazyFrame.collect_batches, which lf.online.fit_predict and the
file-to-file runner read with and py-polars added in 1.34.0; the whole
suite passes on 1.34.0, 1.38.1, 1.44.1 and the 2.0 release candidate with
identical numbers. ModelBank alone works from 1.28.1. The pins are asserted by a test; the matrix is in
docs/RELEASE-READINESS.md.
Which interfaces carry a promise
This library uses two of Polars' extension points, and neither carries a guarantee:
- pyo3-polars' extension types (
ModelBank) — provided "for convenience", with no guarantee beyond the latest definitions working for the latest Polars; - the IO plugin (
lf.online.fit_predict) — documented, but@unstablein py-polars.
Both of them stream, so a break on a new Polars is expected maintenance, not
a surprise. A mismatch is an error, not a crash: ModelBank moves data across
the boundary through the Arrow C Data Interface, and a Polars without the two
private methods it reads fails with a clean AttributeError before any data
moves.
There is a third way across, and it is the one not Polars' to change.
fit_predict_arrow hands each spec's output over the
Arrow PyCapsule interface — an Arrow specification, which py-polars, pyarrow
and duckdb all consume. A break there would be Arrow's rather than Polars'.
It narrows the exposure rather than removing it: only the output side uses it
today, and the frame still goes in as a Polars frame.
How the pin moves
A weekly job (polars-canary.yml)
drops the range from pyproject.toml, installs the newest py-polars, builds
the wheel as CI does and runs the whole suite; only polars moves in that
run, so a red canary means Polars broke us and nothing else. The response
is decided in advance: cap the range at the last release that passed,
in a patch release, so no resolver hands anyone the broken pair; then
fix, and widen again. Every release runs the same check at the moment
it matters, in two legs (release.yml):
| leg | resolves to | blocks the publish |
|---|---|---|
| the newest in-range | newest stable inside <3 |
yes |
| the next major | unpinned, prereleases allowed | no |
The first is a promise: <3 admits every 1.x and 2.x, so a resolver can hand
someone a Polars newer than the one the wheel was built against the day
after it ships, and green on the pinned version is not what the range says.
The second is early warning. The steps for raising the ceiling to a new
major are in docs/RELEASE-READINESS.md.
This package's own versioning
Semantic versioning. While pre-1.0 the minor version carries breaking
changes, and any change to the numbers a model returns, so pin ~=0.7.0 if
you need stability. Widening the Polars range is a minor release; narrowing
it is breaking. See CHANGELOG.md. Output field names are
part of the API (Output field names).
Testing
The guarantees above are only worth what checks them, so the suite is built around oracles and invariants rather than expected values typed in by hand: about 650 Rust tests and 2,200 pytest cases, all green on three OSes. docs/TESTING.md is the ledger of what each part proves.
Against references. ewridge and rls match numpy references to
1e-9, kalman to about 1e-15, huber and quantile to about 1e-13,
ftrl to about 1e-16; rls equals ewridge(ridge_decay=True) solved every
row to below 1e-9. The lasso is checked against the KKT conditions of its
objective rather than a ported solver, which cannot share a bug with it.
river is an independent implementation of several of
the same algorithms: its FTRL recursion agrees with ours to 1e-12 row for
row, its EW moments agree in closed form and in the limit, its quantile and
Huber models agree statistically.
Invariants, for every model, checked at the bank and, where it applies, at the command-line level too:
| chunk invariance | one chunk, seven, four hundred, one row at a time, and with a save and load in the middle |
| thread invariance | 1 thread against 8 |
| group independence | a group's numbers do not depend on what else is in the bank |
| the paths agree | runner ≡ bank for every input source and format; the Arrow output ≡ the Polars one, field for field and null for null |
predict ≡ fit_predict |
of the next row, field for field, with every diagnostic on |
| stream semantics | the null policy, warm-up, and the clock |
n_eff |
the same recursion in every model (crates/online-core/tests/model_contract.rs) |
Hypothesis generates adversarial streams — mixed nulls, duplicate and long-gap clocks, values at ±1e8, zero weights, tiny groups — and asserts the strongest one: changing a row's own target never changes that row's own prediction. IC ≈ 0 on pure-noise targets says the same thing from the other side.
Fixed numbers. One golden stream per model in the Rust core, and the whole pipeline — extraction, fan-out, diagnostics, struct assembly — pinned to fixed output and compared on every OS, so a divergence in polars' vectorized paths on another CPU would show.
Hardening. What the suite does to a bank on purpose:
| everything at once | a 30k-row stream with every output switched on, compared by digest across chunkings, a mid-stream save and load, and thread counts |
| weight scale | all weights ×1e±6 changes nothing but n_eff |
| parameter edges | halflife from 1e-3 to inf |
| a corrupt state file | any byte flipped fails cleanly, and never panics |
| concurrent misuse | two threads calling fit_predict at once get a clean error |
| copying a bank | pickle and copy.deepcopy resume bit-exactly |
| across the FFI | memory safety where two copies of Polars share one process |
| sustained load | a 10M-row soak, opt-in with pytest -m soak |
Contracts that are files. The public API — every name, default and
signature, every output field name — is a checked-in snapshot
(tests/api_surface.txt), so a change is a reviewable diff. Every python
block in this README runs, and so does every example in the API reference.
Everything under examples/ runs unmodified: the TOML through the real
command line, the Pathway operator end to end. docs/VALIDATION.md, where
the defaults were chosen, is regenerated and compared, so the numbers
behind them cannot silently stop being true. A data file, a large file or
generated output that gets tracked fails a test.
Where it runs. ./scripts/gate.sh before every commit — cargo fmt,
clippy -D warnings, cargo test, ruff, mypy, the build, pytest,
sphinx -W. CI runs the same on ubuntu, windows and macos for every push
and pull request. The release build writes a state file on macOS and
continues the stream from it on Windows and Linux. The weekly canary runs
the suite against the newest py-polars. Tests generate or download their
own data; there are no data files in the repo. Downloads are cached under
.cache/ and skipped when offline.
Development
uv sync # Python env (CPython 3.12)
./scripts/gate.sh # everything CI checks
uv run cargo test --workspace # Rust tests
uv run maturin develop --release -m crates/online-py/Cargo.toml
uv run pytest # Python tests
uv run --group docs sphinx-build -W docs/reference docs/_build/html # API reference
uv run python scripts/validate.py > docs/VALIDATION.md # re-run the [validate] experiments
uv run python scripts/regime_experiments.py all # the docs/REGIMES.md experiments
uv run python scripts/benchmark.py # throughput
Prerequisites: uv and a stable Rust toolchain
(rustup). source scripts/env.sh (. .\scripts\env.ps1
in PowerShell) puts both on the PATH for a shell; .vscode/settings.json
does it for VS Code's terminal. cargo runs via uv run because online-py
builds against pyo3's abi3-py312 and needs a 3.12+ interpreter at build
time.
- Every document, and which to read for what: docs/README.md
- A map for coding agents, at the repo root and on the docs site: llms.txt (llmstxt.org)
- API reference: https://hgilde.github.io/polars-online/ — built from the
docstrings and published from every green push to
main - Design and task list: docs/PLAN.md
- Running a bank as a job: docs/RUNNER.md
- Saving, serving, resuming: docs/STATE-WORKFLOW.md
- Measured defaults: docs/VALIDATION.md
- What the regime detectors find: docs/REGIMES.md
- Where the time and memory go: docs/PERFORMANCE.md
- Adding a model: docs/EXTENDING.md
- How the docs are written: docs/WRITING.md
License
Apache-2.0. See CONTRIBUTING.md to make changes, SECURITY.md to report a vulnerability.
1 maintainer
Release files for polars-online 0.7.3
For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
Source distribution (sdist)
| File | Size | Uploaded | |
|---|---|---|---|
| polars_online-0.7.3.tar.gz | 899.0 kB | Details |
Built distributions (wheels)
| File | Reset | |||
|---|---|---|---|---|
| polars_online-0.7.3-cp312-abi3-win_amd64.whl | CPython 3.12 | abi3 | Windows x86-64 | Details |
| polars_online-0.7.3-cp312-abi3-musllinux_1_2_x86_64.whl | CPython 3.12 | abi3 | Linux musl 1.2+ x86-64 | Details |
| polars_online-0.7.3-cp312-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl | CPython 3.12 | abi3 | Linux glibc 2.17+ x86-64 | Details |
| polars_online-0.7.3-cp312-abi3-manylinux_2_17_aarch64.manylinux2014_aarch64.whl | CPython 3.12 | abi3 | Linux glibc 2.17+ ARM64 | Details |
| polars_online-0.7.3-cp312-abi3-macosx_11_0_arm64.whl | CPython 3.12 | abi3 | macOS 11.0+ ARM64 | Details |
| polars_online-0.7.3-cp312-abi3-macosx_10_12_x86_64.whl | CPython 3.12 | abi3 | macOS 10.12+ x86-64 | Details |
Total release size: 52.2 MB
Release files / polars_online-0.7.3.tar.gz
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| Tags | Source |
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