pybiglasso

Lasso and elastic-net logistic regression for data larger than memory.

If your penalized regression won't fit in memory, pybiglasso fits it where the data already is: on disk. A 12 GB design matrix fits under a 3 GB memory limit, on an ordinary desktop, in under two minutes (see Performance).

Save the matrix as a numpy memmap and pybiglasso fits the whole regularization path, with cross-validation to choose the penalty, without loading it into memory.

It's also fast when the data does fit in memory. On a full 100-step lasso path over 5,000 samples by 50,000 features, it is 2.2x faster than R's glmnet, 2.3x faster than R biglasso, and 4.7x faster than skglm, the fastest of the other Python solvers we tested. Across the four benchmark problems, with 1,000 to 50,000 features, it runs 1.9–2.7x faster than glmnet, 2–5x faster than R biglasso, and 4–7x faster than skglm.

It is an unofficial Python port of the R package biglasso, and reproduces its results to floating-point precision (see Validation).

Install

pip install pybiglasso

The core depends only on numba, numpy, and scipy. Extras add optional integrations:

Quick start

import numpy as np
import pybiglasso as bl

# open the matrix on disk without loading it (a read-only memmap); store it
# column-major (Fortran order)
X = np.load("X.npy", mmap_mode="r")
y = np.load("y.npy")

path = bl.biglasso(X, y, alpha=1.0, nlambda=100)   # alpha=1: lasso
path
# BiglassoPath(500000 features, 100 lambdas from 0.112 to 0.000112, alpha=1.0)

path.coef                  # scipy.sparse (features x lambdas)
path.n_nonzero             # model size along the path
path.predict_proba(X_new)  # (rows x lambdas); reads only the columns in use
path.score(X_val, y_val, metric="auc")

path.to_polars()           # lambda_, feature, coefficient (nonzero only)

To write such a file, open it as a column-major memmap and fill it a block of columns at a time, so the whole matrix never has to be in memory:

X = np.lib.format.open_memmap(
    "X.npy", mode="w+", dtype=np.float32,
    shape=(n_samples, n_features), fortran_order=True,
)
for start, block in read_blocks():
    X[:, start : start + block.shape[1]] = block
X.flush()

X can be float64, float32, any integer type, or bool. Use the narrowest type that holds your values exactly: the fit is mostly reading X, so a narrower type is faster as well as smaller (see storage).

Unpenalized covariates (say age, sex, and principal components) take a penalty factor of 0:

pf = np.ones(X.shape[1])
pf[:12] = 0
path = bl.biglasso(X, y, penalty_factor=pf)

scikit-learn

pybiglasso also offers a scikit-learn interface: BiglassoClassifier fits at one penalty strength, and BiglassoClassifierCV chooses it by cross-validation. Both pass scikit-learn's estimator checks, so they work in pipelines, grid searches, and anywhere else a scikit-learn classifier does (install pybiglasso[sklearn]).

from pybiglasso import BiglassoClassifierCV

clf = BiglassoClassifierCV(l1_ratio=1.0, cv=5, rule="1se").fit(X, y)
clf.alpha_, clf.coef_

The estimators use scikit-learn's parameter names, which differ from R's:

Why this exists

At 23andMe, I used R's biglasso package to fit penalized models on large genotype/phenotype datasets without loading them into memory. Over a holiday break, I ported it to Python, partly to gain a better understanding of how it worked and partly because, assuming I could get it working, it would be convenient to stay within the Python ecosystem. I validated it against R biglasso, matching its coefficients, lambda grid, and iteration counts to floating-point precision, and benchmarked it on data both smaller and larger than memory.

In 2026 I revived the port for release, working with coding agents (Claude Code and Codex). That work added the scikit-learn estimators and cross-validation, extended the validation (against R across many more configurations, and with checks independent of R, which turned up the differences listed below), and carried the performance work and benchmarks further.

This is an independent port, not affiliated with or endorsed by the biglasso authors: Yaohui Zeng, Chuyi Wang, Tabitha Peter, and Patrick Breheny. If you use it, please cite their paper (below).

Validation

pybiglasso is checked two ways: against R biglasso, which it ports, and against checks that don't depend on R, which also cover the few places where the two differ (see Differences).

Against R. Every push runs pybiglasso against stored R biglasso 1.7.2 output for 128 configurations, comparing coefficients, deviance, the lambda grid, centering and scaling, strong-rule rejections, and the iteration count at every lambda, with rtol=1e-9. The grid covers wide and tall problems, genotype-like dosage data (including int8 and uint8 storage), memmaps, float32, row subsets, penalty factors (including zeros), user-supplied and linear lambda grids, dfmax truncation, and saturation. The comparison runs pybiglasso with r_compatible=True; for cases with penalty factors it passes R pybiglasso's lambda grid, which sets aside the zero-penalty-factor case under Differences. A weekly job reruns the grid live against the current CRAN release, to catch upstream changes.

Independent of R.

• Optimality. At every lambda along the path, the fit satisfies the elastic-net optimality (KKT) conditions to 1e-6, on wide, correlated, partly unpenalized, and genotype-like designs.
• Other solvers. scikit-learn's saga solver, tightly converged, finds the same coefficients: to about 1e-7 for the lasso and the elastic net alike. In the benchmarks, glum reaches the same elastic-net objective as well.
• Where R differs. R's elastic-net update (reproduced by r_compatible=True) doesn't satisfy the optimality conditions, and its coefficients differ from saga's by 2–50% of their size on the test problem. This is the basis for the elastic-net difference under Differences.
• Shifted data. Adding 1e8 to every column of X leaves the solution unchanged and still optimal; this is the case described under Differences as data far from zero.

uv run pytest               # against stored R output; no R needed
make test-r                 # live, in a container (CONTAINER=podman works too)
make test-r R_VERSION=latest
make soak                   # larger memory-mapped problems; for a big machine

Performance

These benchmarks measure speed only. Correctness is established separately, against R biglasso and by checks independent of it (see Validation). Each solver fits the same problem along the same 100-value lambda path, at its own default tolerance, and its accuracy is reported alongside its time. Machine: AMD Ryzen 5 5600X (6 cores, 12 threads) and 64 GB of RAM, with Python 3.14 and R 4.6.1. Each time is the best of 3 runs. Every multithreaded solver is shown at its fastest thread count: 1, 6, or 12. The scripts and raw results are in benchmarks/.

Which solvers. R biglasso, the original; R's glmnet, whose coordinate descent biglasso builds on; and every maintained Python package, installable with pip, that fits L1 or elastic-net logistic regression on a CPU: scikit-learn (its liblinear and saga solvers), glum, skglm, and statsmodels.

Other Python solvers. Each competitor was stopped once it took 10x as long as pybiglasso, which would otherwise have stretched the run to many hours. Only skglm finishes within that on every dataset, at 4–6x for the lasso and 5–7x for the elastic net. statsmodels (lasso only) ran only on the tall datasets: its L1 fit uses a general-purpose optimizer with dense matrices over twice the columns, which would need about 12 GB and 76 GB on the wide ones. To show how large the gaps get, the smallest problem (5,000 x 1,000) also ran with no cap:

R biglasso 1.7.2. Times are in seconds; "best" is each package at its fastest thread count. For the lasso, both packages fit identical paths. For the elastic net, each ran its own update (see Differences); pybiglasso with r_compatible=True, which matches R, is within about 20% of its default's time.

R's adaptive screening rule is no faster than SSR on these problems.

glmnet 5.1. glmnet fit the standardized matrix as given (standardize = FALSE), with an intercept, along the same lambda grid, at its default tolerance; it runs on one thread. Its objective is the benchmark's. It fit every path in full, at 1.9–2.7x pybiglasso's best time (1.7–2.4x pybiglasso's on one thread), and about as accurately: a worst relative suboptimality of 2e-8 to 3e-6, against pybiglasso's 6e-8 to 3e-6.

Out of core. This test fits a 12 GB float64 matrix (20,000 x 75,000) with memory capped at 3 GB. pybiglasso read a numpy memmap under a cgroup memory limit; R read a file-backed big.matrix in a container with the same limit, and both were measured from their cgroup's accounting. Before each run, the matrix was evicted from the page cache. Both fit the same 20-lambda lasso path and agree to 1e-9, with identical iteration counts.

Under the same limit, R re-reads about twice as much of the matrix from disk. Extra threads hurt here: they evict pages each other still need.

Not compared, by the rule above:

• Other languages: Julia's GLMNet.jl, a wrapper of glmnet's earlier Fortran solver, and Lasso.jl, written in Julia.
• Other hardware: RAPIDS cuML fits on a GPU, and only data that fits in GPU memory.
• Unmaintained: python-glmnet, archived, with its last release in 2020.
• A different problem: celer's logistic regression fits the lasso only, and no intercept. skglm, from the same authors, fits an intercept and the elastic net, and is compared above.
• Not a solver: benchopt is a benchmarking framework; its logistic-regression benchmark fits without an intercept or standardization, which pybiglasso doesn't support yet.

Differences from R biglasso

pybiglasso follows R biglasso 1.7.2 closely, matching it coefficient for coefficient and down to its iteration and screening counts. It departs in a few places, mostly where we think R's behavior may not be what was intended; if we've erred we'd be glad to be corrected. Each departure is marked in the code with a comment beginning "Differs from R biglasso".

• Elastic net. For alpha < 1, R's logistic coordinate update divides by v * (1 + l2), where the elastic-net objective in its documentation calls for v + l2, so the two solve somewhat different problems. pybiglasso uses v + l2, as glmnet and scikit-learn do; r_compatible=True reproduces R exactly. The lasso is the same either way.
• Zero penalty factors. With a penalty.factor of 0 and the default lambda grid, R's grid comes out as lambda = 0 at every step. pybiglasso instead fits the unpenalized columns first, and starts the path at the smallest lambda that keeps every penalized column at zero.
• Default lambda_min. R chooses 0.001 or 0.05 by comparing nrow(X) with ncol(X); pybiglasso compares the number of rows actually fit, which differs when row_indices is given.
• Data far from zero. For columns whose mean is large next to their spread (say, values near 1e8 that vary by 1), standardizing from raw sums loses precision in floating point. R's scales, and so its fit, can be affected without a warning; in our tests some scales came out as NaN. pybiglasso computes these columns' moments from centered values, so a constant shift of X leaves the solution unchanged.
• Invalid input. NaN or infinite values in the rows being fit, and non-finite penalty factors or lambdas, raise ValueError; R instead drops the affected column or returns the null model.
• Deviance. deviance is the deviance, -2 log-likelihood, of the returned model. R reports loss, half the deviance, computed before the final coordinate sweep and with probabilities clipped at 0 and 1, so it can occasionally be infinite. r_compatible=True keeps R's version.
• Saturation. stop_on_saturation=False, an option R doesn't have, fits every lambda, even past R's saturation cutoff.

Threads, cross-validation, and storage

pybiglasso reads the matrix one column at a time, through the memmap, and never loads or copies it; strong-rule screening skips most columns at most steps. Cross-validation folds are row indices into the same matrix on disk.

• A single fit is effectively single-threaded, as is R biglasso's. Coordinate descent updates one coefficient at a time, and that sequential sweep is most of the work: profiling an elastic-net path on 5,000 x 1,000 puts over 80% of the time in it, against 1-2% in the strong-rule and KKT scans that run in parallel (n_threads=). make profile reproduces this with Python 3.15's sampling profiler. Out of core, threads can help when memory to spare holds the page cache, by keeping more disk reads in flight. Under a tight memory limit they hurt (see Performance), so use n_threads=1 there. Results are bit-identical at any thread count.
• Cross-validation scales with cores. BiglassoClassifierCV(n_jobs=...) fits folds in parallel threads that share one X (and, for a memmap, one page cache); results don't depend on n_jobs. This needs numba's tbb or omp threading layer; where numba falls back to workqueue, as on macOS by default, folds run one at a time.
• Store X compactly. Since the work is mostly moving bytes, a narrower dtype is faster: small integers (counts, categories, 0/1 indicators) as int8 or uint8 take 8x less memory and disk than float64, and fit about 2.5x faster, with the same results to about 1e-13. float32 halves both.

How the code is organized

R biglasso implements the logistic solver in two long C++ functions: cdfit_binomial_ssr standardizes, sets up the lambda grid, and runs the lambda loop with its strong rule and KKT checks, and cdfit_binomial_lambda_core runs the coordinate descent at each lambda. That keeps the algorithm in a few places, close to how it's written in the papers.

pybiglasso splits the same algorithm into one small numba kernel per step, each documenting the state it changes, plus a short driver, _fit_lambda, that reads like the algorithm's outline. To my eye that's easier to read, test, and modify. It's a matter of taste, though; some excellent programmers prefer the long inlined function you can read straight through (John Carmack has a good essay on why). The kernels compile to native code, so Python only sequences them, and the solver takes exactly the same iterations as R's at every lambda; the R comparison checks this in every case.

The driver, in plain numpy, works on whole arrays where the C++ writes out loops: the strong rule is one mask over all columns, and the lambda grid one logspace. Inside the kernels, loops are explicit, which lets one pass compute several sums at once. Explicit loops also fix the order of summation, so results are bit-identical at any thread count; that's why the kernels use small dot and seqsum helpers rather than @ and .sum().

Scope

• Binomial (logistic) family only; R's Gaussian and Cox families are not ported.
• SSR (sequential strong rule) screening only. R uses its newer Hybrid and Adaptive rules only for the plain lasso without penalty factors, and they were no faster than SSR on our benchmarks.
• The first call in a session pays a few seconds of numba compilation; after that, compiled kernels are cached on disk.

Citation

Zeng Y, Breheny P (2021). The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in R. The R Journal, 12(2), 6–19. doi:10.32614/RJ-2021-001

License

GPL-3.0-or-later, as R biglasso is GPL-3.