pystatistics 3.16.2

GPU-accelerated statistical computing for Python

PyStatistics

GPU-accelerated statistical computing for Python.

Design Philosophy

PyStatistics maintains two parallel computational paths with distinct goals:

• CPU implementations aim for R-level reproducibility. CPU backends are validated against R reference implementations to near machine precision (rtol = 1e-10). When a CPU result disagrees with R, PyStatistics has a bug.

• GPU implementations prioritize modern numerical performance and scalability. GPU backends use FP32 arithmetic and algorithms optimized for throughput. They are validated against CPU backends, not directly against R.

• Divergence between CPU and GPU outputs may occur due to floating-point precision, algorithmic differences, or both. This is by design, not a defect. The section below specifies exactly how much divergence is acceptable.

Operating Principles

1. Correctness > Fidelity > Performance > Convenience
2. Fail fast, fail loud — no silent fallbacks or "helpful" defaults
3. Explicit over implicit — require parameters, don't assume intent
4. Two-tier validation — CPU vs R, then GPU vs CPU

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Modules

Module	Status	Description
regression/ LM	Complete	Linear models (OLS) with CPU QR and GPU Cholesky
regression/ GLM	Complete	Generalized linear models (Gaussian, Binomial, Poisson, Gamma, Negative Binomial) via IRLS
mvnmle/	Complete	Multivariate normal MLE with missing data (Direct + EM)
descriptive/	Complete	Descriptive statistics, correlation, quantiles, skewness, kurtosis
hypothesis/	Complete	t-test, chi-squared, Fisher exact, Wilcoxon, KS, proportions, F-test, p.adjust
montecarlo/	Complete	Bootstrap (ordinary, balanced, parametric), permutation tests, 5 CI methods, batched GPU solver
survival/	Complete	Survival analysis: Kaplan-Meier, log-rank test, Cox PH (CPU), discrete-time (GPU)
anova/	Complete	ANOVA: one-way, factorial, ANCOVA, repeated measures, Type I/II/III SS, Tukey/Bonferroni/Dunnett, Levene's test
mixed/ LMM/GLMM	Complete	Linear and generalized linear mixed models (random intercepts/slopes, nested/crossed, REML/ML, Satterthwaite df, GLMM Laplace)
ordinal/	Complete	Proportional odds (cumulative link) models matching R MASS::polr
multinomial/	Complete	Multinomial logit (softmax) regression matching R nnet::multinom
multivariate/	Complete	PCA and maximum likelihood factor analysis with varimax/promax rotation
timeseries/	Complete	ACF, PACF, ADF, KPSS, ETS, ARIMA, SARIMA, auto_arima, decompose, STL
gam/	Complete	Generalized additive models with penalized regression splines matching R mgcv::gam
mice/	Complete	Multiple imputation by chained equations: numeric (PMM, Bayesian regression) and categorical (logistic, multinomial, proportional-odds), Rubin's-rules pooling, validated against R mice; CUDA and Apple Silicon (MPS) GPU backend for numeric

See docs/ROADMAP.md for detailed scope, GPU applicability, and implementation priority for each module.

Architecture

Every module follows the same pattern:

DataSource -> Design -> fit() -> Backend.solve() -> Result[Params] -> Solution

• CPU backends are the gold standard, validated against R to rtol = 1e-10.
• GPU backends are validated against CPU backends per the tolerances below.
• Two-tier validation ensures correctness at any scale: Python-CPU vs R, then Python-GPU vs Python-CPU.

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Statistical Equivalence: GPU vs CPU

GPU backends produce results in FP32 (single precision) while CPU backends use FP64 (double precision). This section defines exactly what "statistically equivalent" means and when it breaks down.

All tolerances below are relative (rtol) unless stated otherwise. They apply to well-conditioned problems (condition number < 10^6) at moderate scale (n < 1M, p < 1000). Degradation at larger scale or worse conditioning is documented below.

Tier 1: Parameter Estimates

Quantity	Tolerance	Notes
Coefficients / means	rtol <= 1e-3	Tightest at ~1e-4 for simple LM
Fitted values	rtol <= 1e-3	Directly derived from coefficients
GPU-CPU correlation	> 0.9999	Binding constraint at all scales

Tier 2: Uncertainty Estimates

Quantity	Tolerance	Notes
Standard errors	rtol <= 1e-2	Computed from (X'WX)^-1 which amplifies FP32 rounding
Covariance matrices (MLE)	rtol <= 5e-2	Hessian inversion is sensitive to precision

Standard errors are the weakest link in the GPU pipeline. They depend on the inverse of X'WX (or X'X for LM), which squares the condition number. A well-conditioned problem at FP64 can become a poorly-conditioned inversion at FP32.

Tier 3: Model Fit Statistics

Quantity	Tolerance	Notes
Deviance	rtol <= 1e-4	Scalar reduction — tightest GPU metric
Log-likelihood	abs <= 1.0	Absolute, not relative (log scale)
AIC / BIC values	rtol <= 1e-3	Derived from log-likelihood + rank
R-squared (LM)	rtol <= 1e-3	Ratio of reductions

Tier 4: Inference Decisions

Quantity	Guarantee	Notes
Model ranking under AIC/BIC	Identical	For models with AIC/BIC gap > 2
Rejection at alpha = 0.05	Identical	For p-values outside [0.01, 0.10]
Rejection at alpha = 0.05	Not guaranteed	For p-values in [0.01, 0.10] ("boundary zone")

The boundary zone exists because a ~1% relative difference in a test statistic near the critical value can flip a rejection decision. This is inherent to FP32, not a software defect. If a p-value falls in the boundary zone, use the CPU backend for the definitive answer.

When Guarantees Degrade

Large scale (n > 1M): FP32 accumulation over millions of rows introduces drift. Element-wise tolerance relaxes to rtol = 1e-2, but correlation remains > 0.9999. This means GPU coefficients track CPU coefficients nearly perfectly in direction, with small magnitude drift from accumulated rounding.

Ill-conditioned problems (condition number > 10^6): The GPU backend refuses by default and raises NumericalError. Passing force=True overrides this, but no numerical guarantees apply. Use the CPU backend for ill-conditioned problems.

Pathological missing data patterns (MLE): FP32 L-BFGS-B optimization can stall in near-flat regions of the likelihood surface. Means may deviate by up to rtol = 0.5 in extreme cases. The GPU backend will issue a convergence warning. Use the CPU backend for complex missingness patterns.

Why FP32?

Consumer GPUs (NVIDIA RTX series) execute FP32 at 5-10x the throughput of FP64. Apple Silicon GPUs (MPS) do not support FP64 at all. FP32 is the only path to practical GPU acceleration on hardware that researchers actually have. The tolerances above are the honest cost of that acceleration.

CUDA vs MPS: Not All GPU Backends Are Equal

Certain operations (notably scatter_add_ with sparse targets) are 1000x slower on Apple MPS than on NVIDIA CUDA due to Metal's weaker atomic memory support. PyStatistics detects these cases and either fails fast or routes to CPU. See docs/GPU_BACKEND_NOTES.md for detailed benchmarks and guidance on when GPU helps vs hurts.

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Quick Start

import numpy as np

# --- Descriptive statistics ---
from pystatistics.descriptive import describe, cor, quantile

data = np.random.randn(1000, 5)
result = describe(data)
print(result.mean, result.sd, result.skewness, result.kurtosis)

# Correlation (Pearson, Spearman, Kendall)
r = cor(data, method='spearman')
print(r.correlation_matrix)

# Quantiles (all 9 R types supported)
q = quantile(data, type=7)
print(q.quantiles)

# --- Hypothesis testing ---
from pystatistics.hypothesis import t_test, chisq_test, p_adjust

result = t_test([1,2,3,4,5], [3,4,5,6,7])
print(result.statistic, result.p_value, result.conf_int)
print(result.summary())  # R-style print.htest output

# Multiple testing correction
p_adjusted = p_adjust([0.01, 0.04, 0.03, 0.005], method='BH')

# --- Linear regression ---
from pystatistics.regression import fit

X = np.random.randn(1000, 5)
y = X @ [1, 2, 3, -1, 0.5] + np.random.randn(1000) * 0.1
result = fit(X, y, names=['x1', 'x2', 'x3', 'x4', 'x5'])
print(result.summary())          # R-style output with variable names
print(result.coef)                # {'x1': 1.00, 'x2': 2.00, ...}
print(result.coef['x3'])          # 3.00

# Logistic regression
y_binary = (X @ [1, -1, 0.5, 0, 0] + np.random.randn(1000) > 0).astype(float)
result = fit(X, y_binary, family='binomial')
print(result.summary())

# --- Categorical predictors & interactions ---
# Describe a model as a list of terms (no R-style formula strings):
#   "name"          -> numeric main effect
#   C(name, ref=…)  -> categorical, treatment-coded with a chosen baseline
#   (a, b)          -> interaction (numeric and/or categorical)
from pystatistics import DataSource
from pystatistics.regression import Design, fit, C

ds = DataSource.from_dataframe(df)   # df has age, sex, treatment, response
design = Design.from_datasource(
    ds, y='response',
    terms=['age', C('sex', ref='F'), C('treatment', ref='A'),
           (C('treatment', ref='A'), C('sex', ref='F'))],
)
result = fit(design)                       # also works with family=… for GLMs
print(result.coef['treatment[B]:sex[M]'])  # interaction coefficient

# Cox PH takes the same spec (no intercept):
from pystatistics.survival import coxph
cox = coxph(time, event, ds, terms=['age', C('sex', ref='F')])

# GPU acceleration (any model)
result = fit(X, y, backend='gpu')

# --- Monte Carlo methods ---
from pystatistics.montecarlo import boot, boot_ci, permutation_test

# Bootstrap for the mean
data = np.random.randn(100)
def mean_stat(data, indices):
    return np.array([np.mean(data[indices])])

result = boot(data, mean_stat, R=2000, seed=42)
print(result.t0, result.bias, result.se)

# Bootstrap confidence intervals (all 5 types)
ci_result = boot_ci(result, type='all')
print(ci_result.ci['perc'])  # percentile CI
print(ci_result.ci['bca'])   # BCa CI

# Permutation test
x = np.random.randn(30)
y = np.random.randn(30) + 1.0
def mean_diff(x, y): return np.mean(x) - np.mean(y)
result = permutation_test(x, y, mean_diff, R=9999, seed=42)
print(result.p_value, result.summary())

# --- Survival analysis ---
from pystatistics.survival import kaplan_meier, survdiff, coxph, discrete_time

time = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
event = np.array([1, 0, 1, 1, 0, 1, 1, 0, 1, 1])

# Kaplan-Meier survival curve
km = kaplan_meier(time, event)
print(km.survival, km.se, km.ci_lower, km.ci_upper)

# Log-rank test (compare groups)
group = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])
lr = survdiff(time, event, group)
print(lr.statistic, lr.p_value, lr.summary())

# Cox proportional hazards (CPU only)
X = np.column_stack([np.random.randn(10)])
cox = coxph(time, event, X)
print(cox.coefficients, cox.hazard_ratios, cox.summary())

# Discrete-time survival (GPU-accelerated)
dt = discrete_time(time, event, X, backend='auto')
print(dt.coefficients, dt.hazard_ratios, dt.baseline_hazard)

# --- ANOVA ---
from pystatistics.anova import anova_oneway, anova, anova_rm, anova_posthoc, levene_test

# One-way ANOVA
y = np.concatenate([np.random.randn(20) + mu for mu in [0, 1, 3]])
group = np.array(['A']*20 + ['B']*20 + ['C']*20)
result = anova_oneway(y, group)
print(result.summary())          # R-style ANOVA table
print(result.eta_squared)        # effect sizes

# Post-hoc: Tukey HSD
posthoc = anova_posthoc(result, method='tukey')
print(posthoc.summary())         # pairwise comparisons with adjusted p-values

# Factorial ANOVA (Type II SS, matches R's car::Anova)
result = anova(y, {'treatment': tx, 'dose': dose}, ss_type=2)

# ANCOVA (continuous covariate)
result = anova(y, {'group': group}, covariates={'age': age}, ss_type=2)

# Repeated measures with sphericity correction
result = anova_rm(y, subject=subj, within={'condition': cond}, correction='auto')
print(result.sphericity[0].gg_epsilon)  # Greenhouse-Geisser correction

# Levene's test for homogeneity of variances
lev = levene_test(y, group, center='median')  # Brown-Forsythe variant
print(lev.f_value, lev.p_value)

# --- Mixed models ---
from pystatistics.mixed import lmm, glmm

# Random intercept model (matches R lme4::lmer + lmerTest)
result = lmm(y, X, groups={'subject': subject_ids})
print(result.summary())         # lmerTest-style output with Satterthwaite df
print(result.icc)               # intraclass correlation coefficient
print(result.ranef['subject'])  # BLUPs (conditional modes) per subject

# Random intercept + slope
result = lmm(y, X, groups={'subject': subject_ids},
             random_effects={'subject': ['1', 'time']},
             random_data={'time': time_array})

# Crossed random effects (subjects x items)
result = lmm(y, X, groups={'subject': subj_ids, 'item': item_ids})

# Model comparison via LRT (requires ML, not REML)
m1 = lmm(y, X_reduced, groups={'subject': subj_ids}, reml=False)
m2 = lmm(y, X_full, groups={'subject': subj_ids}, reml=False)
print(m1.compare(m2))  # LRT chi-squared, df, p-value

# GLMM — logistic with random intercept
result = glmm(y_binary, X, groups={'subject': subject_ids},
              family='binomial')
print(result.summary())

# GLMM — Poisson with random intercept
result = glmm(y_count, X, groups={'subject': subject_ids},
              family='poisson')

# --- Gamma GLM ---
from pystatistics.regression import fit

y_positive = np.abs(np.random.randn(200)) + 0.1
X = np.random.randn(200, 3)
result = fit(X, y_positive, family='gamma')
print(result.summary())

# --- Ordinal regression ---
from pystatistics.ordinal import polr

y_ordinal = np.random.choice([1, 2, 3, 4, 5], size=200)
X = np.random.randn(200, 3)
result = polr(y_ordinal, X)
print(result.coefficients, result.thresholds)
print(result.summary())

# --- Time series (ARIMA) ---
from pystatistics.timeseries import arima, auto_arima, acf

ts = np.cumsum(np.random.randn(200))  # random walk
acf_result = acf(ts, nlags=20)
result = arima(ts, order=(1, 1, 1))
print(result.coefficients, result.aic)
best = auto_arima(ts)
print(best.order, best.aic)

# --- GAM ---
from pystatistics.gam import gam, s

x = np.linspace(0, 2 * np.pi, 200)
y = np.sin(x) + np.random.randn(200) * 0.3
result = gam(y, smooths=[s('x1')], smooth_data={'x1': x})
print(result.edf, result.gcv)
print(result.summary())

# --- Multiple imputation (MICE) ---
from pystatistics.mice import mice, pool

# data is an (n, p) array with np.nan marking missing values.
# Predictive mean matching (R default) for numeric columns; seed is required
# so the imputation is fully reproducible.
imp = mice(data, m=5, maxit=5, method='pmm', seed=0)
completed = imp.completed_datasets()        # list of 5 completed (n, p) arrays

# Fit your analysis on each completed dataset, then combine with Rubin's rules:
estimates, variances = [], []
for d in completed:
    X = np.column_stack([np.ones(len(d)), d[:, 1]])
    beta, *_ = np.linalg.lstsq(X, d[:, 0], rcond=None)
    resid = d[:, 0] - X @ beta
    cov = (resid @ resid / (len(d) - 2)) * np.linalg.inv(X.T @ X)
    estimates.append(beta[1]); variances.append(cov[1, 1])

pooled = pool(estimates, variances, dfcom=len(data) - 2)
print(pooled.estimate, pooled.se, pooled.ci_low, pooled.ci_high, pooled.fmi)

Installation

pip install pystatistics

# With GPU support (requires PyTorch)
pip install pystatistics[gpu]

# Development
pip install pystatistics[dev]

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What's New

3.16.2 — Reliable GPU categorical & ordered imputation on imbalanced data

• GPU mice imputation of binary, unordered-categorical, and ordered columns no longer collapses a column onto a single category on imbalanced mixed data (a binary column nearly separated by a covariate, or an ordered column with a very sparse middle category). The GPU fits are numerically stabilized and run in double precision internally on CUDA and CPU, so imputed category proportions track the CPU backend and R's mice. (Apple Silicon / MPS, which has no double precision, is unchanged.)
• A genuinely degenerate GPU categorical/ordered fit now raises a clear error rather than silently imputing every missing cell as category 0.

3.16.1 — Reliable GPU ordered-factor imputation under near-separation

• GPU mice imputation of ordered factors (polr, on CUDA and Apple Silicon) no longer collapses a column onto a single category when chained equations push it into near-separation (a sparse extreme category ordered almost perfectly by a continuous predictor). The GPU fit now matches the CPU polr method, recovering the sparse extreme category instead of assigning nearly every imputed cell the same value.

3.16.0 — Reliable ordered-factor imputation under near-separation

• mice imputation of ordered factors (the polr method) no longer degrades to a predictor-blind marginal draw when chained equations push a column into near-separation (a sparse extreme category ordered almost perfectly by a continuous predictor). A small ridge on the slopes keeps the fit finite and fast, so it stays a proper predictor-aware imputer on exactly the columns where it used to fall back.
• polr gains an optional ridge parameter — an L2 penalty on the slope coefficients that keeps the fit finite and well-conditioned under (quasi-)complete separation. The default ridge=0.0 is the exact maximum-likelihood fit.

3.15.2 — GPU ordered-factor imputation matches R's threshold variability

• GPU mice imputation of ordered factors (polr, on CUDA and Apple Silicon) now draws the proportional-odds thresholds on the natural scale, matching the CPU polr method and R's MASS::polr. Imputed category proportions were already correct, but the between-imputation variability — and the pooled (Rubin's rules) variances and intervals that depend on it — is now correct too.

3.15.1 — Faster, more reliable ordered-factor imputation

• Imputing ordered factors with mice (the polr method) is now several times faster — and faster than R's mice — and no longer falls back to a cruder draw on realistic correlated data. Proportional-odds threshold standard errors now match R's MASS::polr.

3.15.0 — MICE GPU imputes categorical data

• mice(..., backend='gpu') now imputes categorical columns on CUDA and Apple Silicon (MPS), using the same models as R's mice: logreg for binary columns, polyreg for unordered factors, and polr for ordered factors. The fits run batched across all imputations; imputed category distributions match the CPU reference and R within Monte-Carlo tolerance. Categorical predictors are supported too (treatment-dummy-encoded) when imputing numeric columns. Together these let a full mixed-type dataset be imputed on the GPU — incomplete categorical columns were previously refused.

3.14.0 — Faster MICE GPU imputation on Apple Silicon

• MICE GPU imputation runs about 1.7–2x faster on Apple Silicon (MPS), with no change to results. The per-iteration step no longer synchronizes the GPU with the CPU on every step, and for larger problems it replaces solve_triangular (slow on MPS) with a short sequence of matrix multiplications. Measured ~1.8x at n=2000, ~2.0x at n=8000, ~1.7x at n=20000 (20 variables, 100 imputations). Imputations are unchanged within the GPU/FP32 tolerance; the CUDA path is unaffected.

3.13.0 — MICE GPU acceleration on Apple Silicon, faster on every GPU

• mice(..., backend='gpu') now runs on Apple Silicon (MPS), not only CUDA. The batched imputation sweep runs on the Mac GPU in FP32 — about 12x faster than the CPU backend on a large problem (n=20000, p=20, m=100: 3.3 s vs 42 s) — validated against the CPU reference for both pmm and norm. backend='auto' stays on CPU on a Mac; request the GPU explicitly with backend='gpu'. use_fp64=True is rejected on MPS (no double precision there). The GPU posterior draw and donor search were also reworked to run faster on CUDA too.

3.12.0 — MVN MLE rejects rank-deficient input

• mlest now raises SingularMatrixError on (near-)collinear input instead of returning a meaningless "converged" fit with a near-singular covariance — such input has no interior maximum-likelihood estimate. Pass force=True to return the degenerate result anyway (with converged=False and a warning), or collinearity_tol to tune the detection threshold. Collinear columns are never dropped automatically. Full-rank problems are unaffected. This is a behaviour change: collinear input that previously returned a result now raises by default.

3.11.0 — Portable inverse path and selectable inverse algorithm in the GPU objective

• The GPU objective's triangular-solve inverse path now runs on every device (it previously relied on cholesky_inverse, unavailable on Apple Metal).
• The batched GPU kernel functions accept a method argument ("auto", "solve", "blocked") to select the per-pattern inverse algorithm; "auto" keeps the existing device-aware default. Results are identical regardless of method.

3.10.0 — Closed-form GPU gradient: fast, practical wide-data fits on Apple Silicon

• mlest(backend='gpu') now uses a closed-form gradient instead of automatic differentiation, which previously backpropagated through cholesky — pathologically slow on Apple Metal. A 100-variable survey fit on Apple Silicon goes from a >30-minute timeout to roughly 3 minutes (converged), and the per-gradient cost falls about 20-fold. Results are unchanged; CUDA and CPU benefit too.

3.9.0 — GPU MLE scales to wide data within bounded memory

• GPU mlest now evaluates the missing-data objective and gradient in chunks of missingness patterns, so GPU memory stays bounded no matter how many distinct patterns the data has. Wide data (100+ variables, tens of thousands of patterns) that previously hit CUDA out-of-memory now fits. The chunk size is auto-tuned (override via chunk_size); results are unchanged.

3.8.1 — Correct MLE for missing data with >62 variables

• mlest now groups missingness patterns correctly when a dataset has more than 62 variables. An integer-overflow bug in the pattern code previously merged distinct patterns and produced NaN estimates on wide data (e.g. survey instruments with 100+ items). Results are unchanged at ≤62 variables.

3.8.0 — Survival results expose warnings

• All survival results (kaplan_meier, survdiff, coxph, discrete_time) now expose a .warnings attribute, consistent with every other analysis type. Non-fatal issues found during fitting — such as a non-converged Cox model — are now reachable instead of silently dropped.
• The log-rank test (survdiff) now warns when its chi-square approximation may be unreliable: when any group's expected event count is below 5, or when a group has no observed events.

3.7.1 — Correct covariance from the double-precision GPU estimator

• Fixed an incorrect covariance matrix returned by mlest(backend='gpu') in double precision (FP64, NVIDIA/CUDA) when fitting 3 or more variables: the optimiser and the reported result referred to mismatched covariances. The FP64 and FP32 GPU paths now share one validated reconstruction that matches the CPU result to floating-point precision. FP32 GPU and CPU fits were unaffected.

3.7.0 — Much faster GPU MLE on Apple Silicon

• mlest(backend='gpu') (direct / BFGS) on Apple Silicon (MPS) now computes the per-pattern trace term with a matmul-only blocked matrix inversion, sidestepping Metal's slow triangular-solve kernels. For data with many distinct missingness patterns (survey scale), this makes Apple-GPU fits dramatically faster, with results identical to before. CUDA is unchanged.

3.6.0 — Faster GPU MLE for missing-data multivariate normal

• mlest(backend='gpu') (direct / BFGS) now evaluates the per-pattern log-likelihood with a single batched Cholesky across all missingness patterns instead of looping over them one at a time. On data with many distinct patterns — common at survey scale — this is substantially faster. Results are unchanged.
• More numerically stable FP32 covariance computation on the GPU path.

3.5.1 — GPU MICE scales to large datasets

• The GPU predictive-mean-matching donor search now uses the same memory-light windowed approach as the CPU backend, batched across imputation chains. This removes out-of-memory failures on large problems and makes the GPU backend much faster at scale — on an RTX 5070 Ti, GPU PMM is roughly 30–50× faster than the CPU backend at n=20000, and imputes n=100000 in under a second.

3.5.0 — Categorical imputation for MICE

• mice now imputes categorical columns, not only numeric ones. Declare each column's kind via column_kinds ('binary', 'categorical', 'ordered') and it is imputed with logistic, multinomial, or proportional-odds regression respectively — mirroring R mice's logreg/polyreg/polr. Categorical columns are integer category codes.
• method='auto' (the new default) selects the right method per column kind; mixed numeric/categorical datasets impute coherently (categorical predictors are dummy-encoded). Imputed category proportions are validated against R mice.
• GPU acceleration stays numeric-only; categorical imputation runs on the CPU.

3.4.1 — Faster CPU predictive mean matching

• CPU PMM in mice now scales to large datasets: the donor search sorts the observed predictions and scans a small window per missing value (as R's mice does) instead of forming a full distance matrix, cutting time and memory from quadratic to roughly n log n. Large problems that were effectively unusable on the CPU now finish in seconds. Results are statistically unchanged.

3.4.0 — GPU acceleration for MICE

• mice(..., backend='gpu') runs the imputation chains on a CUDA GPU, batching the per-variable solves and the predictive-mean-matching donor search across chains. backend='auto' uses a CUDA GPU when available, else the CPU.
• The GPU advantage grows with sample size (the donor search batches well across chains); see 3.5.1 for current benchmark figures. GPU results match the CPU backend at the GPU/FP32 tolerance; pass use_fp64=True for double precision.
• Requires a CUDA GPU; Apple Silicon (MPS) is not yet supported for MICE.

3.3.0 — Multiple imputation (MICE)

• New mice module: multiple imputation by chained equations for numeric data with missing values. mice(data, m=5, method='pmm', seed=...) returns m completed datasets, using predictive mean matching (the R default) or Bayesian linear regression (method='norm'). Defaults follow R's mice.
• Imputation is fully reproducible — seed is required, and each chain uses an independent random stream.
• pool(estimates, variances) combines per-dataset analyses with Rubin's rules (Barnard–Rubin degrees of freedom, confidence intervals, fraction of missing information).
• Numeric columns on the CPU in this release; validated against R's mice.

3.2.0 — Apple Silicon (MPS) GPU support

• multinom, polr, gam, and arima / arima_batch (Whittle) now run on Apple Silicon GPUs with backend='gpu', in FP32 and entirely on native Metal kernels (no hidden CPU fallback). Results match the CPU backend at the GPU/FP32 tolerance tier.
• DataSource.to('mps') transfers data to the Apple GPU (float64 → float32), so you can pay the host→device copy once and reuse it across fits.
• backend='auto' uses the CPU on Apple Silicon; the Apple GPU is opt-in via an explicit backend='gpu'. CUDA is still auto-selected.
• pca and MVN MLE em GPU paths remain CUDA-only and now raise a clear error on Apple Silicon rather than silently running on the CPU — PCA's SVD/eigendecomposition and the EM scatter/iteration pattern have no efficient Metal equivalent. Use backend='cpu' or 'auto' on a Mac. (MVN MLE direct GPU fitting works on MPS.)
• Whittle ARIMA GPU fits no longer raise a spurious convergence error when the FP32 line search stalls at an already-converged optimum.

3.1.0 — Categorical predictors & interaction terms

• Regression now supports categorical predictors and interactions via a terms= spec on Design.from_datasource: bare names are numeric main effects, C(name, ref=...) marks a categorical predictor with a selectable baseline level, and tuples express interactions (numeric and/or categorical). Works for OLS, all GLM families, and Cox PH (no intercept).
• Expanded columns are labeled sex[M], treatment[B]:sex[M], with coef and inference outputs aligned to those labels. Design matrices match R's model.matrix for factors and interactions.
• DataSource.from_dataframe now keeps non-numeric columns as-is (previously force-cast to float), so categorical columns can feed C(...).
• New public symbol: pystatistics.regression.C.

3.0.1 — Metadata and documentation polish

• Development Status classifier bumped from Alpha to Production/Stable.
• Stale [nonparametric_mcar] optional-dependency extra removed from pyproject.toml (the subpackage itself was removed in 3.0.0).
• README restructured to lead with library identity and module overview rather than changelog.

No API changes.

3.0.0 — MCAR helpers removed (breaking)

Removed (breaking):

• pystatistics.mvnmle.mom_mcar_test and its helpers.
• pystatistics.nonparametric_mcar subpackage in its entirety (propensity_mcar_test, hsic_mcar_test, missmech_mcar_test, NonparametricMCARResult).
• The [nonparametric_mcar] optional-dependency extra.

If you were using these tests, little_mcar_test (the canonical Little 1988 MLE-plug-in test) remains and is unchanged. The removed tests were project-specific feature-extraction utilities rather than textbook methods.

Retained (unchanged): little_mcar_test, MCARTestResult, mlest, analyze_patterns, PatternInfo, and every EM / SQUAREM / monotone-closed-form path.

Bug fixes:

• GAM GPU smooth-term chi-squared no longer diverges from CPU on ill-conditioned penalised normal matrices. The GPU backend now canonicalises the final coefficients via Cholesky-with-LU-fallback to match CPU bit-for-bit.
• GAM GPU FP64 total_edf test tolerance widened to rel=5e-3 on that quantity only, reflecting its linear sensitivity to λ near the GCV optimum.

2.3.0 — Nonparametric MCAR tests (introduced, removed in 3.0.0)

Shipped three distribution-free MCAR tests in a new nonparametric_mcar subpackage. Removed in 3.0.0 — see above.

2.2.0 — Real-data robustness

Four classes of numerical failure on realistic tabular data fixed — Cholesky fast-path crash on GPU FP32 roundoff, bare-RuntimeError wrapping that broke PyStatisticsError catch patterns, M-step sigma PD-check false negatives from FP64 roundoff, and per-pattern Cholesky on indefinite sub-blocks — with a unified regularize=True opt-out-to-strict convention across mlest, little_mcar_test, and the batched E-step.

2.1.0 — EM speedup + monotone closed-form MLE

little_mcar_test on realistic tabular data sped up 1.6–2.1× via batched per-pattern E-step, SQUAREM acceleration, and fully batched log-likelihood. Fully-batched device-resident EM on GPU added: 14.6× at n=569, v=30. New mvnmle.is_monotone, mvnmle.monotone_permutation, and mlest(data, algorithm='monotone') — Anderson (1957) closed-form MLE for monotone missingness, bit-equivalent to R mvnmle on canonical datasets and orders of magnitude faster than EM on larger-v longitudinal data.

2.0.1 — GPU-backend exposure gaps closed

little_mcar_test and auto_arima gained backend= and algorithm=/method= parameters that had been missing, so GPU paths are now reachable from both entry points.

2.0.0 — CPU is the default backend everywhere (breaking)

Every public solver that previously defaulted to backend='auto' now defaults to CPU — the R-reference, validated-for-regulated-industries path. GPU is never selected implicitly. Affected: regression.fit, mvnmle.mlest, survival.discrete_time, montecarlo.boot, montecarlo.permutation_test, descriptive.*, hypothesis.*.

The GPU path is opt-in:

result = fit(X, y, backend='gpu')    # require GPU; fail loud if absent
result = fit(X, y, backend='auto')   # prefer GPU, fall back to CPU

Migration: if you relied on implicit GPU selection on a GPU-equipped box, add backend='auto' or backend='gpu' to the affected calls.

1.9.0 — Device-resident PCA results and batched ARMA fits

• GPU-resident PCAResult (pca(..., device_resident=True)). Numeric fields stay as torch.Tensor on the fit's device. 3.4× speedup on 1M × 100 FP32 PCA by skipping the D2H score copy.
• arima_batch(Y, order=(p, d, q), method='Whittle'). Fits K independent ARMA models on the rows of a (K, n) matrix simultaneously. Crossover at K ≈ 100; 13× at K=1000.

1.8.0 — GPU backends for the 1.6.x modules

GPU backends added across PCA, multinomial logit, ordinal polr, GAM, and ARIMA Whittle. Typical speedups: 3–4× (PCA SVD), up to 100× (PCA Gram on tall-skinny), 49–183× (multinomial), 448× at n=100k (ordinal polr), 10–29× (GAM with 3 smooths), 36× at n=1M (ARIMA Whittle). New DataSource.to(device) API for amortised-transfer workflows. Whittle ARIMA (method='Whittle') added as a FFT-based approximate MLE alongside CSS / ML / CSS-ML. CPU multinomial vcov now uses the analytical block Hessian (29–33× CPU speedup on that step).

Previous Releases

1.7.0 — Performance parity with R on OLS first-call (578 ms → 5 ms), polr (277 ms → 23 ms), and SARIMA airline-model fit (2,100 ms → 14 ms via numba-JIT'd Kalman state-space path).

1.6.2 — Re-shipped 1.6.1 fixes left out of the PyPI wheel. Fail-loud fixes in ARIMA CSS-ML, ARIMA(0,d,0) closed-form MLE, Gamma GLM dispersion, descriptive.var(n=1), scipy 1.18 forward-compat.

1.6.0 — Five new modules (ordinal, multinomial, multivariate, timeseries, gam), two new GLM families (Gamma, NegativeBinomial).

1.2.1 — No silent model switches; backend='gpu' is honest; reproducible Monte Carlo via seed=; module structure refactoring.

1.1 — Named coefficients via names=; result.coef dict; OLS/Cox summary improvements matching R output.

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License

MIT

Author

Hai-Shuo ([e-mail])