rustystats 0.4.6

Fast Generalized Linear Models with a Rust backend - statsmodels compatible

RustyStats 🦀📊

High-performance Generalized Linear Models with a Rust backend and Python API

Codebase Documentation: pricingfrontier.github.io/rustystats/

Features

• Dict-First API - Programmatic model building ideal for automated workflows and agents
• Fast - Parallel Rust backend, 5-10x faster than statsmodels
• Memory Efficient - 4-5x less RAM than statsmodels at scale
• Stable - Step-halving IRLS, warm starts for robust convergence
• Splines - B-splines and natural splines with auto-tuned smoothing and monotonicity
• Target Encoding - Ordered target encoding for high-cardinality categoricals
• Regularisation - Ridge, Lasso, and Elastic Net via coordinate descent
• Validation - Design matrix checks with fix suggestions before fitting
• Complete - 8 families, robust SEs, full diagnostics, VIF, partial dependence
• Minimal - Only numpy and polars required

Installation

uv add rustystats

Quick Start

import rustystats as rs
import polars as pl

# Load data
data = pl.read_parquet("insurance.parquet")

# Fit a Poisson GLM for claim frequency
result = rs.glm_dict(
    response="ClaimCount",
    terms={
        "VehAge": {"type": "linear"},
        "VehPower": {"type": "linear"},
        "Area": {"type": "categorical"},
        "Region": {"type": "categorical"},
    },
    data=data,
    family="poisson",
    offset="Exposure",
).fit()

# View results
print(result.summary())

---

Families & Links

Family	Default Link	Use Case
gaussian	identity	Linear regression
poisson	log	Claim frequency
binomial	logit	Binary outcomes
gamma	log	Claim severity
tweedie	log	Pure premium (var_power=1.5)
quasipoisson	log	Overdispersed counts
quasibinomial	logit	Overdispersed binary
negbinomial	log	Overdispersed counts (proper distribution)

---

Dict-Based API

API built for programmatic model building.

result = rs.glm_dict(
    response="ClaimCount",
    terms={
        "VehAge": {"type": "bs", "monotonicity": "increasing"},  # Monotonic (auto-tuned)
        "DrivAge": {"type": "bs"},                               # Penalized smooth (default)
        "Income": {"type": "bs", "df": 5},                       # Fixed 5 df
        "BonusMalus": {"type": "linear", "monotonicity": "increasing"},  # Constrained coefficient
        "Region": {"type": "categorical"},
        "Brand": {"type": "target_encoding"},
        "Age2": {"type": "expression", "expr": "DrivAge**2"},
    },
    interactions=[
        {
            "VehAge": {"type": "linear"}, 
            "Region": {"type": "categorical"}, 
            "include_main": True
        },
    ],
    data=data,
    family="poisson",
    offset="Exposure",
    seed=42,
).fit(regularization="elastic_net")

Term Types

Type	Parameters	Description
linear	monotonicity (optional)	Raw continuous variable
categorical	levels (optional)	Dummy encoding
bs	df or k, degree=3, monotonicity	B-spline (default: penalized smooth, k=10)
ns	df or k	Natural spline (default: penalized smooth, k=10)
target_encoding	prior_weight=1	Regularized target encoding
expression	expr, monotonicity (optional)	Arbitrary expression (like I())

Interactions

Each interaction is a dict with variable specs. Use include_main to also add main effects.

interactions=[
    # Standard interaction: product terms (main effects + interaction)
    {
        "DrivAge": {"type": "bs", "df": 5}, 
        "Brand": {"type": "target_encoding"},
        "include_main": True
    },
    # Categorical × continuous (interaction only)
    {
        "VehAge": {"type": "linear"}, 
        "Region": {"type": "categorical"}, 
        "include_main": False
    },
    # TE interaction: combined target encoding TE(Brand:Region)
    {
        "Brand": {"type": "categorical"},
        "Region": {"type": "categorical"},
        "target_encoding": True,
        "prior_weight": 1.0,  # optional
    },
    # FE interaction: combined frequency encoding FE(Brand:Region)
    {
        "Brand": {"type": "categorical"},
        "Region": {"type": "categorical"},
        "frequency_encoding": True,
    },
]

Flag	Effect
(none)	Standard product terms (cat×cat, cat×cont, etc.)
target_encoding: True	Combined TE encoding: TE(var1:var2)
frequency_encoding: True	Combined FE encoding: FE(var1:var2)

---

Splines

# Default: penalized smooth with automatic tuning via GCV
result = rs.glm_dict(
    response="ClaimNb",
    terms={
        "Age": {"type": "bs"},           # B-spline (auto-tuned)
        "VehPower": {"type": "ns"},      # Natural spline (auto-tuned)
        "Region": {"type": "categorical"},
    },
    data=data, family="poisson", offset="Exposure",
).fit()

# Fixed degrees of freedom (no penalty)
result = rs.glm_dict(
    response="ClaimNb",
    terms={
        "Age": {"type": "bs", "df": 5},       # Fixed 5 df
        "VehPower": {"type": "ns", "df": 4},  # Fixed 4 df
        "Region": {"type": "categorical"},
    },
    data=data, family="poisson", offset="Exposure",
).fit()

Spline parameters:

• No parameters → penalized smooth with automatic tuning (k=10)
• df=5 → fixed 5 degrees of freedom
• k=15 → penalized smooth with 15 basis functions
• monotonicity="increasing" or "decreasing" → constrained effect (bs only)

When to use each type:

• B-splines (bs): Standard choice, more flexible at boundaries, supports monotonicity
• Natural splines (ns): Better extrapolation, linear beyond boundaries

Monotonic Splines

Constrain the fitted curve to be monotonically increasing or decreasing. Essential when business logic dictates a monotonic relationship.

# Monotonically increasing effect (e.g., age → risk)
result = rs.glm_dict(
    response="ClaimNb",
    terms={
        "Age": {"type": "bs", "monotonicity": "increasing"},
        "Region": {"type": "categorical"},
    },
    data=data, family="poisson", offset="Exposure",
).fit()

# Monotonically decreasing effect (e.g., vehicle value with age)
result = rs.glm_dict(
    response="ClaimAmt",
    terms={"VehAge": {"type": "bs", "df": 4, "monotonicity": "decreasing"}},
    data=data, family="gamma",
).fit()

---

Coefficient Constraints

Constrain coefficient signs using monotonicity on linear and expression terms.

result = rs.glm_dict(
    response="y",
    terms={
        "age": {"type": "linear", "monotonicity": "increasing"},  # β ≥ 0
        "age2": {"type": "expression", "expr": "age ** 2", "monotonicity": "decreasing"},  # β ≤ 0
        "income": {"type": "linear"},
    },
    data=data, family="poisson",
).fit()

Constraint	Term Spec	Effect
β ≥ 0	"monotonicity": "increasing"	Positive effect
β ≤ 0	"monotonicity": "decreasing"	Negative effect

---

Target Encoding

Ordered target encoding for high-cardinality categoricals.

# Dict API
result = rs.glm_dict(
    response="ClaimNb",
    terms={
        "Brand": {"type": "target_encoding"},
        "Model": {"type": "target_encoding", "prior_weight": 2.0},
        "Age": {"type": "linear"},
        "Region": {"type": "categorical"},
    },
    data=data, family="poisson", offset="Exposure",
).fit()

# Sklearn-style API
encoder = rs.TargetEncoder(prior_weight=1.0, n_permutations=4)
train_encoded = encoder.fit_transform(train_categories, train_target)
test_encoded = encoder.transform(test_categories)

Key benefits:

• No target leakage: Ordered target statistics
• Regularization: Prior weight controls shrinkage toward global mean
• High-cardinality: Single column instead of thousands of dummies
• Exposure-aware: For frequency models with offset="Exposure", automatically uses claim rate (ClaimCount/Exposure) instead of raw counts
• Interactions: Use target_encoding: True in interactions to encode variable combinations

---

Expression Terms

result = rs.glm_dict(
    response="y",
    terms={
        "age": {"type": "linear"},
        "age2": {"type": "expression", "expr": "age ** 2"},
        "age3": {"type": "expression", "expr": "age ** 3"},
        "income_k": {"type": "expression", "expr": "income / 1000"},
        "bmi": {"type": "expression", "expr": "weight / (height ** 2)"},
    },
    data=data, family="gaussian",
).fit()

Supported operations: +, -, *, /, ** (power)

---

Regularization

CV-Based Regularization

# Just specify regularization type - cv=5 is automatic
result = rs.glm_dict(
    response="y",
    terms={"x1": {"type": "linear"}, "x2": {"type": "linear"}, "cat": {"type": "categorical"}},
    data=data,
    family="poisson",
).fit(regularization="ridge")  # "ridge", "lasso", or "elastic_net"

print(f"Selected alpha: {result.alpha}")
print(f"CV deviance: {result.cv_deviance}")

Options:

• regularization: "ridge" (L2), "lasso" (L1), or "elastic_net" (mix)
• selection: "min" (best fit) or "1se" (more conservative, default: "min")
• cv: Number of folds (default: 5)

Explicit Alpha

# Skip CV, use specific alpha
result = rs.glm_dict(response="y", terms={"x1": {"type": "linear"}, "x2": {"type": "linear"}}, data=data).fit(alpha=0.1, l1_ratio=0.0)  # Ridge
result = rs.glm_dict(response="y", terms={"x1": {"type": "linear"}, "x2": {"type": "linear"}}, data=data).fit(alpha=0.1, l1_ratio=1.0)  # Lasso
result = rs.glm_dict(response="y", terms={"x1": {"type": "linear"}, "x2": {"type": "linear"}}, data=data).fit(alpha=0.1, l1_ratio=0.5)  # Elastic Net

---

Design Matrix Validation

# Check for issues before fitting
model = rs.glm_dict(
    response="y",
    terms={"x": {"type": "ns", "df": 4}, "cat": {"type": "categorical"}},
    data=data, family="poisson",
)
results = model.validate()  # Prints diagnostics

if not results['valid']:
    print("Issues:", results['suggestions'])

# Validation runs automatically on fit failure with helpful suggestions

Checks performed:

• Rank deficiency (linearly dependent columns)
• High multicollinearity (condition number)
• Zero variance columns
• NaN/Inf values
• Highly correlated column pairs (>0.999)

---

Results

# Coefficients & Inference
result.params              # Coefficients
result.fittedvalues        # Predicted means
result.deviance            # Model deviance
result.bse()               # Standard errors
result.tvalues()           # z-statistics
result.pvalues()           # P-values
result.conf_int(alpha)     # Confidence intervals

# Robust Standard Errors (sandwich estimators)
result.bse_robust("HC1")   # Robust SE (HC0, HC1, HC2, HC3)
result.tvalues_robust()    # z-stats with robust SE
result.pvalues_robust()    # P-values with robust SE
result.conf_int_robust()   # Confidence intervals with robust SE
result.cov_robust()        # Full robust covariance matrix

# Diagnostics (statsmodels-compatible)
result.resid_response()    # Raw residuals (y - μ)
result.resid_pearson()     # Pearson residuals
result.resid_deviance()    # Deviance residuals
result.resid_working()     # Working residuals
result.llf()               # Log-likelihood
result.aic()               # Akaike Information Criterion
result.bic()               # Bayesian Information Criterion
result.null_deviance()     # Null model deviance
result.pearson_chi2()      # Pearson chi-squared
result.scale()             # Dispersion (deviance-based)
result.scale_pearson()     # Dispersion (Pearson-based)
result.family              # Family name

---

Model Diagnostics

# Compute all diagnostics at once
diagnostics = result.diagnostics(
    data=data,
    categorical_factors=["Region", "VehBrand", "Area"],  # Including non-fitted
    continuous_factors=["Age", "Income", "VehPower"],    # Including non-fitted
)

# Export as compact JSON (optimized for LLM consumption)
json_str = diagnostics.to_json()

# Pre-fit data exploration (no model needed)
exploration = rs.explore_data(
    data=data,
    response="ClaimNb",
    categorical_factors=["Region", "VehBrand", "Area"],
    continuous_factors=["Age", "VehPower", "Income"],
    exposure="Exposure",
    family="poisson",
    detect_interactions=True,
)

Diagnostic Features:

• Calibration: Overall A/E ratio, calibration by decile with CIs, Hosmer-Lemeshow test
• Discrimination: Gini coefficient, AUC, KS statistic, lift metrics
• Factor Diagnostics: A/E by level/bin for ALL factors (fitted and non-fitted)
• VIF/Multicollinearity: Variance inflation factors for design matrix columns
• Partial Dependence: Effect plots with shape detection and recommendations
• Overfitting Detection: Compare train vs test metrics when test data provided
• Interaction Detection: Greedy residual-based detection of potential interactions
• Warnings: Auto-generated alerts for high dispersion, poor calibration, missing factors
• Base Model Comparison: Compare new model against existing/benchmark predictions

Comparing Against a Base Model

Compare your new model against predictions from an existing model (e.g., current production model):

# Add base model predictions to your data
data = data.with_columns(pl.lit(old_model_predictions).alias("base_pred"))

# Run diagnostics with base_predictions
diagnostics = result.diagnostics(
    train_data=data,
    categorical_factors=["Region", "VehBrand"],
    continuous_factors=["Age", "VehPower"],
    base_predictions="base_pred",  # Column name with base model predictions
)

# Access comparison results
bc = diagnostics.base_predictions_comparison

# Side-by-side metrics
print(f"Model loss: {bc.model_metrics.loss}, Base loss: {bc.base_metrics.loss}")
print(f"Model Gini: {bc.model_metrics.gini}, Base Gini: {bc.base_metrics.gini}")

# Improvement metrics (positive = new model is better)
print(f"Loss improvement: {bc.loss_improvement_pct}%")
print(f"Gini improvement: {bc.gini_improvement}")
print(f"AUC improvement: {bc.auc_improvement}")

# Decile analysis sorted by model/base prediction ratio
for d in bc.model_vs_base_deciles:
    print(f"Decile {d.decile}: actual={d.actual:.4f}, "
          f"model={d.model_predicted:.4f}, base={d.base_predicted:.4f}")

The comparison includes:

• Side-by-side metrics: Loss (mean deviance), Gini, AUC, A/E ratio for both models
• Improvement metrics: loss_improvement_pct, gini_improvement, auc_improvement
• Decile analysis: Data sorted by model/base ratio, showing where the new model diverges
• Calibration comparison: Count of deciles where each model has better A/E

---

Model Serialization

Save and load fitted models for later use:

# Fit and save
model_bytes = result.to_bytes()

with open("model.bin", "wb") as f:
    f.write(model_bytes)

# Load later
with open("model.bin", "rb") as f:
    loaded = rs.GLMModel.from_bytes(f.read())

# Predict with loaded model
predictions = loaded.predict(new_data)

What's preserved:

• Coefficients and feature names
• Categorical encoding levels
• Spline knot positions
• Target encoding statistics
• Formula, family, link function

Compact storage: Only prediction-essential state is stored (~KB, not MB).

---

Model Export (PMML & ONNX)

Export fitted models to standard formats for deployment — no extra dependencies required. PMML uses stdlib XML; ONNX protobuf serialization is implemented from scratch in Rust.

PMML

# Export to PMML 4.4 XML
pmml_xml = result.to_pmml()
result.to_pmml(path="model.pmml")

# Load & predict (consumer side)
# pip install pypmml
from pypmml import Model
pmml_model = Model.fromFile("model.pmml")

new_data = pl.DataFrame({"VehAge": [3, 5, 1], "Area": ["C", "A", "B"]})
preds = pmml_model.predict(new_data.to_dict(as_series=False))

ONNX

Two modes: scoring (consumer builds design matrix) and full (preprocessing embedded in graph).

# Scoring mode (default) — input is pre-built design matrix
onnx_bytes = result.to_onnx(mode="scoring")
result.to_onnx(path="model.onnx", mode="scoring")

# Full mode — input is raw feature values, preprocessing embedded
result.to_onnx(path="model_full.onnx", mode="full")

# Load & predict on a DataFrame with onnxruntime (consumer side)
# pip install onnxruntime
import onnxruntime as ort
import numpy as np

new_data = pl.DataFrame({
    "VehAge": [3, 5, 1],
    "Area": ["C", "A", "B"],
})

# ── Scoring mode: build design matrix from DataFrame ──
session = ort.InferenceSession("model.onnx")
# Columns match model.feature_names (excluding Intercept): [VehAge, Area_B, Area_C]
X = np.column_stack([
    new_data["VehAge"].to_numpy().astype(np.float64),
    (new_data["Area"] == "B").cast(pl.Float64).to_numpy(),
    (new_data["Area"] == "C").cast(pl.Float64).to_numpy(),
])
preds = session.run(None, {"X": X})[0]  # shape (3, 1)

# ── Full mode: pass raw values, categoricals as integer codes ──
session = ort.InferenceSession("model_full.onnx")
# Map categorical levels to 0-based codes: A=0, B=1, C=2
level_map = {"A": 0, "B": 1, "C": 2}
raw = np.column_stack([
    new_data["VehAge"].to_numpy().astype(np.float64),
    new_data["Area"].map_elements(lambda v: level_map[v], return_dtype=pl.Int64).to_numpy().astype(np.float64),
])
preds = session.run(None, {"input": raw})[0]  # shape (3, 1)

	scoring	full
Input	Pre-built design matrix	Raw feature values
Categoricals	One-hot dummies	Integer codes
Preprocessing	Consumer handles it	Embedded in graph
Size	Smaller	Larger

---

Performance Benchmarks

RustyStats vs Statsmodels — Synthetic data, 101 features (10 continuous + 10 categorical with 10 levels each).

Family	10K rows	250K rows	500K rows
Gaussian	18.3x	6.4x	5.1x
Poisson	19.6x	7.1x	5.2x
Binomial	23.5x	7.1x	5.4x
Gamma	9.0x	13.4x	8.9x
NegBinomial	22.5x	7.2x	5.0x

Average speedup: 10.9x (range: 5.0x – 23.5x)

Memory Usage

Rows	RustyStats	Statsmodels	Reduction
10K	4 MB	72 MB	18x
250K	253 MB	1,796 MB	7.1x
500K	780 MB	3,590 MB	4.6x

Full benchmark details

Family	Rows	RustyStats	Statsmodels	Speedup
Gaussian	10,000	0.085s	1.559s	18.3x
Gaussian	250,000	1.769s	11.363s	6.4x
Gaussian	500,000	3.399s	17.386s	5.1x
Poisson	10,000	0.137s	2.692s	19.6x
Poisson	250,000	2.128s	15.072s	7.1x
Poisson	500,000	4.581s	23.693s	5.2x
Binomial	10,000	0.093s	2.189s	23.5x
Binomial	250,000	1.851s	13.155s	7.1x
Binomial	500,000	3.842s	20.862s	5.4x
Gamma	10,000	0.486s	4.353s	9.0x
Gamma	250,000	2.377s	31.885s	13.4x
Gamma	500,000	5.202s	46.167s	8.9x
NegBinomial	10,000	0.141s	3.177s	22.5x
NegBinomial	250,000	2.128s	15.278s	7.2x
NegBinomial	500,000	4.900s	24.331s	5.0x

Times are median of 3 runs. Benchmark scripts in benchmarks/.

---

Dependencies

Rust

• ndarray, nalgebra - Linear algebra
• rayon - Parallel iterators (multi-threading)
• statrs - Statistical distributions
• pyo3 - Python bindings

Python

• numpy - Array operations (required)
• polars - DataFrame support (required)

---

License

Elastic License 2.0 (ELv2) — Free to use, modify, and distribute. Cannot be offered as a hosted/managed service.