rustystats 0.2.1

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/

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	15.6x	5.7x	4.3x
Poisson	16.3x	6.2x	4.2x
Binomial	19.5x	6.8x	4.4x
Gamma	33.7x	13.4x	8.4x
NegBinomial	26.7x	6.7x	5.0x

Average speedup: 10.5x (range: 4.2x – 33.7x)

Memory Usage

RustyStats uses significantly less RAM by reusing buffers and avoiding Python object overhead:

Rows	RustyStats	Statsmodels	Reduction
10K	38 MB	72 MB	1.9x
250K	460 MB	1,796 MB	3.9x
500K	836 MB	3,590 MB	4.3x

Memory advantage grows with data size — at 500K rows, RustyStats uses ~4x less RAM.

Full benchmark details

Family	Rows	RustyStats	Statsmodels	Speedup
Gaussian	10,000	0.100s	1.559s	15.6x
Gaussian	250,000	1.991s	11.363s	5.7x
Gaussian	500,000	4.023s	17.386s	4.3x
Poisson	10,000	0.165s	2.692s	16.3x
Poisson	250,000	2.429s	15.072s	6.2x
Poisson	500,000	5.668s	23.693s	4.2x
Binomial	10,000	0.112s	2.189s	19.5x
Binomial	250,000	1.946s	13.155s	6.8x
Binomial	500,000	4.708s	20.862s	4.4x
Gamma	10,000	0.129s	4.353s	33.7x
Gamma	250,000	2.385s	31.885s	13.4x
Gamma	500,000	5.499s	46.167s	8.4x
NegBinomial	10,000	0.119s	3.177s	26.7x
NegBinomial	250,000	2.281s	15.278s	6.7x
NegBinomial	500,000	4.821s	24.331s	5.0x

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

---

Features

• Fast - Parallel Rust backend, 4-30x faster than statsmodels
• Memory Efficient - 4x less RAM than statsmodels at scale
• Stable - Step-halving IRLS, warm starts for robust convergence
• Splines - B-splines bs(), natural splines ns(), and monotonic splines ms() in formulas
• Polynomials - Identity terms I(x ** 2) for polynomial and arithmetic expressions
• Target Encoding - CatBoost-style TE() for high-cardinality categoricals (exposure-aware)
• 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(
    "ClaimCount ~ VehAge + VehPower + C(Area) + C(Region)",
    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)

---

Formula Syntax

# Main effects
"y ~ x1 + x2 + C(category)"

# Single-level categorical indicators
"y ~ C(Region, level='Paris')"              # 0/1 indicator for Paris only
"y ~ C(Region, levels=['Paris', 'Lyon'])"   # Indicators for specific levels

# Interactions
"y ~ x1*x2"              # x1 + x2 + x1:x2
"y ~ C(area):age"        # Area-specific age effects
"y ~ C(area)*C(brand)"   # Categorical × categorical

# Splines (non-linear effects)
"y ~ bs(age, df=5)"      # B-spline basis
"y ~ ns(income, df=4)"   # Natural spline (better extrapolation)
"y ~ ms(age, df=5)"      # Monotonic spline (increasing)
"y ~ ms(veh_age, df=4, increasing=false)"  # Monotonic decreasing

# Identity terms (polynomial/arithmetic expressions)
"y ~ I(age ** 2)"        # Polynomial terms
"y ~ I(x1 * x2)"         # Explicit products
"y ~ I(income / 1000)"   # Scaled variables

# Coefficient constraints
"y ~ pos(age)"           # Coefficient ≥ 0
"y ~ neg(risk)"          # Coefficient ≤ 0
"y ~ neg(I(age ** 2))"   # Force downward curvature

# Target encoding (high-cardinality categoricals)
"y ~ TE(brand) + TE(model)"

# Combined
"y ~ bs(age, df=5) + C(region)*income + ns(vehicle_age, df=3) + TE(brand) + I(age ** 2)"

---

Dict-Based API

Alternative to formula strings for programmatic model building. Useful for automated workflows and agentic systems.

result = rs.glm_dict(
    response="ClaimCount",
    terms={
        "VehAge": {"type": "ms", "df": 4, "monotonicity": "increasing"},  # Monotonic spline
        "DrivAge": {"type": "bs", "df": 5},
        "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()

Term Types

Type	Parameters	Description
linear	-	Raw continuous variable
categorical	levels (optional)	Dummy encoding
bs	df, degree=3	B-spline basis
ns	df	Natural spline (better extrapolation)
ms	df, monotonicity	Monotonic spline (I-spline)
target_encoding	prior_weight=1	Regularized target encoding
expression	expr	Arbitrary expression (like I())

Add "monotonicity": "increasing" or "decreasing" to linear or expression terms to constrain coefficient sign.

Interactions

Each interaction is a dict with variable specs and include_main:

interactions=[
    # Main effects + interaction (like x*y)
    {
        "DrivAge": {"type": "bs", "df": 5}, 
        "Brand": {"type": "target_encoding"},
        "include_main": True
    },
    # Interaction only (like x:y)
    {
        "VehAge": {"type": "linear"}, 
        "Region": {"type": "categorical"}, 
        "include_main": False
    },
]

---

Results Methods

# 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

---

Regularization

CV-Based Regularization (Recommended)

# Just specify regularization type - cv=5 is automatic
result = rs.glm("y ~ x1 + x2 + C(cat)", 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("y ~ x1 + x2", data).fit(alpha=0.1, l1_ratio=0.0)  # Ridge
result = rs.glm("y ~ x1 + x2", data).fit(alpha=0.1, l1_ratio=1.0)  # Lasso
result = rs.glm("y ~ x1 + x2", data).fit(alpha=0.1, l1_ratio=0.5)  # Elastic Net

---

Interaction Terms

# Continuous × Continuous interaction (main effects + interaction)
result = rs.glm(
    "ClaimNb ~ Age*VehPower",  # Equivalent to Age + VehPower + Age:VehPower
    data, family="poisson", offset="Exposure"
).fit()

# Categorical × Continuous interaction
result = rs.glm(
    "ClaimNb ~ C(Area)*Age",  # Each area level has different age effect
    data, family="poisson", offset="Exposure"
).fit()

# Categorical × Categorical interaction
result = rs.glm(
    "ClaimNb ~ C(Area)*C(VehBrand)",
    data, family="poisson", offset="Exposure"
).fit()

# Pure interaction (no main effects added)
result = rs.glm(
    "ClaimNb ~ Age + C(Area):VehPower",  # Area-specific VehPower slopes
    data, family="poisson", offset="Exposure"
).fit()

---

Spline Basis Functions

# Use splines in formulas - automatic parsing
result = rs.glm(
    "ClaimNb ~ bs(Age, df=5) + ns(VehPower, df=4) + C(Region)",
    data=data,
    family="poisson",
    offset="Exposure"
).fit()

# Combine splines with interactions
result = rs.glm(
    "y ~ bs(age, df=4)*C(gender) + ns(income, df=3)",
    data=data,
    family="gaussian"
).fit()

# Direct basis computation for custom use
import numpy as np
x = np.linspace(0, 10, 100)
basis = rs.bs(x, df=5)  # 5 degrees of freedom (4 basis columns)
basis_ns = rs.ns(x, df=5)  # Natural splines - linear extrapolation at boundaries

When to use each spline type:

• B-splines (bs): Standard choice, more flexible at boundaries
• Natural splines (ns): Better extrapolation, linear beyond boundaries (recommended for actuarial work)
• Monotonic splines (ms): Constrained to be monotonically increasing or decreasing

---

Monotonic Splines

Monotonic splines (I-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(
    "ClaimNb ~ ms(Age, df=5) + C(Region)",
    data=data,
    family="poisson",
    offset="Exposure"
).fit()

# Monotonically decreasing effect (e.g., vehicle value with age)
result = rs.glm(
    "ClaimAmt ~ ms(VehAge, df=4, increasing=false)",
    data=data,
    family="gamma"
).fit()

# Combine with other spline types
result = rs.glm(
    "y ~ ms(age, df=5) + bs(income, df=4) + ns(experience, df=3)",
    data=data,
    family="gaussian"
).fit()

# Direct basis computation
basis = rs.ms(x, df=5)  # Monotonically increasing basis
basis_dec = rs.ms(x, df=5, increasing=False)  # Decreasing

Key properties:

• All basis values in [0, 1]
• Each column monotonically increasing from 0 → 1 (or decreasing)
• With non-negative coefficients, fitted curve is guaranteed monotonic
• Prevents implausible "wiggles" that can occur with unconstrained splines

When to use:

Use Case	Formula
Age → claim frequency	ms(age, df=5)
Vehicle age → value	ms(veh_age, df=4, increasing=false)
Credit score → risk	ms(score, df=5, increasing=false)

---

Coefficient Constraints

Constrain coefficient signs using pos() (β ≥ 0) and neg() (β ≤ 0). Useful for enforcing business logic on linear and polynomial terms.

# Constrain age coefficient to be positive
result = rs.glm(
    "y ~ pos(age) + income",
    data=data,
    family="poisson"
).fit()

# Force quadratic to bend downward (diminishing returns)
result = rs.glm(
    "y ~ age + neg(I(age ** 2))",
    data=data,
    family="gaussian"
).fit()

# Combine with monotonic splines
result = rs.glm(
    "ClaimNb ~ ms(VehAge, df=4) + pos(BonusMalus) + neg(I(DrivAge ** 2))",
    data=data,
    family="poisson",
    offset="Exposure"
).fit()

Supported patterns:

Constraint	Effect	Example
pos(x)	β ≥ 0	pos(age) - positive effect
neg(x)	β ≤ 0	neg(risk) - negative effect
pos(I(x ** 2))	β ≥ 0	Upward curvature
neg(I(x ** 2))	β ≤ 0	Downward curvature

---

Quasi-Families for Overdispersion

# Fit a standard Poisson model first
result_poisson = rs.glm("ClaimNb ~ Age + C(Region)", data, family="poisson", offset="Exposure").fit()

# Check for overdispersion: Pearson χ² / df >> 1 indicates overdispersion
dispersion_ratio = result_poisson.pearson_chi2() / result_poisson.df_resid
print(f"Dispersion ratio: {dispersion_ratio:.2f}")  # If >> 1, use quasi-family

# Fit QuasiPoisson if overdispersed
result_quasi = rs.glm("ClaimNb ~ Age + C(Region)", data, family="quasipoisson", offset="Exposure").fit()

# Coefficients are IDENTICAL to Poisson, but standard errors are inflated by √φ
print(f"Estimated dispersion (φ): {result_quasi.scale():.3f}")

# For binary data with overdispersion
result_qb = rs.glm("Binary ~ x1 + x2", data, family="quasibinomial").fit()

Key properties of quasi-families:

• Point estimates: Identical to base family (Poisson/Binomial)
• Standard errors: Inflated by √φ where φ = Pearson χ²/(n-p)
• P-values: More conservative (larger), accounting for extra variance

---

Negative Binomial for Overdispersed Counts

# Automatic θ estimation (default when theta not supplied)
result = rs.glm("ClaimNb ~ Age + C(Region)", data, family="negbinomial", offset="Exposure").fit()
print(result.family)  # "NegativeBinomial(theta=2.1234)"

# Fixed θ value
result = rs.glm("ClaimNb ~ Age + C(Region)", data, family="negbinomial", theta=1.0, offset="Exposure").fit()

# θ controls overdispersion: Var(Y) = μ + μ²/θ
# - θ=0.5: Strong overdispersion (variance = μ + 2μ²)
# - θ=1.0: Moderate overdispersion (variance = μ + μ²)
# - θ→∞: Approaches Poisson (variance = μ)

NegativeBinomial vs QuasiPoisson:

Aspect	QuasiPoisson	NegativeBinomial
Variance	φ × μ	μ + μ²/θ
True distribution	No (quasi)	Yes
AIC/BIC valid	Questionable	Yes
Prediction intervals	Not principled	Proper

---

Target Encoding for High-Cardinality Categoricals

# Formula API - TE() in formulas
result = rs.glm(
    "ClaimNb ~ TE(Brand) + TE(Model) + Age + C(Region)",
    data=data,
    family="poisson",
    offset="Exposure"
).fit()

# With options
result = rs.glm(
    "y ~ TE(brand, prior_weight=2.0, n_permutations=8) + age",
    data=data,
    family="gaussian"
).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", TE() automatically uses claim rate (ClaimCount/Exposure) instead of raw counts, preventing near-constant encoded values

---

Identity Terms for Polynomials

# Polynomial terms
result = rs.glm(
    "y ~ age + I(age ** 2) + I(age ** 3)",
    data=data,
    family="gaussian"
).fit()

# Arithmetic expressions
result = rs.glm(
    "y ~ I(income / 1000) + I(weight * height)",
    data=data,
    family="gaussian"
).fit()

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

---

Design Matrix Validation

# Check for issues before fitting
model = rs.glm("y ~ ns(x, df=4) + C(cat)", 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)

---

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

---

RustyStats vs Statsmodels

Feature	RustyStats	Statsmodels
Parallel IRLS Solver	✅ Multi-threaded	❌ Single-threaded only
Native Polars Support	✅ Polars only	❌ Pandas only
Built-in Lasso/Elastic Net for GLMs	✅ Fast coordinate descent with all families	⚠️ Limited
Relativities Table	✅ result.relativities() for pricing	❌ Must compute manually
Robust Standard Errors	✅ HC0, HC1, HC2, HC3 sandwich estimators	✅ HC0-HC3

---

Project Structure

rustystats/
├── Cargo.toml                    # Workspace config
├── pyproject.toml                # Python package config
│
├── crates/
│   ├── rustystats-core/          # Pure Rust GLM library
│   │   └── src/
│   │       ├── families/         # Gaussian, Poisson, Binomial, Gamma, Tweedie, Quasi, NegativeBinomial
│   │       ├── links/            # Identity, Log, Logit
│   │       ├── solvers/          # IRLS, coordinate descent
│   │       ├── inference/        # P-values, CIs, robust SE (HC0-HC3)
│   │       ├── interactions/     # Lazy interaction term computation
│   │       ├── splines/          # B-spline and natural spline basis functions
│   │       ├── design_matrix/    # Categorical encoding, interaction matrices
│   │       ├── formula/          # R-style formula parsing
│   │       ├── target_encoding/  # Ordered target statistics
│   │       └── diagnostics/      # Residuals, dispersion, AIC/BIC, calibration, loss
│   │
│   └── rustystats/               # Python bindings (PyO3)
│       └── src/lib.rs
│
├── python/rustystats/            # Python package
│   ├── __init__.py               # Main exports
│   ├── formula.py                # Formula API with DataFrame support
│   ├── interactions.py           # Interaction terms, I() expressions, design matrix
│   ├── splines.py                # bs() and ns() spline basis functions
│   ├── target_encoding.py        # Target encoding (exposure-aware)
│   ├── diagnostics.py            # Model diagnostics with JSON export
│   └── families.py               # Family wrappers
│
├── examples/
│   └── frequency.ipynb           # Claim frequency example
│
└── tests/python/                 # Python test suite

---

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

MIT