genriesz 0.1.10

Generalized Riesz Regression under Bregman divergences

genriesz — Generalized Riesz Regression (GRR)

This repository packages a Python library for Generalized Riesz Regression under Bregman divergences.

• Document

The key idea is:

• you specify a linear functional m(X, γ) (the estimand),
• you specify a basis φ(X),
• you specify a Bregman generator g(X, α),

and the library:

1. builds the automatic-covariate-balancing (ACB) link function from g,
2. fits a Riesz representer α̂(X) via GRR,
3. optionally fits an outcome model γ̂(X),
4. returns DM / IPW / AIPW estimates with standard errors, confidence intervals, and p-values (optionally with cross-fitting).

Notation: in this library the regressor is called X and the outcome is called Y. If you prefer the paper's notation, you can think of X as the full regressor vector (often X=[D,Z]).

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Installation

From PyPI:

pip install genriesz

Optional extras:

# scikit-learn integrations (random forest leaf basis)
pip install "genriesz[sklearn]"

# PyTorch integrations (neural-network feature maps)
pip install "genriesz[torch]"

From a local checkout (editable install):

python -m pip install -U pip
pip install -e .

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Quickstart: ATE (Average Treatment Effect)

The ATE can be estimated as a special case of grr_functional.

import numpy as np
from genriesz import (
    grr_ate,
    UKLGenerator,
    PolynomialBasis,
    TreatmentInteractionBasis,
)

# Example layout: X = [D, Z]
#   D: treatment (0/1)
#   Z: covariates
n, d_z = 1000, 5
rng = np.random.default_rng(0)
Z = rng.normal(size=(n, d_z))
D = (rng.normal(size=n) > 0).astype(float)
Y = 2.0 * D + Z[:, 0] + rng.normal(size=n)

X = np.column_stack([D, Z])

# Base basis on Z (or on all of X if you prefer).
psi = PolynomialBasis(degree=2)

# ATE-friendly basis: interact the base basis with treatment.
phi = TreatmentInteractionBasis(base_basis=psi)

# A common generator choice for ATE-style balancing.
# The branch function chooses the sign of alpha depending on the treatment.
# Here: positive for treated (D=1), negative for control (D=0).
gen = UKLGenerator(C=1.0, branch_fn=lambda x: int(x[0] == 1.0)).as_generator()

res = grr_ate(
    X=X,
    Y=Y,
    basis=phi,
    generator=gen,
    cross_fit=True,
    folds=5,
    riesz_penalty="l2",
    riesz_lam=1e-3,
    estimators=("dm", "ipw", "aipw"),
)

print(res.summary_text())

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General API: grr_functional

grr_functional is the most general entry point.

You provide:

• m(X, gamma) — the estimand,
• a basis(X) — feature map,
• a Bregman generator g(X, alpha) (or a pre-built generator).

Example skeleton:

import numpy as np
from genriesz import grr_functional, BregmanGenerator

def m(x, gamma):
    # x is a single row (1D array)
    # gamma is a callable gamma(w)
    # return a scalar
    return gamma(x)

def g(x, alpha):
    # x is a single row; alpha is a scalar
    # return g(x, alpha)
    return 0.5 * alpha**2

def basis(X):
    # X is (n,d); return (n,p)
    return np.c_[np.ones(len(X)), X]

X = np.random.randn(200, 3)
Y = np.random.randn(200)

generator = BregmanGenerator(g=g)  # gradients/inverse-grad can be auto-derived numerically

res = grr_functional(
    X=X,
    Y=Y,
    m=m,
    basis=basis,
    generator=generator,
    estimators=("ipw",),
)

print(res.summary_text())

Providing g' and (g')^{-1}

If you can analytically implement the derivative g_grad(X_i, alpha) and the inverse derivative g_inv_grad(X_i, v), pass them to BregmanGenerator(g=..., grad=..., inv_grad=...).

If you omit them, the library falls back to:

• finite differences for g', and
• scalar root-finding for (g')^{-1}.

---

Basis functions

Polynomial basis

from genriesz import PolynomialBasis

psi = PolynomialBasis(degree=3)
Phi = psi(X)  # (n,p)

RKHS-style bases

You can approximate an RBF kernel either with random Fourier features or a Nyström basis.

from genriesz import RBFRandomFourierBasis, RBFNystromBasis

rff = RBFRandomFourierBasis(n_features=500, sigma=1.0, standardize=True, random_state=0)
Phi_rff = rff(X)

nys = RBFNystromBasis(n_centers=500, sigma=1.0, standardize=True, random_state=0)
Phi_nys = nys(X)

Nearest-neighbor matching (kNN catchment-area basis)

Nearest-neighbor matching can be expressed using a catchment-area indicator basis

(\phi_j(z) = \mathbf{1}{c_j \in \mathrm{NN}_k(z)}),

where ({c_j}) are a set of centers and (\mathrm{NN}_k(z)) is the set of k nearest centers of (z).

This library provides KNNCatchmentBasis:

from genriesz import KNNCatchmentBasis

basis = KNNCatchmentBasis(n_neighbors=3).fit(centers)
Phi = basis(queries)  # dense (n_queries, n_centers)

See examples/ate_synthetic_nn_matching.py for an end-to-end matching-style ATE estimate.

Random forest leaves (scikit-learn)

If you have scikit-learn installed, you can use a random forest as a feature map by encoding leaf indices.

from sklearn.ensemble import RandomForestRegressor
from genriesz.sklearn_basis import RandomForestLeafBasis

rf = RandomForestRegressor(n_estimators=200, random_state=0)
leaf_basis = RandomForestLeafBasis(rf)
Phi_rf = leaf_basis(X)

Neural network features (PyTorch)

If you have PyTorch installed, you can use a neural network as a fixed feature map.

See src/genriesz/torch_basis.py for a minimal wrapper.

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Included estimands

• ATE: grr_ate, or m=ATEFunctional(...)
• AME (average marginal effect / average derivative): grr_ame, or m=AverageDerivativeFunctional(...)
• Average policy effect: grr_policy_effect, or m=PolicyEffectFunctional(...)

Jupyter notebook

An end-to-end notebook with runnable examples is provided at:

• notebooks/GRR_end_to_end_examples.ipynb

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References

If you use genriesz in academic work, please cite:

• Masahiro Kato. Riesz Representer Fitting under Bregman Divergence: A Unified Framework for Debiased Machine Learning. https://arxiv.org/abs/2601.07752
  • Note: https://arxiv.org/abs/2601.07752 consolidates earlier related drafts: https://arxiv.org/abs/2509.22122, https://arxiv.org/abs/2510.26783, and https://arxiv.org/abs/2510.23534.
• Masahiro Kato. Direct Bias-Correction Term Estimation for Propensity Scores and Average Treatment Effect Estimation. https://arxiv.org/abs/2509.22122
• Masahiro Kato. Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression. https://arxiv.org/abs/2510.24433

License

GNU General Public License v3.0 (GPL-3.0).