RieszNet Procedure

RieszNet is the second inference procedure. It reaches the same debiased estimate as the influence-function procedure, but it learns the bias correction with a neural network instead of deriving it from the model’s Hessian (the “automatic debiasing” idea of Chernozhukov, Newey, Quintas-Martinez, Syrgkanis 2022). It is available as riesz_inference(...); see the API reference for the full signature.

This page is the practical how-to. For the full derivation (the Riesz representer, the double-robustness property, why the Riesz loss recovers the representer, and why this equals the FLM correction), read Theory: RieszNet.

How it works, in brief

RieszNet trains one network with two heads: a regression head for the outcome model \(g(Z)\) and a linear Riesz head for the representer \(a(Z)\). It then debiases with the doubly-robust moment

\[\psi = (\tilde g_1 - \tilde g_0) + a(Z)\,(Y - \tilde g),\]

averaged over a cross-fit, where \(\tilde g = g + \varepsilon a\) is the targeted-regularized regression. “Doubly robust” means the estimate stays valid if either the outcome model \(g\) or the representer \(a\) is learned well. The payoff for implementation is that you never derive a Hessian or a propensity by hand. That is all you need to run it; the why is in Theory.

When to use it

  • You want debiasing without deriving model-specific curvature.

  • You want an independent, doubly-robust check on the influence-function result. In the Replications tables the two procedures are run side by side on known-truth data. Where both are valid they agree, and the page flags the cases where RieszNet is unreliable (for example heavy-tailed count outcomes, where its empirical standard error is inflated by divergent repeats).

Usage

import numpy as np
from deep_inference import riesz_inference

rng = np.random.default_rng(0)
n = 1500
X = rng.standard_normal((n, 3))
e = 1 / (1 + np.exp(-(0.8 * X[:, 0])))     # confounded binary treatment
T = (rng.random(n) < e).astype(float)
Y = 1.0 + 0.5 * X[:, 0] + (0.5 + 0.3 * X[:, 1]) * T + rng.standard_normal(n)

result = riesz_inference(Y, T, X, outcome='linear', n_folds=5, n_repeats=3)
print(result.summary())

outcome is one of linear, logit, poisson, gamma, negbin, probit. The estimand is the ATE contrast E[g(1, X) - g(0, X)]. Arguments are documented on the API page.

Evidence

The ported riesz_inference was run on known-truth data, M=40 replications per family (exploration/riesz_coverage.py). The interval should cover the truth about 95% of the time with a standard-error ratio near 1.

Outcome

Truth

Mean estimate

Bias

SE-ratio

Coverage

linear

0.5012

0.5052

+0.0041

0.96

95%

logit

0.1812

0.1807

-0.0006

0.91

92%

Both are valid (the logit 92% sits within Monte-Carlo noise of the band at M=40, with bias essentially zero). These reproduce the prototype’s larger M=100 study reported on the Replications page (linear 97%, logit 100%), where RieszNet is run side by side with the influence-function method and the oracle. The unit tests in src/deep_inference/tests/test_riesz.py check the same recovery on every commit.

See also