Riesz representer

Causal inference promises to answer “what if” questions from observational data. But the standard approach — specify a parametric model, fit it, report the estimate — breaks down under misspecification. And misspecification is the norm, not the exception.

Doubly Robust Inference via Calibration TL;DR Van der Laan, Luedtke, and Carone introduce “calibrated debiased machine learning” (calibrated DML), a method that achieves doubly robust asymptotic normality for causal inference estimators by simply adding an isotonic regression calibration step to standard DML pipelines.

TL;DR In the paper Automatic Debiased Machine Learning via Riesz Regression by Chernozhukov et al. (2024), the critical radius is a key concept for understanding how accurately machine learning (ML) can estimate the Riesz representer—a function used to debias ML estimates of economic parameters like treatment effects.

Introduction Here are my notes on propensity scores, mainly from Prof. Ding’s textbook (2024). The traditional propensity score analysis workflow is shown in the image below, which I will not cover in detail.

Introduction To estimate ATE, we can either use outcome regression or inverse propensity weighting (IPW). While each approach has merits, combining them offers significant advantage – double robustness. In this post, I summarize the intuition for doubly robust estimator from Professor Ding’s textbook (Ding 2024), and connects this framework to debiased machine learning (DML) through Riesz representation theory.

Debiased machine learning (DML) is a generic recipe. The idea behind it is adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality.

Motivation In empirical research, one of the challenges to causal inference is the potential presence of unobserved confounding. Even when we adjust for a wide range of observed covariates, there’s often a lingering concern: what if there are important variables we’ve failed to measure or include?