Double Machine Learning for Causal Inference under Shared-State Interference

TL;DR

This work defines shared-state interference (SSI) where spillovers propagate through a low-dimensional shared state that evolves over time, and provides a general semi-parametric framework to identify causal effects under this structure. It extends the double machine learning (DML) methodology to SSI by leveraging a Markovian shared state and an auxiliary sample for nuisance estimation, achieving $ oot 2 ext{-}T$-consistent inference and a consistent variance estimator. The authors instantiate the approach for two key estimands: average direct effects (ADE) in observational settings and global average treatment effects (GATE) in switchback experiments, with simulations demonstrating unbiased ADE estimation, reduced variance for GATE, and valid confidence intervals compared to several naive benchmarks. The framework supports flexible, nonparametric nuisance estimation via machine learning while maintaining rigorous inference, offering practical tools for analyzing causal effects in markets and recommender systems with shared information dynamics.

Abstract

Researchers and practitioners often wish to measure treatment effects in settings where units interact via markets and recommendation systems. In these settings, units are affected by certain shared states, like prices, algorithmic recommendations or social signals. We formalize this structure, calling it shared-state interference, and argue that our formulation captures many relevant applied settings. Our key modeling assumption is that individuals' potential outcomes are independent conditional on the shared state. We then prove an extension of a double machine learning (DML) theorem providing conditions for achieving efficient inference under shared-state interference. We also instantiate our general theorem in several models of interest where it is possible to efficiently estimate the average direct effect (ADE) or global average treatment effect (GATE).

Figures (6)

• Figure 1: Dependency structure of shared-state interference.
• Figure 2: Estimates of the average direct effect with our double machine learning estimator versus naive Horvitz-Thompson, naive plug-in and naive DML estimators.
• Figure 3: Coverage rates of 95% confidence intervals for the ADE constructed using our estimators (DML4SSI), shared state as covariates (SSAC) estimators, naive Horvitz-Thompson estimators, plug-in estimators and naive DML estimators. The HT, plug-in and naive DML estimators coverage overlap around 0. We plot standard errors of the simulations in lighter-colored ribbons around the coverage point estimates.
• Figure 4: Estimates of the global average treatment effect in switchback experiments with our double machine learning estimator versus naive estimators.
• Figure 5: Estimates of the GATE in switchback experiments with the double machine learning estimator versus the switchback Horvitz-Thompson estimator. The DML estimator has substantially lower variance.

Theorems & Definitions (19)

• Theorem 3.3
• Theorem 4.3
• Theorem 5.3
• Definition A.1: Gateaux derivative
• Definition A.2: Neyman orthogonality
• Theorem C.1: Theorem 2, chan_discussion_1994
• Theorem C.2: Theorem 1, hoeffding_central_1948
• Lemma C.3: Corollary to \ref{['thm:clt']}
• Lemma C.4
• Lemma C.5: Theorem 2, jones_markov_2005