Efficient Online Estimation of Causal Effects by Deciding What to Observe

TL;DR

This paper introduces an online framework for efficiently estimating causal effects by dynamically selecting which data sources to observe, optimizing data acquisition to improve estimation accuracy over time.

Contribution

It proposes the online moment selection (OMS) framework with two strategies, enabling optimal data source querying for causal effect estimation with proven asymptotic performance.

Findings

Both OMS-ETC and OMS-ETG achieve zero asymptotic regret in mean squared error.

Framework effectively incorporates structural causal assumptions into data acquisition decisions.

Applicable to various causal inference scenarios with multiple data sources.

Abstract

Researchers often face data fusion problems, where multiple data sources are available, each capturing a distinct subset of variables. While problem formulations typically take the data as given, in practice, data acquisition can be an ongoing process. In this paper, we aim to estimate any functional of a probabilistic model (e.g., a causal effect) as efficiently as possible, by deciding, at each time, which data source to query. We propose online moment selection (OMS), a framework in which structural assumptions are encoded as moment conditions. The optimal action at each step depends, in part, on the very moments that identify the functional of interest. Our algorithms balance exploration with choosing the best action as suggested by current estimates of the moments. We propose two selection strategies: (1) explore-then-commit (OMS-ETC) and (2) explore-then-greedy (OMS-ETG), proving that both achieve zero asymptotic regret as assessed by MSE. We instantiate our setup for average treatment effect estimation, where structural assumptions are given by a causal graph and data sources may include subsets of mediators, confounders, and instrumental variables.