Sequential Underspecified Instrument Selection for Cause-Effect Estimation

TL;DR

This paper introduces a method for estimating causal effects in high-dimensional treatment settings with limited instruments, by combining partial estimates and iteratively selecting the most informative instruments to improve overall causal inference.

Contribution

It proposes a novel approach to recover treatment effect projections in underspecified IV problems and an algorithm for iterative instrument selection to enhance causal estimation.

Findings

Reliable recovery of treatment effect projections in underspecified IV problems

Development of a method to combine partial estimates from different instrument sets

An iterative algorithm for selecting the most informative instruments

Abstract

Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome indirectly via the treatment variable(s). Most IV applications focus on low-dimensional treatments and crucially require at least as many instruments as treatments. This assumption is restrictive: in the natural sciences we often seek to infer causal effects of high-dimensional treatments (e.g., the effect of gene expressions or microbiota on health and disease), but can only run few experiments with a limited number of instruments (e.g., drugs or antibiotics). In such underspecified problems, the full treatment effect is not identifiable in a single experiment even in the linear case. We show that one can still reliably recover the projection of the treatment effect onto the instrumented subspace and develop techniques to consistently combine such partial estimates from different sets of instruments. We then leverage our combined estimators in an algorithm that iteratively proposes the most informative instruments at each round of experimentation to maximize the overall information about the full causal effect.