Kilbertus group
Sequential Underspecified Instrument Selection for Cause Effect Estimation
Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. 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.
In this talk we will discuss two things: first, how to recover the projection of the treatment effect onto the instrumented subspace and how to consistently combine such partial estimates in the linear case; secondly, how to approach this problem in the nonlinear case.