Optimal Causal Imputation for Control

Abstract

The widespread applicability of analytics in cyber-physical systems has motivated research into causal inference methods. Predictive estimators are not sufficient when analytics are used for decision making; rather, the flow of causal effects must be determined. Generally speaking, these methods focus on estimation of a causal structure from experimental data. In this paper, we consider the dual problem: we fix the causal structure and optimize over causal imputations to achieve desirable system behaviors for a minimal imputation cost. First, we present the optimal causal imputation problem, and then we analyze the problem in two special cases: 1) when the causal imputations can only impute to a fixed value, 2) when the causal structure has linear dynamics with additive Gaussian noise. This optimal causal imputation framework serves to bridge the gap between causal structures and control.