# Optimal Causal Imputation for Control

## TL;DR

This paper introduces an optimal causal imputation framework that optimizes causal interventions within fixed structures to improve system behavior at minimal cost, bridging causal inference and control.

## Contribution

It formulates the optimal causal imputation problem and analyzes it in special cases, connecting causal inference with control strategies.

## Key findings

- Analyzed the problem for fixed-value imputations.
- Studied linear dynamic causal structures with Gaussian noise.
- Provided insights into causal interventions for system 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.