  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.
