Optimal Causal Imputation for Control

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.

[1]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[2]  C. Gouriéroux,et al.  Kullback Causality Measures , 1987 .

[3]  D. Rubin.  Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[4]  Judea Pearl,et al.  Graphical Models for Probabilistic and Causal Reasoning , 1997, The Computer Science and Engineering Handbook.

[5]  Dean Karlan,et al.  A multifaceted program causes lasting progress for the very poor: Evidence from six countries , 2015, Science.

[6]  Claire J. Tomlin,et al.  Residential demand response targeting using machine learning with observational data , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[7]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[8]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[9]  Jiuyong Li,et al.  Causal Decision Trees , 2015, IEEE Transactions on Knowledge and Data Engineering.

[10]  Steffen L. Lauritzen,et al.  Causal Inference from Graphical Models , 2001 .

[11]  D. Heckerman,et al.  A Bayesian Approach to Causal Discovery , 2006 .

[12]  G. Imbens,et al.  Machine Learning Methods for Estimating Heterogeneous Causal Eects , 2015 .

[13]  S. Bressler,et al.  Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Clive W. J. Granger,et al.  A Bivariate Causality between Stock Prices and Exchange Rates: Evidence from Recent Asia Flu , 1998 .

[15]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[16]  A. Dawid.  Causal Inference without Counterfactuals , 2000 .

[17]  Susan Athey,et al.  Recursive partitioning for heterogeneous causal effects , 2015, Proceedings of the National Academy of Sciences.

[18]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[19]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[20]  C. Blumberg.  Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction , 2016 .

[21]  Olivier J. J. Michel,et al.  The relation between Granger causality and directed information theory: a review , 2012, Entropy.

[22]  Bernhard Schölkopf,et al.  Nonlinear causal discovery with additive noise models , 2008, NIPS.