Simplifying Probabilistic Expressions in Causal Inference

Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application of do-calculus. Often we are left with a complicated expression which can lead to biased or inefficient estimates when missing data or measurement errors are involved. We present an automatic simplification algorithm that seeks to eliminate symbolically unnecessary variables from these expressions by taking advantage of the structure of the underlying graphical model. Our method is applicable to all causal effect formulas and is readily available in the R package causaleffect.

[1]  Santtu Tikka,et al.  Identifying Causal Effects with the R Package causaleffect , 2017, 1806.07161.

[2]  Frederick Eberhardt,et al.  Do-calculus when the True Graph Is Unknown , 2015, UAI.

[3]  I. Shpitser,et al.  CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS. , 2014, Annals of statistics.

[4]  Elias Bareinboim,et al.  Meta-Transportability of Causal Effects: A Formal Approach , 2013, AISTATS.

[5]  Elias Bareinboim,et al.  A General Algorithm for Deciding Transportability of Experimental Results , 2013, ArXiv.

[6]  Elias Bareinboim,et al.  Causal Inference by Surrogate Experiments: z-Identifiability , 2012, UAI.

[7]  James M. Robins,et al.  An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Models , 2011, UAI.

[8]  D. Koller,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[9]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[10]  C. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[11]  Marco Valtorta,et al.  Pearl's Calculus of Intervention Is Complete , 2006, UAI.

[12]  J. Pearl,et al.  Identification of Joint Interventional Distributions in Recursive Semi-Markovian Causal Models , 2006, AAAI.

[13]  Judea Pearl,et al.  Identification of Conditional Interventional Distributions , 2006, UAI.

[14]  Jacques Carette,et al.  Understanding expression simplification , 2004, ISSAC '04.

[15]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[16]  Stig K. Andersen,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[17]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[18]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[19]  Jonathan M. Borwein,et al.  Automated simplification of large symbolic expressions , 2014, J. Symb. Comput..

[20]  Judea Pearl,et al.  A Theory of Inferred Causation , 1991, KR.

[21]  J. Pearl.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1989, Morgan Kaufmann series in representation and reasoning.

[22]  Causality : Models , Reasoning , and Inference , 2022 .