Stability of linear structural equation models of causal inference

Sankararaman, KA and Louis, A and Goyal, N (2019) Stability of linear structural equation models of causal inference. In: 35th Conference on Uncertainty in Artificial Intelligence, UAI 2019, 22-25 Jul 2019, Tel Aviv, Israel.

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Abstract

We consider numerical stability of the parameter recovery problem in Linear Structural Equation Model (LSEM) of causal inference. Numerical stability is essential for the recovered parameters to be reliable. A long line of work starting from Wright (1920) has focused on understanding which sub-classes of LSEM allow for efficient parameter recovery. Despite decades of study, this question is not yet fully resolved. The goal of the present paper is complementary to this line of work: we want to understand the stability of the recovery problem in the cases when efficient recovery is possible. Numerical stability of Pearl�s notion of causality was first studied in Schulman and Srivastava (2016) using the concept of condition number where they provide ill-conditioned examples. In this work, we provide a condition number analysis for the LSEM. First we prove that under a sufficient condition, for a certain sub-class of LSEM that are bow-free (Brito and Pearl (2002)), parameter recovery is numerically stable. We further prove that randomly chosen input parameters for this family satisfy the condition with a substantial probability. Hence for this family, on a large subset of parameter space, recovery is stable. Next we construct an example of LSEM on four vertices with unbounded condition number. We then corroborate our theoretical findings via simulations as well as real-world experiments for a sociology application. Finally, we provide a general heuristic for estimating the condition number of any LSEM instance. The authors thank Amit Sharma, Ilya Shpitser and Piyush Srivastava for useful discussions on causality and Shohei Shimizu for providing us with the sociology dataset. Part of this work was done when KAS was visiting Indian Institute of Science, Bangalore. KAS was supported in part by NSF Awards CNS 1010789, CCF 1422569, CCF-1749864 and research awards from Adobe, Amazon, and Google. Anand Louis was supported in part by SERB Award ECR/2017/003296. AL is also grateful to Microsoft Research for supporting this collaboration. © 2019 Association For Uncertainty in Artificial Intelligence (AUAI). All rights reserved.

Item Type:	Conference Paper
Publication:	35th Conference on Uncertainty in Artificial Intelligence, UAI 2019
Publisher:	Association For Uncertainty in Artificial Intelligence (AUAI)
Additional Information:	Copyright of this article belongs to Association For Uncertainty in Artificial Intelligence (AUAI)
Keywords:	Artificial intelligence; Behavioral research; Number theory; Stability; Telecommunication services, Causal inferences; Condition numbers; Indian institute of science; Microsoft researches; Parameter recovery; Real world experiment; Structural equation modeling; Structural equation models, Recovery
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Apr 2021 07:27
Last Modified:	25 Sep 2022 07:14
URI:	https://eprints.iisc.ac.in/id/eprint/65400

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