Learning and testing causal models with interventions
Name
NeurIPS-2018-learning-and-testing-causal-models-with-interventions-Paper.pdf
Description
Published version
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390.57 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Acharya, J
Bhattacharyya, A
Daskalakis, C
Kandasamy, S
Date Issued
January 1, 2018
Journal
Advances in Neural Information Processing Systems
Citation
Acharya, J, Bhattacharyya, A, Daskalakis, C and Kandasamy, S. 2018. "Learning and testing causal models with interventions." Advances in Neural Information Processing Systems, 2018-December.
Version
Final published version
Abstract
© 2018 Curran Associates Inc.All rights reserved. We consider testing and learning problems on causal Bayesian networks as defined by Pearl [Pea09]. Given a causal Bayesian network M on a graph with n discrete variables and bounded in-degree and bounded “confounded components”, we show that O(log n) interventions on an unknown causal Bayesian network X on the same graph, and O(n/2) samples per intervention, suffice to efficiently distinguish whether X = M or whether there exists some intervention under which X and M are farther than in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: Ω(log n) interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://papers.nips.cc/paper/2018/hash/78631a4bb5303be54fa1cfdcb958c00a-Abstract.html
