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Paper IDL.1.2
Paper Title Provable Efficient Skeleton Learning of Encodable Discrete Bayes Nets in Poly-Time and Sample Complexity
Authors Adarsh Barik, Jean Honorio, Purdue University, United States
Session L.1: Application-Specific Learning
Presentation Lecture
Track Statistics and Learning Theory
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract In this paper, we study the problem of skeleton learning for Bayesian networks from data. In particular, we focus on nodes taking discrete values, and the learning of all the edges while disregarding their directionality, i.e., the skeleton of the Bayesian network. The problem of learning the structure of a Bayesian network is NP-hard in general. However, we show that under certain conditions we can recover the true skeleton with sufficient number of samples. We develop a mathematical model which does not assume any specific conditional probability distributions for the nodes. We use a primal-dual witness construction to prove that, under some technical conditions on the interaction between node pairs, we can do exact recovery of the parents and children of a node by performing group l_12-regularized multivariate regression. Thus, we recover the true Bayesian network skeleton. If degree of a node is bounded then the sample complexity of our proposed approach grows logarithmically with respect to the number of nodes in the Bayesian network. Furthermore, our method runs in polynomial time.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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