Learning discrete Bayesian networks in polynomial time and sample complexity
Abstract
In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NPhard in general but we show that under certain conditions we can recover the true structure of a Bayesian network 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 primaldual 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_12regularized multivariate regression. Thus, we recover the true Bayesian network structure. 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.04087
 Bibcode:
 2018arXiv180304087B
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning
 EPrint:
 IEEE International Symposium on Information Theory (ISIT), 2020