Learning Bayesian Networks with Incomplete Data by Augmentation

TL;DR

This paper introduces novel algorithms for learning Bayesian networks from incomplete data by transforming the problem into a standard learning task, including an exact method and a scalable approximate approach, validated through extensive experiments.

Contribution

It presents the first exact algorithm for Bayesian network learning with missing data and develops a scalable approximate method based on data augmentation.

Findings

Exact algorithm successfully recasts the problem into standard Bayesian network learning.

Approximate algorithm scales to large domains with suitable structure learning methods.

Experiments demonstrate the effectiveness of the new approach.

Abstract

We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. To the best of our knowledge, this is the first exact algorithm for this problem. As expected, the exact algorithm does not scale to large domains. We build on the exact method to create an approximate algorithm using a hill-climbing technique. This algorithm scales to large domains so long as a suitable standard structure learning method for complete data is available. We perform a wide range of experiments to demonstrate the benefits of learning Bayesian networks with such new approach.