Monotonicity Extraction for Monotonic Bayesian Networks Parameter Learning

Abstract

Bayesian networks (BNs) parameter learning is a challenging task as it relies on a large amount of reliable and representative training data. Unfortunately, it is often difficult to obtain sufficient samples in many real-world applications. Monotonicity, as a class of prior information, widely exist in various practical tasks. This information is helpful for BN parameter learning. However, monotonicity is set by users traditionally. In this paper, we propose a data-dependent BN parameter learning method which can construct monotonicity constraints for BN parameters automatically. Firstly, we introduce rank mutual information (RMI) and Spearman rank correlation coefficient (RHO) to detect monotonicity among network nodes, and then construct monotonicity constraints for BN parameters. Finally, we transform the problem of parameter learning with monotonicity constraints into a convex Lagrange function and obtain the global optimum solution in polynomial time. Experimental results on real-world classification data and standard BNs show the effectiveness of our proposed algorithms with limited data.