Monotonicity Induced Parameter Learning for Bayesian Networks with Limited Data

Jingzhuo Yang, Yu Wang, Shenglei Pei, Qinghua Hu

Abstract: Parameter learning of Bayesian networks (BNs) is a challenging task as it depends heavily on a large number of reliable training data. Unfortunately, it is often difficult to obtain sufficient samples in many real-world applications. Fortunately, monotonicity relationship among variables widely exists in many practical tasks, and has been proven to be effective in learning the parameters of BN with limited data. Most researches utilize monotonicity relationship provided manually by domain experts, but it is difficult and costly to obtain all the prior knowledge of monotonicity accurately if the structure of BN is quite complex. In this paper, we propose a data-dependent method to learn the parameters of BN with limited data. Firstly, Spearman rank correlation coefficient (RHO) is leverages to detect the monotonicity relationship between the network nodes. Secondly, the monotonicity relationship is transformed into a set of monotonicity constraints for the network parameters, and then integrated into the log-likehood function as a penalty item (RHO-PML). Finally, the parameters of BN are obtained by the gradient descent method. Moreover, to reinforce the impact of the monotonicity relationship, bidirectional monotonicity constraints are introduced into RHO-PML as RHO-BPML. Experiments on various datasets show the effectiveness of the proposed RHO-PML and RHO-BPML algorithms with limited data.