Bayesian Network Structure Learning from Limited Datasets through Graph Evolution

Abstract

Bayesian networks are stochastic models, widely adopted to encode knowledge in several fields. One of the most interesting features of a Bayesian network is the possibility of learning its structure from a set of data, and subsequently use the resulting model to perform new predictions. Structure learning for such models is a NP-hard problem, for which the scientific community developed two main approaches: score-and-search metaheuristics, often evolutionary-based, and dependency-analysis deterministic algorithms, based on stochastic tests. State-of-the-art solutions have been presented in both domains, but all methodologies start from the assumption of having access to large sets of learning data available, often numbering thousands of samples. This is not the case for many real-world applications, especially in the food processing and research industry. This paper proposes an evolutionary approach to the Bayesian structure learning problem, specifically tailored for learning sets of limited size. Falling in the category of score-and-search techniques, the methodology exploits an evolutionary algorithm able to work directly on graph structures, previously used for assembly language generation, and a scoring function based on the Akaike Information Criterion, a well-studied metric of stochastic model performance. Experimental results show that the approach is able to outperform a state-of-the-art dependency-analysis algorithm, providing better models for small datasets.