Bayesian Network Structure Learning with a Focus on Networks with Background Information and Incomplete Information

Andreevski, Jovan (2024) Bayesian Network Structure Learning with a Focus on Networks with Background Information and Incomplete Information. Bachelor's Thesis, Mathematics.

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Abstract

Bayesian networks are a widely-used probabilistic graphical model in which random variables, and the conditional dependencies between these variables, are represented using a directed acyclic graph (DAG). Bayesian network structure learning refers to the highly sought-after, yet challenging, task of inferring Bayesian networks from data. In this paper, we formally introduce the task of structure learning and focus on structure learning in networks with background information and networks with incomplete information. First, we provide a formal definition of networks with background information through the treatment of maximally oriented partially directed acyclic graphs (MPDAGs). Moreover, we study the differences between regular networks and networks with background information, and develop theory regarding dependencies in MPDAGs as a starting point for performing structure learning in networks with background information. Second, we introduce networks with incomplete information, and provide a detailed exposition of the belief propagation algorithm as an efficient approach for calculating marginal distributions of unobserved variables. Moreover, we provide an adaptation of the belief propagation algorithm to Bayesian networks, discuss the exactness of the algorithm, and propose an approach for using the algorithm to sample missing data in discrete Bayesian networks. Finally, we offer a comprehensive implementation of the algorithm in the programming language R.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Grzegorczyk, M.A. and Sterk, A.E.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	12 Jul 2024 09:20
Last Modified:	12 Jul 2024 09:20
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/33268

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