Induction of Bayesian Networks and Distribution-Based Methods: A Comprehensive Approach to Probabilistic Modelling

Bayesian networks have emerged as a powerful tool for modelling complex probabilistic relationships in uncertain environments. The process of inducing Bayesian networks involves learning both the structure of the network and the parameters of the associated probability distributions. This paper provides a detailed examination of the two main approaches to Bayesian network induction: structure learning and parameter estimation, highlighting the use of both constraint-based and score-based techniques. Furthermore, the role of distribution-based methods in the estimation and inference of probabilistic models is explored. These methods, including Maximum Likelihood Estimation, Bayesian Estimation, and Monte Carlo techniques, offer robust ways to handle parameter uncertainty and facilitate efficient inference in large, complex models. This comprehensive view aims to bridge the gap between the theoretical foundations and practical applications of these methods, providing insights for researchers and practitioners in the field of machine learning and probabilistic reasoning.