Bayesian Network
A Bayesian Network (Bayes Net) is a probabilistic graphical model that represents a joint probability distribution over a set of random variables. It captures dependencies among variables using a directed acyclic graph, where nodes correspond to variables and edges represent direct probabilistic influence.
Each random variable in the network is associated with a conditional probability table, which specifies . The joint probability distribution over all variables is then given by the factorization rule for Bayes Nets:
where the factorization follows from the assumption that every node is conditionally independent of all its ancestors given its parents.