Essence of Bayesian networks
DAGs, conditional probability tables, d-separation, and variable elimination. The foundations of probabilistic reasoning in AI.
A Bayesian network combines a Directed Acyclic Graph with Conditional Probability Tables to represent a probability distribution over a set of variables. The DAG encodes which variables influence which others; the CPTs quantify how strongly. The Markov assumption makes this tractable: each variable is conditionally independent of its non-descendants given its parents, so you store one small table per variable instead of one exponentially large joint distribution.
The article covers the DAG structure and Markov assumption, d-separation as a graphical method for reading independence relationships directly from the graph, network pruning to remove irrelevant variables before computation, and variable elimination as the core inference algorithm for computing marginal and conditional probabilities. Published on Medium, October 2020.