Bayesian Networks

Mon, 31 Aug 2026 00:29:54 +1000

a joint probability distribution over \(n\) binary variables is a table with \(2^n - 1\) free numbers. at \(n = 30\) that is a billion parameters for a toy problem — nobody can elicit them, store them, or estimate them from data. the bayesian network is the classical answer: encode the independencies of the distribution in a directed acyclic graph, and the joint collapses into a product of small local tables. 𐃏 the graph is simultaneously a data structure for storage, a calculus for reading off independence, and the substrate on which every inference algorithm runs.

D-Separation on Aayush Bajaj's Augmenting Infrastructure

Bayesian Networks