Exact Inference

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

a bayesian network stores a joint distribution; inference is spending that investment — computing probabilities the tables do not state directly. exact inference is np-hard in general, but its true cost is exponential only in a structural parameter of the graph (the treewidth), not in the number of variables. this page builds the exact toolchain in the order the ideas force themselves on you: factors, variable elimination, the fight for a good elimination order, and finally the jointree algorithm — variable elimination industrialised into a message-passing scheme that answers every marginal at once. 𐃏

Jointree on Aayush Bajaj's Augmenting Infrastructure

Exact Inference