Approximate Inference

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

exact inference costs \(\exp(\text{treewidth})\), and real networks — image grids, dense diagnostic models, unrolled dbns — routinely have treewidth in the hundreds. approximate inference trades guaranteed answers for tractable ones, along two philosophically different roads: sampling replaces the distribution with draws from it (anytime, asymptotically exact, embarrassingly parallel), and approximate message passing runs exact-style propagation on graphs where its correctness proof no longer holds. this page walks the sampling ladder in the order each rung fixes the last one’s failure — forward, rejection, likelihood weighting, gibbs — then closes with loopy belief propagation. 𐃏

Belief-Propagation on Aayush Bajaj's Augmenting Infrastructure

Approximate Inference