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Probabilistic graphical models (PGMs) provide a compact representation ofknowledge that can be queried in a flexible way: after learning the parametersof a graphical model once, new probabilistic queries can be answered at testtime without retraining. However, when using undirected PGMS with hiddenvariables, two sources of error typically compound in all but the simplestmodels (a) learning error (both computing the partition function andintegrating out the hidden variables is intractable); and (b) prediction error(exact inference is also intractable). Here we introduce query training (QT), amechanism to learn a PGM that is optimized for the approximate inferencealgorithm that will be paired with it. The resulting PGM is a worse model ofthe data (as measured by the likelihood), but it is tuned to produce bettermarginals for a given inference algorithm. Unlike prior works, our approachpreserves the querying flexibility of the original PGM: at test time, we canestimate the marginal of any variable given any partial evidence. Wedemonstrate experimentally that QT can be used to learn a challenging8-connected grid Markov random field with hidden variables and that itconsistently outperforms the state-of-the-art AdVIL when tested on threeundirected models across multiple datasets.

Query Training: Learning a Worse Model to Infer Better Marginals in Undirected Graphical Models with Hidden Variables