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This paper introduces a new technique for quantifying the approximation errorof a broad class of probabilistic inference programs, including ones based onboth variational and Monte Carlo approaches. The key idea is to derive asubjective bound on the symmetrized KL divergence between the distributionachieved by an approximate inference program and its true target distribution.The bound's validity (and subjectivity) rests on the accuracy of two auxiliaryprobabilistic programs: (i) a "reference" inference program that defines a goldstandard of accuracy and (ii) a "meta-inference" program that answers thequestion "what internal random choices did the original approximate inferenceprogram probably make given that it produced a particular result?" The paperincludes empirical results on inference problems drawn from linear regression,Dirichlet process mixture modeling, HMMs, and Bayesian networks. Theexperiments show that the technique is robust to the quality of the referenceinference program and that it can detect implementation bugs that are notapparent from predictive performance.

Quantifying the probable approximation error of probabilistic inference programs