  Approximate probabilistic inference algorithms are central to many fields.
Examples include sequential Monte Carlo inference in robotics, variational
inference in machine learning, and Markov chain Monte Carlo inference in
statistics. A key problem faced by practitioners is measuring the accuracy of
an approximate inference algorithm on a specific data set. This paper
introduces the auxiliary inference divergence estimator (AIDE), an algorithm
for measuring the accuracy of approximate inference algorithms. AIDE is based
on the observation that inference algorithms can be treated as probabilistic
models and the random variables used within the inference algorithm can be
viewed as auxiliary variables. This view leads to a new estimator for the
symmetric KL divergence between the approximating distributions of two
inference algorithms. The paper illustrates application of AIDE to algorithms
for inference in regression, hidden Markov, and Dirichlet process mixture
models. The experiments show that AIDE captures the qualitative behavior of a
broad class of inference algorithms and can detect failure modes of inference
algorithms that are missed by standard heuristics.
