AIDE: An algorithm for measuring the accuracy of probabilistic inference algorithms

TL;DR

AIDE is a novel algorithm that accurately measures the divergence between approximate inference algorithms, helping practitioners evaluate their performance and detect failures across various probabilistic models.

Contribution

The paper introduces AIDE, a new estimator for the symmetric KL divergence that leverages auxiliary variables to assess inference accuracy.

Findings

AIDE effectively captures the qualitative behavior of inference algorithms.

AIDE detects failure modes missed by standard heuristics.

Application to diverse models demonstrates its broad utility.

Abstract

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.