A Targeted Accuracy Diagnostic for Variational Approximations
This addresses a practical problem for users of variational inference who need reliable accuracy assessments for specific posterior estimates, though it is an incremental improvement over existing diagnostics.
The paper tackles the challenge of evaluating the accuracy of variational approximations in variational inference by proposing TADDAA, a diagnostic that uses short parallel MCMC chains to provide lower bounds on errors for specific posterior functionals, validated on synthetic and real-data examples like sparse logistic regression and Bayesian neural networks.
Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the accuracy of variational approximations remains a challenge. Existing methods characterize the quality of the whole variational distribution, which is almost always poor in realistic applications, even if specific posterior functionals such as the component-wise means or variances are accurate. Hence, these diagnostics are of practical value only in limited circumstances. To address this issue, we propose the TArgeted Diagnostic for Distribution Approximation Accuracy (TADDAA), which uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest. We also develop a reliability check for TADDAA to determine when the lower bounds should not be trusted. Numerical experiments validate the practical utility and computational efficiency of our approach on a range of synthetic distributions and real-data examples, including sparse logistic regression and Bayesian neural network models.