While it’s always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. Aalto University and FCAI professor Aki Vehtari proposes with his colleagues two diagnostic algorithms to alleviate this problem.
The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement for joint distributions, while simultaneously improving the error in the estimate. The variational simulation-based calibration (VSBC) assesses the average performance of point estimates.
The paper by Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman, ‘Yes, but Did It Work?: Evaluating Variational Inference’ has been accepted to the International Conference on Machine Learning ICML 2018.