Robust, Accurate Stochastic Optimization for Variational Inference
This addresses robustness issues in variational inference for machine learning practitioners, though it is incremental as it builds on existing stochastic optimization methods.
The paper tackled the problem of poor variational approximations in stochastic optimization for variational inference, even when the true posterior is in the variational family, and proposed a robust framework with a diagnostic and stopping rule that works well across diverse models.
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution,(2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation