Variational Tempering
This work addresses a specific bottleneck in variational inference for large-scale Bayesian models, offering incremental improvements over existing methods.
The paper tackles the problem of variational inference (VI) suffering from poor local optima in large datasets by introducing variational tempering, which uses latent temperature variables to create adaptive annealing schedules, resulting in improved predictive likelihoods on held-out data.
Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This approach uses a decreasing temperature parameter which deterministically deforms the objective during the course of the optimization. A well-known drawback to this annealing approach is the choice of the cooling schedule. We therefore introduce variational tempering, a variational algorithm that introduces a temperature latent variable to the model. In contrast to related work in the Markov chain Monte Carlo literature, this algorithm results in adaptive annealing schedules. Lastly, we develop local variational tempering, which assigns a latent temperature to each data point; this allows for dynamic annealing that varies across data. Compared to the traditional VI, all proposed approaches find improved predictive likelihoods on held-out data.