Smoothed Gradients for Stochastic Variational Inference

Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic gradients whose expectations are equal to the true gradients. In this paper, we explore the idea of following biased stochastic gradients in SVI. Our method replaces the natural gradient with a similarly constructed vector that uses a fixed-window moving average of some of its previous terms. We will demonstrate the many advantages of this technique. First, its computational cost is the same as for SVI and storage requirements only multiply by a constant factor. Second, it enjoys significant variance reduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient. We test our method on latent Dirichlet allocation with three large corpora.Comment: Appears in Neural Information Processing Systems, 201

Patterns of Scalable Bayesian Inference

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assumptions about model structure, underlying computational resources, and the importance of asymptotic correctness. As a result, there is a zoo of ideas with few clear overarching principles. In this paper, we seek to identify unifying principles, patterns, and intuitions for scaling Bayesian inference. We review existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, we characterize the general principles that have proven successful for designing scalable inference procedures and comment on the path forward