Inference Networks for Sequential Monte Carlo in Graphical Models

Abstract We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We describe a procedure for constructing and learning a structured neural network which represents an inverse factorization of the graphical model, resulting in a conditional density estimator that takes as input particular values of the observed random variables, and returns an approximation to the distribution of the latent variables. This recognition model can be learned offline, independent from any particular dataset, prior to performing inference. The output of these networks can be used as automatically-learned high-quality proposal distributions to accelerate sequential Monte Carlo across a diverse range of problem settings

Variational Sequential Monte Carlo

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits

Tensor Monte Carlo: particle methods for the GPU era

Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly: as the latent dimensionality grows, they require exponentially many samples to retain the benefits of importance weighting. While sequential Monte-Carlo (SMC) can address this problem, it is prohibitively slow because the resampling step imposes sequential structure which cannot be parallelised, and moreover, resampling is non-differentiable which is problematic when learning approximate posteriors. To address these issues, we developed tensor Monte-Carlo (TMC) which gives exponentially many importance samples by separately drawing $K$ samples for each of the $n$ latent variables, then averaging over all $K^n$ possible combinations. While the sum over exponentially many terms might seem to be intractable, in many cases it can be computed efficiently as a series of tensor inner-products. We show that TMC is superior to IWAE on a generative model with multiple stochastic layers trained on the MNIST handwritten digit database, and we show that TMC can be combined with standard variance reduction techniques