Revisiting Reweighted Wake-Sleep for Models with Stochastic Control Flow

Stochastic control-flow models (SCFMs) are a class of generative models that involve branching on choices from discrete random variables. Amortized gradient-based learning of SCFMs is challenging as most approaches targeting discrete variables rely on their continuous relaxations---which can be intractable in SCFMs, as branching on relaxations requires evaluating all (exponentially many) branching paths. Tractable alternatives mainly combine REINFORCE with complex control-variate schemes to improve the variance of naive estimators. Here, we revisit the reweighted wake-sleep (RWS) (Bornschein and Bengio, 2015) algorithm, and through extensive evaluations, show that it outperforms current state-of-the-art methods in learning SCFMs. Further, in contrast to the importance weighted autoencoder, we observe that RWS learns better models and inference networks with increasing numbers of particles. Our results suggest that RWS is a competitive, often preferable, alternative for learning SCFMs.Comment: Tuan Anh Le and Adam R. Kosiorek contributed equally; accepted to Uncertainty in Artificial Intelligence 201

Natural Evolution Strategies as a Black Box Estimator for Stochastic Variational Inference

Stochastic variational inference and its derivatives in the form of variational autoencoders enjoy the ability to perform Bayesian inference on large datasets in an efficient manner. However, performing inference with a VAE requires a certain design choice (i.e. reparameterization trick) to allow unbiased and low variance gradient estimation, restricting the types of models that can be created. To overcome this challenge, an alternative estimator based on natural evolution strategies is proposed. This estimator does not make assumptions about the kind of distributions used, allowing for the creation of models that would otherwise not have been possible under the VAE framework

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

Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Bounds

This paper introduces novel results for the score function gradient estimator of the importance weighted variational bound (IWAE). We prove that in the limit of large $K$ (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as $\sqrt{K}$. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as $1/\sqrt{K}$. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with $K$ without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models