On importance-weighted autoencoders

Abstract

The importance weighted autoencoder (IWAE) (Burda et al., 2016) is a popular variational-inference method which achieves a tighter evidence bound (and hence a lower bias) than standard variational autoencoders by optimising a multi-sample objective, i.e. an objective that is expressible as an integral over $K>1$ Monte Carlo samples. Unfortunately, IWAE crucially relies on the availability of reparametrisations and even if these exist, the multi-sample objective leads to inference-network gradients which break down as $K$ is increased (Rainforth et al., 2018). This breakdown can only be circumvented by removing high-variance score-function terms, either by heuristically ignoring them (which yields the 'sticking-the-landing' IWAE (IWAE-STL) gradient from Roeder et al. (2017)) or through an identity from Tucker et al. (2019) (which yields the 'doubly-reparametrised' IWAE (IWAE-DREG) gradient). In this work, we argue that directly optimising the proposal distribution in importance sampling as in the reweighted wake-sleep (RWS) algorithm from Bornschein & Bengio (2015) is preferable to optimising IWAE-type multi-sample objectives. To formalise this argument, we introduce an adaptive-importance sampling framework termed adaptive importance sampling for learning (AISLE) which slightly generalises the RWS algorithm. We then show that AISLE admits IWAE-STL and IWAE-DREG (i.e. the IWAE-gradients which avoid breakdown) as special cases.

References in corpus (9)

• Auto-Encoding Variational Bayes
• The pseudo-marginal approach for efficient Monte Carlo computations
• Variational Bayesian Inference with Stochastic Search
• Auto-Encoding Sequential Monte Carlo
• Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference
• Reinterpreting Importance-Weighted Autoencoders
• Importance Weighting and Variational Inference
• Revisiting Reweighted Wake-Sleep for Models with Stochastic Control Flow
• Tensor Monte Carlo: particle methods for the GPU era

Cited by in corpus (3)

• Markovian Score Climbing: Variational Inference with KL(p||q)
• Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoff
• On the Impact of Sampling on Deep Sequential State Estimation