Variational Dropout and the Local Reparameterization Trick

TL;DR

This paper introduces a local reparameterization technique for variational Bayesian inference that reduces gradient variance and accelerates convergence, and proposes variational dropout with learnable dropout rates for improved model performance.

Contribution

It presents a novel local reparameterization method that reduces gradient variance and introduces variational dropout with learnable rates, enhancing Bayesian inference and model flexibility.

Findings

Reduced gradient variance leads to faster convergence.

Variational dropout with learned rates improves model performance.

Connection established between dropout and local reparameterization.

Abstract

We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments.