Variational Dropout and the Local Reparameterization Trick
This work addresses a bottleneck in variational Bayesian inference for machine learning practitioners, offering a more efficient and flexible method, though it is incremental as it builds on existing SGVB and dropout techniques.
The paper tackles the problem of high variance in stochastic gradients for variational Bayesian inference by introducing a local reparameterization technique that reduces variance and improves convergence speed, with experiments showing it leads to better models through learned dropout rates.
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.