Quantized Variational Inference

TL;DR

Quantized Variational Inference introduces a novel algorithm that uses optimal Voronoi tessellation to achieve variance-free gradients for ELBO maximization, improving convergence speed with manageable bias.

Contribution

The paper proposes a new quantization-based variational inference method that reduces gradient variance and enhances convergence speed, with bias correction techniques.

Findings

Fast convergence for score function and reparametrized gradients

Variance-free gradients via Voronoi tessellation

Effective bias correction with Richardson extrapolation

Abstract

We present Quantized Variational Inference, a new algorithm for Evidence Lower Bound maximization. We show how Optimal Voronoi Tesselation produces variance free gradients for ELBO optimization at the cost of introducing asymptotically decaying bias. Subsequently, we propose a Richardson extrapolation type method to improve the asymptotic bound. We show that using the Quantized Variational Inference framework leads to fast convergence for both score function and the reparametrized gradient estimator at a comparable computational cost. Finally, we propose several experiments to assess the performance of our method and its limitations.