Noisy Natural Gradient as Variational Inference

TL;DR

This paper introduces a novel approach using noisy natural gradient methods to efficiently train Bayesian neural networks with various variational posteriors, improving uncertainty estimation and scalability.

Contribution

It reveals that natural gradient ascent with adaptive weight noise implicitly optimizes the ELBO, enabling scalable training of complex variational distributions in neural networks.

Findings

Outperforms existing methods in predictive accuracy on regression benchmarks.

Provides better uncertainty estimates matching Hamiltonian Monte Carlo.

Enhances exploration in active learning and reinforcement learning.

Abstract

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo's predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.