Noisy Natural Gradient as Variational Inference
This work addresses the challenge of scaling Bayesian uncertainty estimation to modern neural networks for researchers and practitioners in machine learning, offering a more efficient and accurate method.
The paper tackles the tradeoff between simplicity and accuracy in variational Bayesian neural networks by showing that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the ELBO, enabling scalable training of full-covariance or factorized Gaussian posteriors. On regression benchmarks, their noisy K-FAC algorithm improves predictions, matches Hamiltonian Monte Carlo's predictive variances better than existing methods, and enhances exploration in active learning and reinforcement learning.
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.