Eigenvalue Corrected Noisy Natural Gradient

Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive posteriors by adding weight noise to regular natural gradient updates. Noisy K-FAC is an instance of noisy natural gradient that fits a matrix-variate Gaussian posterior with minor changes to ordinary K-FAC. Nevertheless, a matrix-variate Gaussian posterior does not capture an accurate diagonal variance. In this work, we extend on noisy K-FAC to obtain a more flexible posterior distribution called eigenvalue corrected matrix-variate Gaussian. The proposed method computes the full diagonal re-scaling factor in Kronecker-factored eigenbasis. Empirically, our approach consistently outperforms existing algorithms (e.g., noisy K-FAC) on regression and classification tasks.