Sampling-Free Variational Inference of Bayesian Neural Networks by Variance Backpropagation
Manuel Haußmann, Fred A. Hamprecht, Melih Kandemir
Abstract
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variational inference on this construction enables a sampling-free computation of the evidence lower bound which is a more effective approximation than the widely applied Monte Carlo sampling and CLT related techniques. We evaluate the model on a range of regression and classification tasks against BNN inference alternatives, showing competitive or improved performance over the current state-of-the-art.
BibTeX
@InProceedings{pmlr-v115-haussmann20a,
title = {Sampling-Free Variational Inference of Bayesian Neural Networks by Variance Backpropagation},
author = {Hau{\ss}mann, Manuel and Hamprecht, Fred A. and Kandemir, Melih},
booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference},
pages = {563--573},
year = {2020},
editor = {Adams, Ryan P. and Gogate, Vibhav},
volume = {115},
series = {Proceedings of Machine Learning Research},
month = {22--25 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v115/haussmann20a/haussmann20a.pdf},
url = {https://proceedings.mlr.press/v115/haussmann20a.html},
abstract = { We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variational inference on this construction enables a sampling-free computation of the evidence lower bound which is a more effective approximation than the widely applied Monte Carlo sampling and CLT related techniques. We evaluate the model on a range of regression and classification tasks against BNN inference alternatives, showing competitive or improved performance over the current state-of-the-art. }
}