Reparameterized Importance Sampling for Robust Variational Bayesian Neural Networks

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 samplingfree 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. 1 See Section 2.7 for the extension to classification. 2 We suppress the bias from the notation as it can directly be incorporated by extending the respective weights matrices.