Bayesian neural networks for sparse coding

Deep learning is actively used in the area of sparse coding. In current deep sparse coding methods uncertainty of predictions is rarely estimated, thus providing the results that lack the quantitative justification. Bayesian learning provides the way to estimate the uncertainty of predictions in neural networks (NNs) by imposing the prior distributions on weights, propagating the resulting uncertainty through the layers and computing the posterior distributions of predictions. We propose a novel method of propagating the uncertainty through the sparsity-promoiting layers of NNs for the first time. We design a Bayesian Learned Iterative Shrinkage-Thresholding network (BayesLIsTA). An efficient posterior inference algorithm based on probabilistic backpropagation is developed. Experiments on sparse coding show that the proposed framework provides both accurate predictions and sensible estimates of uncertainty in these predictions.