Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior distributions for convolutional neural networks, deep weight prior (dwp), that exploit generative models to encourage a specific structure of trained convolutional filters e.g., spatial correlations. We define dwp in a form of an implicit distribution and propose a method for variational inference with such type of implicit priors. In experiments, we show that dwp improves the performance of Bayesian neural networks when training data are limited, and initialization of weights with samples from dwp accelerates training of conventional convolutional neural networks.
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.
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