An Equivalence between Bayesian Priors and Penalties in Variational Inference

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contains a Kullback--Leibler divergence term between the approximate posterior and a Bayesian prior. We fully characterize the regularizers that can arise according to this procedure, and provide a systematic way to compute the prior …

bayesian cs.lg divergence inference loss machine machine learning math.st parameters probabilistic model regularization stat.ml stat.th terms tractable values