Date of Original Version
Abstract or Description
Prior work has shown that features which appear to be biologically plausible as well as empirically useful can be found by sparse coding with a prior such as a laplacian (L1 ) that promotes sparsity. We show how smoother priors can preserve the beneﬁts of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Additionally, we show how to calculate the derivative of the MAP estimate efﬁciently with implicit differentiation. One prior that can be differentiated this way is KL-regularization. We demonstrate its effectiveness on a wide variety of applications, and ﬁnd that online optimization of the parameters of the KL-regularized model can signiﬁcantly improve prediction performance.