Bayesian Learning with Deep Q-Exponential Process
Keywords: Deep Models, Inhomogeneous Subjects, Regularization, Latent Representation, Model Expressiveness
TL;DR: We generalize Q-exponential process (QEP) to deep QEP to improve model expressiveness and impose sharper regularization than deep Gaussian process for modeling inhomogeneous subjects.
Abstract: Motivated by deep neural networks, the deep Gaussian process (DGP) generalizes the standard GP by stacking multiple layers of GPs. Despite the enhanced expressiveness, GP, as an $L_2$ regularization prior, tends to be over-smooth and sub-optimal for inhomogeneous subjects, such as images with edges. Recently, Q-exponential process (Q-EP) has been proposed as an $L_q$ relaxation to GP and demonstrated with more desirable regularization properties through a parameter $q>0$ with $q=2$ corresponding to GP. Sharing the similar tractability of posterior and predictive distributions with GP, Q-EP can also be stacked to improve its modeling flexibility. In this paper, we generalize Q-EP to deep Q-EP to enjoy both proper regularization and improved expressiveness. The generalization is realized by introducing shallow Q-EP as a latent variable model and then building a hierarchy of the shallow Q-EP layers. Sparse approximation by inducing points and scalable variational strategy are applied to facilitate the inference. We demonstrate the numerical advantages of the proposed deep Q-EP model by comparing with multiple state-of-the-art deep probabilistic models.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 4965
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