Rényi Neural Processes

Xuesong Wang, He Zhao, Edwin V. Bonilla

Keywords: Neural processes, variational inference, meta learning, robust divergence

TL;DR: Using Rényi divergence for robust inference of neural processes

Abstract:

Neural Processes (NPs) are deep probabilistic models that represent stochastic processes by conditioning their prior distributions on a set of context points. Despite their obvious advantages in uncertainty estimation for complex distributions, NPs enforce parameterization coupling between the conditional prior model and the posterior model, thereby risking introducing a misspecified prior distribution. We hereby revisit the NP objectives and propose Rényi Neural Processes (RNP) to ameliorate the impacts of prior misspecification by optimizing an alternative posterior that achieves better marginal likelihood. More specifically, by replacing the standard KL divergence with the Rényi divergence between the model posterior and the true posterior, we scale the density ratio $\frac{p}{q}$ by the power of (1-$\alpha$) in the divergence gradients with respect to the posterior. This hyper parameter $\alpha$ allows us to dampen the effects of the misspecified prior for the posterior update, which has been shown to effectively avoid oversmoothed predictions and improve the expressiveness of the posterior model.
Our extensive experiments show consistent log-likelihood improvements over state-of-the-art NP family models which adopt both the variational inference or maximum likelihood estimation objectives. We validate the effectiveness of our approach across multiple benchmarks including regression and image inpainting tasks, and show significant performance improvements of RNPs in real-world regression problems where the underlying prior model is misspecifed.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 4482