Deep Variational Implicit Processes

TL;DR

This paper introduces Deep Variational Implicit Processes (DVIP), a flexible deep learning framework that extends implicit processes with scalable inference, outperforming previous methods in regression and classification tasks, especially on large datasets.

Contribution

It proposes a novel multi-layer deep implicit process model with a scalable variational inference algorithm, enhancing expressiveness and performance over existing IP-based models.

Findings

DVIP outperforms previous IP-based methods and deep GPs in experiments.

DVIP demonstrates strong scalability on datasets with millions of data points.

Extensive experiments validate the improved predictive performance of DVIP.

Abstract

Implicit processes (IPs) are a generalization of Gaussian processes (GPs). IPs may lack a closed-form expression but are easy to sample from. Examples include, among others, Bayesian neural networks or neural samplers. IPs can be used as priors over functions, resulting in flexible models with well-calibrated prediction uncertainty estimates. Methods based on IPs usually carry out function-space approximate inference, which overcomes some of the difficulties of parameter-space approximate inference. Nevertheless, the approximations employed often limit the expressiveness of the final model, resulting, e.g., in a Gaussian predictive distribution, which can be restrictive. We propose here a multi-layer generalization of IPs called the Deep Variational Implicit process (DVIP). This generalization is similar to that of deep GPs over GPs, but it is more flexible due to the use of IPs as the prior distribution over the latent functions. We describe a scalable variational inference algorithm for training DVIP and show that it outperforms previous IP-based methods and also deep GPs. We support these claims via extensive regression and classification experiments. We also evaluate DVIP on large datasets with up to several million data instances to illustrate its good scalability and performance.