Implicit Posterior Variational Inference for Deep Gaussian Processes
This work addresses the problem of biased or costly inference in DGPs for researchers and practitioners in machine learning, representing a novel method rather than an incremental improvement.
The paper tackles the challenge of intractable inference in deep Gaussian processes (DGPs) by introducing an implicit posterior variational inference (IPVI) framework that recovers an unbiased posterior belief while maintaining time efficiency, and empirical results show it outperforms state-of-the-art approximation methods.
A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.