Semi-described and semi-supervised learning with Gaussian processes

TL;DR

This paper introduces a Bayesian variational framework for Gaussian processes that effectively handles semi-described and semi-supervised learning, improving uncertainty propagation and performance in forecasting and missing data tasks.

Contribution

It develops novel variational methods for semi-described inputs in GPs and integrates them with algorithms for imputing missing data in a Bayesian manner.

Findings

Significant performance improvements in forecasting tasks.

Effective handling of missing data in regression and classification.

Validated on simulated and real-world datasets.

Abstract

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problems (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.