Multi-task Learning for Aggregated Data using Gaussian Processes

TL;DR

This paper introduces a multi-task Gaussian process model designed for aggregated data across different scales, enabling joint learning and flexible likelihood modeling, with applications demonstrated in synthetic, demographic, and environmental datasets.

Contribution

The paper presents a novel multi-task Gaussian process framework that handles aggregated data at multiple scales and allows for different likelihood models per task.

Findings

Effective in synthetic data, fertility, and air pollution tasks.

Supports different likelihood models per task.

Scalable with stochastic variational inference.

Abstract

Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this paper, we present a novel multi-task learning model based on Gaussian processes for joint learning of variables that have been aggregated at different input scales. Our model represents each task as the linear combination of the realizations of latent processes that are integrated at a different scale per task. We are then able to compute the cross-covariance between the different tasks either analytically or numerically. We also allow each task to have a potentially different likelihood model and provide a variational lower bound that can be optimised in a stochastic fashion making our model suitable for larger datasets. We show examples of the model in a synthetic example, a fertility dataset, and an air pollution prediction application.