Aligned Multi-Task Gaussian Process

TL;DR

This paper introduces a Bayesian Gaussian process model that automatically accounts for temporal misalignments in multi-task time-series data, improving predictive accuracy and uncertainty quantification.

Contribution

It extends previous work by incorporating a Bayesian monotonic warping function with efficient sampling, enabling full uncertainty modeling in aligned multi-task Gaussian processes.

Findings

Improved predictive performance on synthetic and real data.

Better uncertainty quantification compared to baseline methods.

Effective modeling of temporal misalignments in multi-task learning.

Abstract

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process(vs baseline MAP alignment approach).