Cluster-Specific Predictions with Multi-Task Gaussian Processes
Arthur Leroy, Pierre Latouche, Benjamin Guedj, Servane Gey; 24(5):1−49, 2023.
Abstract
This study introduces a model that utilizes Gaussian processes (GPs) to handle multitask learning, clustering, and prediction for multiple functional data simultaneously. The model serves as both a model-based clustering method for functional data and a learning step for predicting new tasks. It is implemented as a mixture of multi-task GPs with common mean processes. To optimize the hyper-parameters and estimate the hyper-posteriors of latent variables and processes, a variational EM algorithm is derived. We provide explicit formulas for incorporating the mean processes and latent clustering variables into a predictive distribution, accounting for uncertainty in both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which improves performance when dealing with group-structured data. The model can handle irregular grids of observations and offers various hypotheses on the covariance structure for sharing additional information across tasks. We evaluate the model’s performance on both clustering and prediction tasks using simulated scenarios and real data sets. The overall algorithm, named MagmaClust, is publicly available as an R package.
[abs]