Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting

• URL: http://arxiv.org/abs/2406.10327v1
• Date: Fri, 14 Jun 2024 17:59:25 GMT
• Title: Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting
• Authors: Romain Ilbert, Malik Tiomoko, Cosme Louart, Ambroise Odonnat, Vasilii Feofanov, Themis Palpanas, Ievgen Redko,
• Abstract summary: We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models.
• Score: 16.640336442849282
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

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