Online Multi-Task Learning with Recursive Least Squares and Recursive Kernel Methods

• URL: http://arxiv.org/abs/2308.01938v2
• Date: Sun, 17 Mar 2024 16:22:39 GMT
• Title: Online Multi-Task Learning with Recursive Least Squares and Recursive Kernel Methods
• Authors: Gabriel R. Lencione, Fernando J. Von Zuben,
• Abstract summary: We introduce two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We achieve exact and approximate recursions with quadratic per-instance cost on the dimension of the input space. We compare our online MTL methods to other contenders in a real-world wind speed forecasting case study.
• Score: 50.67996219968513
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We employ a high performance graph-based MTL formulation and develop two alternative recursive versions based on the Weighted Recursive Least Squares (WRLS) and the Online Sparse Least Squares Support Vector Regression (OSLSSVR) strategies. Adopting task-stacking transformations, we demonstrate the existence of a single matrix incorporating the relationship of multiple tasks and providing structural information to be embodied by the MT-WRLS method in its initialization procedure and by the MT-OSLSSVR in its multi-task kernel function. Contrasting the existing literature, which is mostly based on Online Gradient Descent (OGD) or cubic inexact approaches, we achieve exact and approximate recursions with quadratic per-instance cost on the dimension of the input space (MT-WRLS) or on the size of the dictionary of instances (MT-OSLSSVR). We compare our online MTL methods to other contenders in a real-world wind speed forecasting case study, evidencing the significant gain in performance of both proposed approaches.

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