Online Multi-Task Learning with Recursive Least Squares and Recursive Kernel Methods
arxiv(2023)
摘要
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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