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arXiv 2209.03028stat.MLcs.LG
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面向多任务问题的特征空间贝叶斯学习

Bayesian learning of feature spaces for multitasks problems

Aalto University(阿尔托大学);Universidad Carlos III de Madrid(马德里卡洛斯三世大学)

Carlos Sevilla-Salcedo, Ascensión Gallardo-Antolín, Vanessa Gómez-Verdejo, Emilio Parrado-Hernández

AI总结:

该研究提出RFF-BLR贝叶斯多任务回归模型,通过RFF近似关联KM与ELM,同时优化核参数、模型复杂度并实现跨任务知识迁移,性能优于现有多任务非线性回归方法。

摘要:

本文提出了一种新的多任务回归方法,该方法利用RBF核的随机傅里叶特征(Random Fourier Features, RFFs)近似,将核机器(Kernel Machines, KMs)与极限学习机(Extreme Learning Machines, ELMs)联系起来。从这个角度来看,本文的贡献之一在于证明了对于所提出的模型,KM和ELM的公式化表达可被视为同一事物的两个方面。这些被称为RFF-BLR的模型基于一个贝叶斯框架,该框架同时实现两个主要设计目标:一方面,它拟合基于配备RBF核的KM的多任务回归器;另一方面,它能够引入一个跨任务共享的先验,在ELM视角下促进多输出稀疏性。这种贝叶斯方法有助于同时考虑KM和ELM两种视角,从而实现:(i)在概率框架内优化RBF核参数$γ$;(ii)优化模型复杂度;(iii)实现任务间高效的知识迁移。实验结果表明,与多任务非线性回归领域的现有最优方法相比,该框架能够带来显著的性能提升。

英文摘要:

This paper introduces a novel approach for multi-task regression that connects Kernel Machines (KMs) and Extreme Learning Machines (ELMs) through the exploitation of the Random Fourier Features (RFFs) approximation of the RBF kernel. In this sense, one of the contributions of this paper shows that for the proposed models, the KM and the ELM formulations can be regarded as two sides of the same coin. These proposed models, termed RFF-BLR, stand on a Bayesian framework that simultaneously addresses two main design goals. On the one hand, it fits multitask regressors based on KMs endowed with RBF kernels. On the other hand, it enables the introduction of a common-across-tasks prior that promotes multioutput sparsity in the ELM view. This Bayesian approach facilitates the simultaneous consideration of both the KM and ELM perspectives enabling (i) the optimisation of the RBF kernel parameter $γ$ within a probabilistic framework, (ii) the optimisation of the model complexity, and (iii) an efficient transfer of knowledge across tasks. The experimental results show that this framework can lead to significant performance improvements compared to the state-of-the-art methods in multitask nonlinear regression.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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