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Regression with Linear Factored Functions
Citation key Boehmer15b
Author Böhmer, W. and Obermayer, K.
Title of Book Machine Learning and Knowledge Discovery in Databases
Pages 119-134
Year 2015
ISBN 978-3-319-23527-1, 978-3-319-23528-8
ISSN 0302-9743
DOI 10.1007/978-3-319-23528-8_8
Volume 9284
Publisher Springer International Publishing
Series Lecture Notes in Computer Science
Abstract Many applications that use empirically estimated functions face a curse of dimensionality, because integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications like belief propagation and reinforcement learning can exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively to Gaussian processes on benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.
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