Regression with linear factored functions

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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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APA

Böhmer, W., & Obermayer, K. (2015). Regression with linear factored functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9284, pp. 119–134). Springer Verlag. https://doi.org/10.1007/978-3-319-23528-8_8

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