Regression with Linear Factored Functions
Abstract
Many applications that use empirically estimated functions face a curse of dimensionality, because the 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2014
- DOI:
- 10.48550/arXiv.1412.6286
- arXiv:
- arXiv:1412.6286
- Bibcode:
- 2014arXiv1412.6286B
- Keywords:
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- Computer Science - Machine Learning;
- Statistics - Machine Learning
- E-Print:
- Under review as conference paper at ECML/PKDD 2015