Search Machine Learning Repository: The Falling Factorial Basis and Its Statistical Applications
Authors: Yu-xiang Wang, Alex Smola and Ryan Tibshirani
Conference: Proceedings of the 31st International Conference on Machine Learning (ICML-14)
Year: 2014
Pages: 730-738
Abstract: We study a novel spline-like basis, which we name the {\it falling factorial basis}, bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factorial functions are not actually splines, but are close enough to splines that they provably retain some of the favorable properties of the latter functions. We examine their application in two problems: trend filtering over arbitrary input points, and a higher-order variant of the two-sample Kolmogorov-Smirnov test.
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