The Falling Factorial Basis and Its Statistical Applications

Yu-Xiang Wang, Alex Smola, Ryan Tibshirani
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):730-738, 2014.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-wange14, title = {The Falling Factorial Basis and Its Statistical Applications}, author = {Wang, Yu-Xiang and Smola, Alex and Tibshirani, Ryan}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {730--738}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/wange14.pdf}, url = {https://proceedings.mlr.press/v32/wange14.html}, 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.} }
Endnote
%0 Conference Paper %T The Falling Factorial Basis and Its Statistical Applications %A Yu-Xiang Wang %A Alex Smola %A Ryan Tibshirani %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-wange14 %I PMLR %P 730--738 %U https://proceedings.mlr.press/v32/wange14.html %V 32 %N 2 %X 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.
RIS
TY - CPAPER TI - The Falling Factorial Basis and Its Statistical Applications AU - Yu-Xiang Wang AU - Alex Smola AU - Ryan Tibshirani BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-wange14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 730 EP - 738 L1 - http://proceedings.mlr.press/v32/wange14.pdf UR - https://proceedings.mlr.press/v32/wange14.html AB - 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. ER -
APA
Wang, Y., Smola, A. & Tibshirani, R.. (2014). The Falling Factorial Basis and Its Statistical Applications. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):730-738 Available from https://proceedings.mlr.press/v32/wange14.html.

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