The Falling Factorial Basis and Its Statistical Applications

2014/05/03 by Yuxiang Wang, Alex Smola, Wang, Yu-Xiang +3 · 1 citation
Computer Science · Environmental Science · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Soil Geostatistics and Mapping #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1405.0558

openalex publication_date 2014/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a novel spline-like basis, which we name the "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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• Fast and Flexible ADMM Algorithms for Trend Filtering

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