手法を比較

	回帰スプラインと平滑化スプライン	多変量適応回帰スプライン（MARS）	多項式回帰
分野	機械学習	機械学習	統計学
系統	Machine learning	Machine learning	Regression model
提唱年	1996	1991	2012
提唱者	Spline regression literature; P-splines by Eilers & Marx	Jerome H. Friedman	Montgomery, Peck & Vining (textbook treatment); classical least squares
種類	Piecewise-polynomial nonparametric regression	Adaptive piecewise-linear regression	Linear regression in transformed predictors
原典	Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121.	Friedman, J. H. (1991). Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1–67.	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811
別名	splines, cubic splines, natural splines, smoothing splines	multivariate adaptive regression splines, earth algorithm, MARS regression, çok değişkenli uyarlamalı regresyon spline'ları	polynomial least squares, curvilinear regression, Polinom Regresyonu
関連	4	4	4
概要	Regression splines model a nonlinear relationship by fitting piecewise polynomials that join smoothly at a set of points called knots. Cubic and natural splines are the most common, and smoothing splines add a roughness penalty that automatically balances fit against smoothness. Splines are the standard flexible building block for univariate nonlinear regression and the basis of generalized additive models.	Multivariate adaptive regression splines, introduced by Jerome Friedman in 1991, is a flexible nonparametric regression method that automatically models nonlinearities and interactions by combining piecewise-linear 'hinge' functions. It builds the model in a forward stagewise pass that adds basis functions where they help most, then prunes back the overgrown model, yielding an interpretable additive-plus-interaction form that adapts its complexity to the data.	Polynomial regression is a regression method that models non-linear relationships by including squared and higher-degree terms of an explanatory variable, and it is a core tool of response surface analysis. As developed in Montgomery, Peck and Vining's Introduction to Linear Regression Analysis (2012), it remains linear in its parameters even though the fitted curve bends.