Порівняння методів

	Регресійні та згладжувальні сплайни	Узагальнена адитивна модель (GAM)	Багатовимірні адаптивні сплайнові регресії (MARS)	Поліноміальна регресія
Галузь	Машинне навчання	Машинне навчання	Машинне навчання	Статистика
Родина	Machine learning	Machine learning	Machine learning	Regression model
Рік появи	1996	1986	1991	2012
Автор методу	Spline regression literature; P-splines by Eilers & Marx	Trevor Hastie & Robert Tibshirani	Jerome H. Friedman	Montgomery, Peck & Vining (textbook treatment); classical least squares
Тип	Piecewise-polynomial nonparametric regression	Semi-parametric additive regression model	Adaptive piecewise-linear regression	Linear regression in transformed predictors
Основоположне джерело	Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121.	Hastie, T., & Tibshirani, R. (1986). Generalized additive models. Statistical Science, 1(3), 297–310.	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
Інші назви	splines, cubic splines, natural splines, smoothing splines	GAM, additive model, spline-based additive regression, Genelleştirilmiş toplamsal model	multivariate adaptive regression splines, earth algorithm, MARS regression, çok değişkenli uyarlamalı regresyon spline'ları	polynomial least squares, curvilinear regression, Polinom Regresyonu
Пов'язані	4	4	4	4
Підсумок	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.	A generalized additive model, introduced by Trevor Hastie and Robert Tibshirani in 1986, extends the generalized linear model by replacing each linear term with a smooth, data-driven function of the predictor. This lets the model capture nonlinear relationships while preserving the additive, term-by-term interpretability of regression: each predictor contributes its own estimated curve, and the curves simply add up (on a link scale) to predict the response.	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.