Сравнение методов

	Обобщенная аддитивная модель (GAM)	Полиномиальная регрессия	Регрессионные и сглаживающие сплайны
Область	Машинное обучение	Статистика	Машинное обучение
Семейство	Machine learning	Regression model	Machine learning
Год появления	1986	2012	1996
Автор метода	Trevor Hastie & Robert Tibshirani	Montgomery, Peck & Vining (textbook treatment); classical least squares	Spline regression literature; P-splines by Eilers & Marx
Тип	Semi-parametric additive regression model	Linear regression in transformed predictors	Piecewise-polynomial nonparametric regression
Основополагающий источник	Hastie, T., & Tibshirani, R. (1986). Generalized additive models. Statistical Science, 1(3), 297–310.	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811	Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121.
Другие названия	GAM, additive model, spline-based additive regression, Genelleştirilmiş toplamsal model	polynomial least squares, curvilinear regression, Polinom Regresyonu	splines, cubic splines, natural splines, smoothing splines
Связанные	4	4	4
Сводка	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.	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.	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.