方法对比

	广义可加模型 (GAM)	多项式回归	回归与平滑样条
领域	机器学习	统计学	机器学习
方法族	Machine learning	Regression model	Machine learning
起源年份	1986	2012	1996
提出者	Trevor Hastie & Robert Tibshirani	Montgomery, Peck & Vining (textbook treatment); classical least squares	Spline regression literature; P-splines by Eilers & Marx
类型	Semi-parametric additive regression model	Linear regression in transformed predictors	Piecewise-polynomial nonparametric regression
开创性文献	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.
别名	GAM, additive model, spline-based additive regression, Genelleştirilmiş toplamsal model	polynomial least squares, curvilinear regression, Polinom Regresyonu	splines, cubic splines, natural splines, smoothing splines
相关	4	4	4
摘要	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.