方法对比

	回归与平滑样条	LOESS / LOWESS局部回归	多项式回归
领域	机器学习	机器学习	统计学
方法族	Machine learning	Machine learning	Regression model
起源年份	1996	1979	2012
提出者	Spline regression literature; P-splines by Eilers & Marx	William S. Cleveland	Montgomery, Peck & Vining (textbook treatment); classical least squares
类型	Piecewise-polynomial nonparametric regression	Local nonparametric regression smoother	Linear regression in transformed predictors
开创性文献	Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121.	Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829–836.	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811
别名	splines, cubic splines, natural splines, smoothing splines	LOWESS, local regression, locally weighted scatterplot smoothing, yerel regresyon	polynomial least squares, curvilinear regression, Polinom Regresyonu
相关	4	3	4
摘要	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.	LOESS (locally estimated scatterplot smoothing), introduced by William Cleveland in 1979 and extended with Susan Devlin in 1988, fits a smooth curve through data by performing a separate weighted polynomial regression in the neighbourhood of each point. Nearby observations count more than distant ones, so the method follows local structure without assuming any global functional form, making it a popular exploratory smoother for scatterplots.	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.