方法对比

	多项式回归	Lasso 回归	普通最小二乘法 (OLS) 回归
领域	统计学	机器学习	计量经济学
方法族	Regression model	Machine learning	Regression model
起源年份	2012	1996	2019
提出者	Montgomery, Peck & Vining (textbook treatment); classical least squares	Tibshirani, R.	Wooldridge (textbook treatment); classical least squares
类型	Linear regression in transformed predictors	Regularized linear regression (L1 penalty)	Linear regression
开创性文献	Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811	Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
别名	polynomial least squares, curvilinear regression, Polinom Regresyonu	LASSO Regresyonu, lasso, L1-regularized regression, L1 regularization	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
相关	4	4	5
摘要	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.	Lasso regression, introduced by Robert Tibshirani in 1996, is a linear regression method that adds an L1 penalty to the loss so that it shrinks coefficients and performs variable selection at the same time, producing a sparse model. By driving some coefficients exactly to zero it keeps only the predictors that matter.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).