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In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. [1] It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.
Python: the KernelReg class for mixed data types in the statsmodels.nonparametric sub-package (includes other kernel density related classes), the package kernel_regression as an extension of scikit-learn (inefficient memory-wise, useful only for small datasets) R: the function npreg of the np package can perform kernel regression. [7] [8]
The resulting function is smooth, and the problem with the biased boundary points is reduced. Local linear regression can be applied to any-dimensional space, though the question of what is a local neighborhood becomes more complicated. It is common to use k nearest training points to a test point to fit the local linear regression.
Simon Haykin, Adaptive Filter Theory, Prentice Hall, 2002, ISBN 0-13-048434-2 M.H.A Davis, R.B. Vinter, Stochastic Modelling and Control , Springer, 1985, ISBN 0-412-16200-8 Weifeng Liu, Jose Principe and Simon Haykin, Kernel Adaptive Filtering: A Comprehensive Introduction , John Wiley, 2010, ISBN 0-470-44753-2
In the more general multiple regression model, there are independent variables: = + + + +, where is the -th observation on the -th independent variable.If the first independent variable takes the value 1 for all , =, then is called the regression intercept.
In Gaussian process regression, also known as Kriging, a Gaussian prior is assumed for the regression curve. The errors are assumed to have a multivariate normal distribution and the regression curve is estimated by its posterior mode. The Gaussian prior may depend on unknown hyperparameters, which are usually estimated via empirical Bayes. The ...
Regression splines. In this method, the data is fitted to a set of spline basis functions with a reduced set of knots, typically by least squares. No roughness penalty is used. (See also multivariate adaptive regression splines.) Penalized splines. This combines the reduced knots of regression splines, with the roughness penalty of smoothing ...
InterpretML, a Python package for fitting GAMs via bagging and boosting. mgcv, an R package for GAMs using penalized regression splines. mboost, an R package for boosting including additive models. gss, an R package for smoothing spline ANOVA. INLA software for Bayesian Inference with GAMs and more.