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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.
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
Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function—approximately speaking, the kernel function specifies how to "blur" the influence of the data points so that their values can be used to predict the value for nearby locations.
Outline of regression analysis; Index of statistics articles; List of scientific method topics; List of analyses of categorical data; List of fields of application of statistics; List of graphical methods; List of statistical software. Comparison of statistical packages; List of graphing software; Comparison of Gaussian process software
Consider a set of data points, (,), (,), …, (,), and a curve (model function) ^ = (,), that in addition to the variable also depends on parameters, = (,, …,), with . It is desired to find the vector of parameters such that the curve fits best the given data in the least squares sense, that is, the sum of squares = = is minimized, where the residuals (in-sample prediction errors) r i are ...
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 ...
ADALINE (Adaptive Linear Neuron or later Adaptive Linear Element) is an early single-layer artificial neural network and the name of the physical device that implemented it. [ 2 ] [ 3 ] [ 1 ] [ 4 ] [ 5 ] It was developed by professor Bernard Widrow and his doctoral student Marcian Hoff at Stanford University in 1960.
Parametric statistics is a branch of statistics which leverages models based on a fixed (finite) set of parameters. [1] Conversely nonparametric statistics does not assume explicit (finite-parametric) mathematical forms for distributions when modeling data.