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MATLAB: A free MATLAB toolbox with implementation of kernel regression, kernel density estimation, kernel estimation of hazard function and many others is available on these pages (this toolbox is a part of the book [6]).
A free MATLAB toolbox with implementation of kernel regression, kernel density estimation, kernel estimation of hazard function and many others is available on these pages (this toolbox is a part of the book [30]).
Multivariate Kernel Smoothing and Its Applications is a comprehensive book on many topics in kernel smoothing, including density estimation. Includes ks package code snippets in R. kde2d.m A Matlab function for bivariate kernel density estimation. libagf A C++ library for multivariate, variable bandwidth kernel density estimation.
In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable.
www.kernel-machines.org "Support Vector Machines and Kernel based methods (Smola & Schölkopf)". www.gaussianprocess.org "Gaussian Processes: Data modeling using Gaussian Process priors over functions for regression and classification (MacKay, Williams)". www.support-vector.net "Support Vector Machines and kernel based methods (Cristianini)".
Output after kernel PCA, with a Gaussian kernel. Note in particular that the first principal component is enough to distinguish the three different groups, which is impossible using only linear PCA, because linear PCA operates only in the given (in this case two-dimensional) space, in which these concentric point clouds are not linearly separable.
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.
Kernel PCR then proceeds by (usually) selecting a subset of all the eigenvectors so obtained and then performing a standard linear regression of the outcome vector on these selected eigenvectors. The eigenvectors to be used for regression are usually selected using cross-validation. The estimated regression coefficients (having the same ...