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In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y .
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. [1]
Unsupervised multiple kernel learning algorithms have also been proposed by Zhuang et al. The problem is defined as follows. Let = be a set of unlabeled data. The kernel definition is the linear combined kernel ′ = =. In this problem, the data needs to be "clustered" into groups based on the kernel distances.
Equivalently, kernel regression is simply linear regression in the feature space (i.e. the range of the feature map defined by the chosen kernel). Note that kernel regression is typically a nonlinear regression in the input space, which is a major strength of the algorithm. Just as it’s possible to perform linear regression using iterative ...
Here > is a constant and ^ is the regularization operator corresponding to the selected kernel. A general Bayesian evidence framework was developed by MacKay, [3] [4] [5] and MacKay has used it to the problem of regression, forward neural network and classification network.
GRNN can be used for regression, prediction, and classification. GRNN can also be a good solution for online dynamical systems. GRNN represents an improved technique in the neural networks based on the nonparametric regression. The idea is that every training sample will represent a mean to a radial basis neuron. [2]
Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when x = x'), it has a ready interpretation as a similarity measure. [2] The feature space of the kernel has an infinite number of dimensions; for =, its expansion using the multinomial theorem is: [3]
Kernel methods are a well-established tool to analyze the relationship between input data and the corresponding output of a function. Kernels encapsulate the properties of functions in a computationally efficient way and allow algorithms to easily swap functions of varying complexity.