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CVEK (version 0.1-2)

kernel_nn: Generating A Single Matrix-wise Function Using Neural Network

Description

Generate matrix-wise functions for two matrices using neural network kernel.

Usage

kernel_nn(l, p, sigma)

Arguments

l

(numeric) A numeric number indicating the hyperparameter (flexibility) of a specific kernel.

p

(integer) For polynomial, p is the power; for matern, v = p + 1 / 2; for rational, alpha = p.

sigma

(numeric) The covariance coefficient for neural network kernel.

Value

matrix_wise

(function) A function calculating the relevance of two matrices.

Details

Neural Network Kernels $$k_{NN}(x, x')=\frac{2}{\pi}sin^{-1}\Big(\frac{2\tilde{x}^T \tilde{x}'}{\sqrt{(1+2\tilde{x}^T \tilde{x})(1+2\tilde{x}'^T \tilde{x}')}}\Big)$$

References

The MIT Press. Gaussian Processes for Machine Learning, 2006.