Package src :: Package stats306b :: Package lecture4 :: Module kernel

Module kernel

source code

This module describes how to use the 'kernel' trick for nonparametric regression. Kernels used are: Gaussian, piecewise linear, polynomial.

Functions

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plinear(x, y)
Piecewise linear kernel:

source code

polynomial(x, y, order=1)
Polynomial kernel

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gaussian(x, y, sigma=1.0)
Gaussian kernel with a given sigma.

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Function Details

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plinear(x, y)

source code

Piecewise linear kernel:

K(x,y) = min(x,y)

x, y must be non-negative, and have the shape (q,1) for some q

polynomial(x, y, order=1)

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Polynomial kernel

(dot(x,y))**order

x, y are p-vectors and must have the shape (q,p) for some q

gaussian(x, y, sigma=1.0)

source code

Gaussian kernel with a given sigma.

K(x,y)=exp(-(x-y)**2/(2*sigma**2))

x, y are p-vectors and must have the shape (q,p) for some q