Non Linear Methods for Regression

Kernel Ridge Regression

class mlpy.KernelRidge(lmb=1.0, kernel=None)

Kernel Ridge Regression (dual).


Parameters :
lmb : float (>= 0.0)

regularization parameter

kernel : None or mlpy.Kernel object.

if kernel is None, K and Kt in .learn() and in .pred() methods must be precomputed kernel matricies, else K and Kt must be training (resp. test) data in input space.


Return alpha.


Return b.

learn(K, y)

Compute the regression coefficients.

K: 2d array_like object
precomputed training kernel matrix (if kernel=None); training data in input space (if kernel is a Kernel object)
y : 1d array_like object (N)
target values

Compute the predicted response.

Parameters :
Kt : 1d or 2d array_like object

precomputed test kernel matrix. (if kernel=None); test data in input space (if kernel is a Kernel object).

Returns :
p : integer or 1d numpy darray

predicted response


>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import mlpy
>>> np.random.seed(0)
>>> x = np.arange(0, 2, 0.05).reshape(-1, 1) # training points
>>> y = np.ravel(np.exp(x)) + np.random.normal(1, 0.2, x.shape[0]) # target values
>>> xt = np.arange(0, 2, 0.01).reshape(-1, 1) # testing points
>>> K = mlpy.kernel_gaussian(x, x, sigma=1) # training kernel matrix
>>> Kt = mlpy.kernel_gaussian(xt, x, sigma=1) # testing kernel matrix
>>> krr = KernelRidge(lmb=0.01)
>>> krr.learn(K, y)
>>> yt = krr.pred(Kt)
>>> fig = plt.figure(1)
>>> plot1 = plt.plot(x[:, 0], y, 'o')
>>> plot2 = plt.plot(xt[:, 0], yt)

Support Vector Regression

See Support Vector Machines (SVMs)

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