Gaussian Process Regressor: Effect of parameters

                Gaussian Process Regressor-Effect of parameters on output 

Gaussian Process Regressor technique is tested here to see their accuracy in terms of output.

Python program:

>>> import numpy as np

>>> import matplotlib.pyplot as plt

>>> from matplotlib.colors import ListedColormap

>>> from sklearn import neighbors, datasets

>>> n_neighbors = 24

>>> iris = datasets.load_iris()

>>> x = iris.data[:, :2]

>>> y = iris.target

>>> h = .02

>>> cmap_bold = ListedColormap(['firebrick', 'lime', 'blue'])

>>> cmap_light = ListedColormap(['pink', 'lightgreen', 'paleturquoise'])

//Plotting the analysis//
a) Effect of alpha:

>>> for alpha in [0.0001, 0.0005, 0.001, 0.05, 0.1, 0.2, 0.5]:
...         clf = gaussian_process.GaussianProcessRegressor(alpha=alpha)
...         clf.fit(x, y)
...         x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...         y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...         xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...         z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...         z = z.reshape(xx.shape)
...         plt.figure()
...         plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...         plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...         plt.xlim(xx.min(), xx.max())
...         plt.ylim(yy.min(), yy.max())
...         plt.title("GaussianProcessRegressor (alpha='%s')" %(alpha))
...

>>> for alpha in [0.75, 1, 2, 5, 15, 25, 50, 100, 250, 500, 1000]:
...         clf = gaussian_process.GaussianProcessRegressor(alpha=alpha)
...         clf.fit(x, y)
...         x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...         y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...         xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...         z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...         z = z.reshape(xx.shape)
...         plt.figure()
...         plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...         plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...         plt.xlim(xx.min(), xx.max())
...         plt.ylim(yy.min(), yy.max())
...         plt.title("GaussianProcessRegressor (alpha='%s')" %(alpha))
...

b) Effect of number of optimizer restarts (n_restarts_optimizer):

>>> for n_restarts_optimizer in [1, 2, 5, 25, 50, 250, 750, 2500, 5000]:
...         clf = gaussian_process.GaussianProcessRegressor(n_restarts_optimizer=n_restarts_optimizer)
...         clf.fit(x, y)
...         x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...         y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...         xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...         z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...         z = z.reshape(xx.shape)
...         plt.figure()
...         plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...         plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...         plt.xlim(xx.min(), xx.max())
...         plt.ylim(yy.min(), yy.max())
...         plt.title("GaussianProcessRegressor (n_restarts_optimizer='%s')" %(n_restarts_optimizer))
...

c) Effect of normalization of y: 

>>> for normalize_y in ['False', None, 'True']:
...         clf = gaussian_process.GaussianProcessRegressor(normalize_y=normalize_y)
...         clf.fit(x, y)
...         x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...         y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...         xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...         z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...         z = z.reshape(xx.shape)
...         plt.figure()
...         plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...         plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...         plt.xlim(xx.min(), xx.max())
...         plt.ylim(yy.min(), yy.max())
...         plt.title("GaussianProcessRegressor (normalize_y='%s')" %(normalize_y))
...

No effect on output.

d) Effect of random state (random_state):

>>> for random_state in [1, 2, 5, 25, 100, 250]:
...         clf = gaussian_process.GaussianProcessRegressor(random_state=random_state)
...         clf.fit(x, y)
...         x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...         y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...         xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...         z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...         z = z.reshape(xx.shape)
...         plt.figure()
...         plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...         plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...         plt.xlim(xx.min(), xx.max())
...         plt.ylim(yy.min(), yy.max())
...         plt.title("GaussianProcessRegressor (random_state='%s')" %(random_state))
...

No effect on output.