100 lines
2.9 KiB
Python
100 lines
2.9 KiB
Python
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"""
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=================================================================
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Iso-probability lines for Gaussian Processes classification (GPC)
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=================================================================
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A two-dimensional classification example showing iso-probability lines for
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the predicted probabilities.
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"""
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# Author: Vincent Dubourg <vincent.dubourg@gmail.com>
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# Adapted to GaussianProcessClassifier:
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# Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
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# License: BSD 3 clause
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import numpy as np
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from matplotlib import cm
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from matplotlib import pyplot as plt
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from sklearn.gaussian_process import GaussianProcessClassifier
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from sklearn.gaussian_process.kernels import ConstantKernel as C
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from sklearn.gaussian_process.kernels import DotProduct
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# A few constants
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lim = 8
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def g(x):
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"""The function to predict (classification will then consist in predicting
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whether g(x) <= 0 or not)"""
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return 5.0 - x[:, 1] - 0.5 * x[:, 0] ** 2.0
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# Design of experiments
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X = np.array(
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[
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[-4.61611719, -6.00099547],
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[4.10469096, 5.32782448],
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[0.00000000, -0.50000000],
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[-6.17289014, -4.6984743],
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[1.3109306, -6.93271427],
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[-5.03823144, 3.10584743],
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[-2.87600388, 6.74310541],
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[5.21301203, 4.26386883],
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]
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)
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# Observations
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y = np.array(g(X) > 0, dtype=int)
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# Instantiate and fit Gaussian Process Model
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kernel = C(0.1, (1e-5, np.inf)) * DotProduct(sigma_0=0.1) ** 2
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gp = GaussianProcessClassifier(kernel=kernel)
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gp.fit(X, y)
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print("Learned kernel: %s " % gp.kernel_)
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# Evaluate real function and the predicted probability
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res = 50
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x1, x2 = np.meshgrid(np.linspace(-lim, lim, res), np.linspace(-lim, lim, res))
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xx = np.vstack([x1.reshape(x1.size), x2.reshape(x2.size)]).T
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y_true = g(xx)
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y_prob = gp.predict_proba(xx)[:, 1]
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y_true = y_true.reshape((res, res))
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y_prob = y_prob.reshape((res, res))
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# Plot the probabilistic classification iso-values
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fig = plt.figure(1)
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ax = fig.gca()
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ax.axes.set_aspect("equal")
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plt.xticks([])
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plt.yticks([])
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ax.set_xticklabels([])
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ax.set_yticklabels([])
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plt.xlabel("$x_1$")
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plt.ylabel("$x_2$")
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cax = plt.imshow(y_prob, cmap=cm.gray_r, alpha=0.8, extent=(-lim, lim, -lim, lim))
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norm = plt.matplotlib.colors.Normalize(vmin=0.0, vmax=0.9)
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cb = plt.colorbar(cax, ticks=[0.0, 0.2, 0.4, 0.6, 0.8, 1.0], norm=norm)
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cb.set_label(r"${\rm \mathbb{P}}\left[\widehat{G}(\mathbf{x}) \leq 0\right]$")
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plt.clim(0, 1)
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plt.plot(X[y <= 0, 0], X[y <= 0, 1], "r.", markersize=12)
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plt.plot(X[y > 0, 0], X[y > 0, 1], "b.", markersize=12)
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plt.contour(x1, x2, y_true, [0.0], colors="k", linestyles="dashdot")
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cs = plt.contour(x1, x2, y_prob, [0.666], colors="b", linestyles="solid")
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plt.clabel(cs, fontsize=11)
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cs = plt.contour(x1, x2, y_prob, [0.5], colors="k", linestyles="dashed")
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plt.clabel(cs, fontsize=11)
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cs = plt.contour(x1, x2, y_prob, [0.334], colors="r", linestyles="solid")
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plt.clabel(cs, fontsize=11)
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plt.show()
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