115 lines
3.1 KiB
Python
115 lines
3.1 KiB
Python
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from statsmodels.compat.python import lzip
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import numpy as np
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from statsmodels.tools.validation import array_like
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from . import kernels
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#TODO: should this be a function?
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class KDE:
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"""
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Kernel Density Estimator
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Parameters
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----------
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x : array_like
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N-dimensional array from which the density is to be estimated
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kernel : Kernel Class
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Should be a class from *
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"""
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#TODO: amend docs for Nd case?
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def __init__(self, x, kernel=None):
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x = array_like(x, "x", maxdim=2, contiguous=True)
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if x.ndim == 1:
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x = x[:,None]
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nobs, n_series = x.shape
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if kernel is None:
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kernel = kernels.Gaussian() # no meaningful bandwidth yet
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if n_series > 1:
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if isinstance( kernel, kernels.CustomKernel ):
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kernel = kernels.NdKernel(n_series, kernels = kernel)
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self.kernel = kernel
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self.n = n_series #TODO change attribute
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self.x = x
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def density(self, x):
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return self.kernel.density(self.x, x)
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def __call__(self, x, h="scott"):
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return np.array([self.density(xx) for xx in x])
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def evaluate(self, x, h="silverman"):
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density = self.kernel.density
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return np.array([density(xx) for xx in x])
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if __name__ == "__main__":
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from numpy import random
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import matplotlib.pyplot as plt
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import statsmodels.nonparametric.bandwidths as bw
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from statsmodels.sandbox.nonparametric.testdata import kdetest
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# 1-D case
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random.seed(142)
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x = random.standard_t(4.2, size = 50)
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h = bw.bw_silverman(x)
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#NOTE: try to do it with convolution
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support = np.linspace(-10,10,512)
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kern = kernels.Gaussian(h = h)
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kde = KDE( x, kern)
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print(kde.density(1.015469))
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print(0.2034675)
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Xs = np.arange(-10,10,0.1)
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fig = plt.figure()
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ax = fig.add_subplot(111)
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ax.plot(Xs, kde(Xs), "-")
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ax.set_ylim(-10, 10)
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ax.set_ylim(0,0.4)
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# 2-D case
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x = lzip(kdetest.faithfulData["eruptions"], kdetest.faithfulData["waiting"])
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x = np.array(x)
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x = (x - x.mean(0))/x.std(0)
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nobs = x.shape[0]
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H = kdetest.Hpi
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kern = kernels.NdKernel( 2 )
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kde = KDE( x, kern )
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print(kde.density( np.matrix( [1,2 ]))) #.T
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plt.figure()
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plt.plot(x[:,0], x[:,1], 'o')
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n_grid = 50
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xsp = np.linspace(x.min(0)[0], x.max(0)[0], n_grid)
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ysp = np.linspace(x.min(0)[1], x.max(0)[1], n_grid)
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# xsorted = np.sort(x)
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# xlow = xsorted[nobs/4]
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# xupp = xsorted[3*nobs/4]
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# xsp = np.linspace(xlow[0], xupp[0], n_grid)
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# ysp = np.linspace(xlow[1], xupp[1], n_grid)
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xr, yr = np.meshgrid(xsp, ysp)
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kde_vals = np.array([kde.density( np.matrix( [xi, yi ]) ) for xi, yi in
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zip(xr.ravel(), yr.ravel())])
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plt.contour(xsp, ysp, kde_vals.reshape(n_grid, n_grid))
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plt.show()
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# 5 D case
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# random.seed(142)
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# mu = [1.0, 4.0, 3.5, -2.4, 0.0]
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# sigma = np.matrix(
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# [[ 0.6 - 0.1*abs(i-j) if i != j else 1.0 for j in xrange(5)] for i in xrange(5)])
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# x = random.multivariate_normal(mu, sigma, size = 100)
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# kern = kernel.Gaussian()
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# kde = KernelEstimate( x, kern )
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