stats

class snippets.stats.GaussianKernelDensity(bandwidth: float | str | None = None, bounds: ndarray | None = None)

Gaussian kernel density estimator.

The implementation employs gaussian_kde to facilitate more sophisticated kernel covariances than supported by KernelDensity which only admits isotropic kernels.

Parameters:

• bandwidth – Bandwidth selection method or scalar factor (see gaussian_kde for details).

• bounds – Array of lower and upper bounds for each dimension (use nan for unbounded or semi-bounded domains). Test samples are reflected at the supplied boundaries as part of score_samples() to account for probability mass that has “leaked out of” the support (see Boneva et al. (1971) for details).

Example

from matplotlib import pyplot as plt
import numpy as np
from sklearn.neighbors import KernelDensity
from snippets.stats import GaussianKernelDensity

fig, axes = plt.subplots(2, 2, sharex="row", sharey="row")

# One-dimensional bounds.
x = np.random.uniform(0, 1, (10_000, 1))
kdes = [
    GaussianKernelDensity(),
    GaussianKernelDensity(bounds=[0, 1]),
]
lin = np.linspace(0, 1)
for ax, kde in zip(axes[0], kdes):
    kde.fit(x)
    ax.plot(lin, np.exp(kde.score_samples(lin[:, None])))

# Two-dimensional bounds.
x = np.random.uniform(0, 1, (10_000, 2))
kdes = [
    GaussianKernelDensity(),
    GaussianKernelDensity(bounds=[[0, 1], [0, 1]]),
]
lin = np.linspace(0, 1)
xx, yy = np.meshgrid(lin, lin)
xy = np.stack([xx, yy], axis=-1).reshape((-1, 2))
for ax, kde in zip(axes[1], kdes):
    kde.fit(x)
    score = kde.score_samples(xy).reshape(xx.shape)
    im = ax.imshow(np.exp(score), extent=(0, 1, 0, 1))
    fig.colorbar(im, ax=ax)

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