N维数据经验分布估计的累积概率

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import numpy as np
data = np.random.randint(1, 100, size=(1000, 4))
array([[28, 52, 91, 66],
       [78, 94, 95, 12],
       [60, 63, 43, 37],
       [81, 68, 45, 46],
       [14, 38, 91, 46],
       [37, 51, 68, 97]])
new_data = np.random.randint(1, 100, size=(1, 4))
array([[75, 24, 39, 94]])

import scipy.stats
kde = scipy.stats.gaussian_kde(data.T)
kde.pdf(new_data)

from sklearn.neighbors import KernelDensity
model = KernelDensity()
model.fit(data)
np.exp(model.score_samples(new_data))

from statsmodels.distributions.empirical_distribution import ECDF
ecdf = ECDF(data[:, 0])
ecdf(new_data[0][0])

np.random.seed(0)
data = np.random.randint(1, 100, size=(1000, 4))
new_data = np.random.randint(1, 100, size=(2, 4))
def ecdf_mv(new_data, data):
    new_data = np.atleast_2d(new_data)
    ecdf = []
    for row in new_data:
        ecdf.append((data <= row).all(1).mean())
    return np.asarray(ecdf)
ecdf_mv(new_data, data)
array([0.039, 0.002])

ecdf_mv(np.ones(4) * 100 / 2, data), 0.5**4
(array([0.067]), 0.0625)
marginal = 100 * np.ones((4, 4)) - 50 * np.eye(4)
ecdf_mv(marginal, data)
array([0.521, 0.515, 0.502, 0.54 ])

import numpy as np
def ecdf_mv(new_data, data):
    rows = np.expand_dims(new_data, axis=1)
    ecdf = (data < rows).all(axis=2).mean(axis=1)
    return np.asarray(ecdf)

from statsmodels.nonparametric.kernel_density import KDEMultivariate
def cdf_kde_mv(new_data, data, data_type):
    data_kde = KDEMultivariate(data, var_type=data_type)
    return data_kde.cdf(new_data)

import numpy as np
import matplotlib.pyplot as plt
sample_size = 10_000
bins_count= 20
sample = np.random.multivariate_normal([0, 0], [[1, 0.0], [0.0, 1]] , sample_size)
bins_edges = np.linspace(-4, 4, bins_count + 1)
bins_centers = (bins_edges[:-1] + bins_edges[1:]) / 2
X, Y = np.meshgrid(bins_centers, bins_centers)
x, y = X.ravel(), Y.ravel()
evaluation_points = np.stack([x, y], axis=1)
cummulative_probability = cdf_kde_mv(evaluation_points, sample, "cc")
# Alternatively:
cummulative_probability = ecdf_mv(evaluation_points, sample)
cummulative_probability = cummulative_probability.reshape(bins_count, bins_count)
# Plotting
fig = plt.figure(figsize=(10, 10), constrained_layout=True)
ax = fig.add_subplot(projection='3d')
ax.view_init(elev=20., azim=-135)

N维数据经验分布估计的累积概率

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