Python中的多变量核密度估计

Question

我正在尝试使用SciPy的gaussian_kde函数来估计多变量数据的密度.在我的下面的代码中,我采样了一个3D多元法线并且符合内核密度,但我不确定如何评估我的拟合.

import numpy as np
from scipy import stats

mu = np.array([1, 10, 20])
sigma = np.matrix([[4, 10, 0], [10, 25, 0], [0, 0, 100]])
data = np.random.multivariate_normal(mu, sigma, 1000)
values = data.T
kernel = stats.gaussian_kde(values)

我看到了这个,但不知道如何将它扩展到3D.

还不确定我怎么开始评估拟合密度？我如何想象这个？

Answer 1

您可以通过多种方式在3D中显示结果.

最简单的方法是在用于生成高斯KDE的点处评估高斯KDE,然后通过密度估计对点进行着色.

例如:

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

mu=np.array([1,10,20])
sigma=np.matrix([[4,10,0],[10,25,0],[0,0,100]])
data=np.random.multivariate_normal(mu,sigma,1000)
values = data.T

kde = stats.gaussian_kde(values)
density = kde(values)

fig, ax = plt.subplots(subplot_kw=dict(projection='3d'))
x, y, z = values
ax.scatter(x, y, z, c=density)
plt.show()

如果您有一个更复杂的(即不是全部位于平面中)分布,那么您可能想要在常规3D网格上评估KDE并可视化体积的等值面(3D轮廓).最简单的方法是使用Mayavi进行可视化:

import numpy as np
from scipy import stats
from mayavi import mlab

mu=np.array([1,10,20])
# Let's change this so that the points won't all lie in a plane...
sigma=np.matrix([[20,10,10],
                 [10,25,1],
                 [10,1,50]])

data=np.random.multivariate_normal(mu,sigma,1000)
values = data.T

kde = stats.gaussian_kde(values)

# Create a regular 3D grid with 50 points in each dimension
xmin, ymin, zmin = data.min(axis=0)
xmax, ymax, zmax = data.max(axis=0)
xi, yi, zi = np.mgrid[xmin:xmax:50j, ymin:ymax:50j, zmin:zmax:50j]

# Evaluate the KDE on a regular grid...
coords = np.vstack([item.ravel() for item in [xi, yi, zi]])
density = kde(coords).reshape(xi.shape)

# Visualize the density estimate as isosurfaces
mlab.contour3d(xi, yi, zi, density, opacity=0.5)
mlab.axes()
mlab.show()