Python中的多元核密度估计 [英] Multivariate kernel density estimation in Python

问题描述

我正在尝试使用 SciPy 的 gaussian_kde 函数来估计多元数据的密度.在我下面的代码中，我采样了一个 3D 多元法线并拟合了核密度，但我不确定如何评估我的拟合.

I am trying to use SciPy's gaussian_kde function to estimate the density of multivariate data. In my code below I sample a 3D multivariate normal and fit the kernel density but I'm not sure how to evaluate my fit.

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)

我看到了这个但不确定如何将其扩展到 3D.

I saw this but not sure how to extend it to 3D.

我也不确定如何开始评估拟合密度?我如何将其形象化?

Also not sure how do I even begin to evaluate the fitted density? How do I visualize this?

推荐答案

您可以通过多种方式在 3D 中可视化结果.

There are several ways you might visualize the results in 3D.

最简单的方法是在用于生成它的点处评估高斯 KDE，然后通过密度估计为点着色.

The easiest is to evaluate the gaussian KDE at the points that you used to generate it, and then color the points by the density estimate.

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()

如果您有更复杂的分布(即并非全部位于平面内)，那么您可能希望在常规 3D 网格上评估 KDE 并可视化体积的等值面(3D 轮廓).使用 Mayavi 进行可视化最简单:

If you had a more complex (i.e. not all lying in a plane) distribution, then you might want to evaluate the KDE on a regular 3D grid and visualize isosurfaces (3D contours) of the volume. It's easiest to use Mayavi for the visualiztion:

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()

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