scikit-learn：如何使用拟合概率模型？

Question

所以我已经使用scikit-learn的Gaussian mixture models(http://scikit-learn.org/stable/modules/mixture.html)来拟合我的数据，现在我想使用模型，我该怎么做呢？具体来说：

1. 如何绘制概率密度分布？
2. 如何计算拟合模型的均方误差？

这是您可能需要的代码：

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from sklearn import mixture
import matplotlib as mpl

from matplotlib.patches import Ellipse
%matplotlib inline

n_samples = 300

# generate random sample, two components
np.random.seed(0)
shifted_gaussian = np.random.randn(n_samples, 2) + np.array([20, 5])
sample= shifted_gaussian 

# fit a Gaussian Mixture Model with two components
clf = mixture.GMM(n_components=2, covariance_type='full')
clf.fit(sample)

# plot sample scatter
plt.scatter(sample[:, 0], sample[:, 1])

# 1. Plot the probobility density distribution
# 2. Calculate the mean square error of the fitting model

更新： 我可以通过以下方式绘制分布：

x = np.linspace(-20.0, 30.0)
y = np.linspace(-20.0, 40.0)
X, Y = np.meshgrid(x, y)
XX = np.array([X.ravel(), Y.ravel()]).T
Z = -clf.score_samples(XX)[0]
Z = Z.reshape(X.shape)

CS = plt.contour(X, Y, Z, norm=LogNorm(vmin=1.0, vmax=1000.0),
                 levels=np.logspace(0, 3, 10))
CB = plt.colorbar(CS, shrink=0.8, extend='both')

但这不是很奇怪吗？有没有更好的办法呢？我可以画这样的东西吗？

Answer 1

我认为结果是合理的，如果你稍微调整一下xlim和ylim：

# plot sample scatter
plt.scatter(sample[:, 0], sample[:, 1], marker='+', alpha=0.5)

# 1. Plot the probobility density distribution
# 2. Calculate the mean square error of the fitting model
x = np.linspace(-20.0, 30.0, 100)
y = np.linspace(-20.0, 40.0, 100)
X, Y = np.meshgrid(x, y)
XX = np.array([X.ravel(), Y.ravel()]).T
Z = -clf.score_samples(XX)[0]
Z = Z.reshape(X.shape)

CS = plt.contour(X, Y, Z, norm=LogNorm(vmin=1.0, vmax=10.0),
                 levels=np.logspace(0, 1, 10))
CB = plt.colorbar(CS, shrink=0.8, extend='both')
plt.xlim((10,30))
plt.ylim((-5, 15))