python - 绘制从多峰分布确定的单峰分布

Question

我使用GaussianMixture来分析多峰分布。从 GaussianMixture 类中，我可以使用属性means_和访问均值和协方差covariances_。我现在如何使用它们来绘制两个潜在的单峰分布？

我想过使用scipy.stats.norm但我不知道该选择什么作为loc和的参数scale。所需的输出将类似于附图所示。

这个问题的示例代码是从这里的答案修改的。

import numpy as np
import matplotlib.pyplot as plt
from sklearn import mixture
from scipy.stats import norm

ls = np.linspace(0, 60, 1000)
multimodal_norm = norm.pdf(ls, 0, 5) + norm.pdf(ls, 20, 10)
plt.plot(ls, multimodal_norm)

# concatenate ls and multimodal to form an array of samples
# the shape is [n_samples, n_features]
# we reshape them to create an additional axis and concatenate along it
samples = np.concatenate([ls.reshape((-1, 1)), multimodal_norm.reshape((-1,1))], axis=-1)
print(samples.shape)

gmix = mixture.GaussianMixture(n_components = 2, covariance_type = "full")
fitted = gmix.fit(samples)

print(fitted.means_)
print(fitted.covariances_)

# The idea is something like the following (not working):
new_norm1 = norm.pdf(ls, fitted.means_, fitted.covariances_)
new_norm2 = norm.pdf(ls, fitted.means_, fitted.covariances_)
plt.plot(ls, new_norm1, label='Norm 1')
plt.plot(ls, new_norm2, label='Norm 2')

标签： pythondistributiongaussianmultimodal

Answer 1

目前尚不清楚您要完成什么。您正在将 GaussianMixture 模型拟合到在均匀网格上采样的两个高斯的 pdf 值的总和以及 unifrom 网格本身的串联。这不是要拟合高斯混合模型的方式。通常，将模型拟合到从某个分布中抽取的随机观察值（通常未知，但可能是模拟的）。

让我假设您希望将 GaussianMixture 模型拟合到从 Gaussian Mixture 分布中抽取的样本。假设您知道预期结果是什么，可以测试拟合效果如何。这是执行此操作的代码，用于模拟正确的分布和拟合模型。它打印从样本中恢复的拟合参数——我们观察到它们确实接近我们用来模拟样本的参数。最后生成适合数据的 GaussianMixture 分布的密度图

import numpy as np
import matplotlib.pyplot as plt
from sklearn import mixture
from scipy.stats import norm

# set simulation parameters
mean1, std1, w1 = 0,5,0.5
mean2, std2, w2 = 20,10,1-w1

# simulate constituents
n_samples = 100000
np.random.seed(2021)
gauss_sample_1 = np.random.normal(loc = mean1,scale = std1,size = n_samples)
gauss_sample_2 = np.random.normal(loc = mean2,scale = std2,size = n_samples)
binomial = np.random.binomial(n=1, p=w1, size = n_samples)

# simulate gaussian mixture
mutlimodal_samples = (gauss_sample_1 * binomial + gauss_sample_2 * (1-binomial)).reshape(-1,1)

# define and fit the mixture model
gmix = mixture.GaussianMixture(n_components = 2, covariance_type = "full")
fitted = gmix.fit(mutlimodal_samples)

print('fitted means:',fitted.means_[0][0],fitted.means_[1][0])
print('fitted stdevs:',np.sqrt(fitted.covariances_[0][0][0]),np.sqrt(fitted.covariances_[1][0][0]))
print('fitted weights:',fitted.weights_)

# Plot component pdfs and a joint pdf
ls = np.linspace(-50, 50, 1000)
new_norm1 = norm.pdf(ls, fitted.means_[0][0], np.sqrt(fitted.covariances_[0][0][0]))
new_norm2 = norm.pdf(ls, fitted.means_[1][0], np.sqrt(fitted.covariances_[1][0][0]))
multi_pdf = w1*new_norm1 + (1-w1)*new_norm2
plt.plot(ls, new_norm1, label='Norm pdf 1')
plt.plot(ls, new_norm2, label='Norm pdf 2')
plt.plot(ls, multi_pdf, label='multi-norm pdf')
plt.legend(loc = 'best')
plt.show()

结果是

fitted means: 22.358448018824642 0.8607494960575028
fitted stdevs: 8.770962351118127 5.58538485134623
fitted weights: [0.42517515 0.57482485]

正如我们所见，它们与模拟中的内容很接近（取决于它们的顺序，当然模型无法恢复，但无论如何它都无关紧要）：

mean1, std1, w1 = 0,5,0.5
mean2, std2, w2 = 20,10,1-w1

以及密度及其部分的图。回想一下，GaussianMixture 的 pdf不是pdf的总和，而是带有权重的加权平均值w1, 1-w1：