python - 计算多元正态分布python的均值向量

Question

我无法将多元高斯分布拟合到我的数据集，更具体地说，是找到一个均值向量(或多个均值向量)。我的数据集是一个 N x 8 矩阵，目前我正在使用此代码:

muVector = np.mean(Xtrain, axis=0) 其中 Xtrain 是我的训练数据集。

对于协方差，我使用任意方差值 (.5) 构建它并执行以下操作:

covariance = np.dot(.5, np.eye(N,N) 其中 N 是观测值的数量。

但是当我构建我的 Phi 矩阵时，我得到的全是零。这是我的代码:

muVector = np.mean(Xtrain, axis=0)
# get covariance matrix from Xtrain
cov = np.dot(var, np.eye(N,N))
cov = np.linalg.inv(cov)  

# build Xtrain Phi
Phi = np.ones((N,M))
for row in range(N):
  temp = Xtrain[row,:] - muVector
  temp.shape = (1,M)
  temp = np.dot((-.5), temp)
  temp = np.dot(temp, cov)
  temp = np.dot(temp, (Xtrain[row,:] - muVector))
  Phi[row,:] = np.exp(temp)

感谢任何帮助。我想我可能必须使用 np.random.multivariate_normal()？但我不知道在这种情况下如何使用它。

Answer 1

我认为“Phi”是指您要估计的概率密度函数 (pdf)。在这种情况下，协方差矩阵应为 MxM，输出 Phi 将为 Nx1:

# -*- coding: utf-8 -*-

import numpy as np

N = 1024
M = 8
var = 0.5

# Creating a Xtrain NxM observation matrix.
# Its muVector is [0, 1, 2, 3, 4, 5, 6, 7] and the variance for all
# independent random variables is 0.5.
Xtrain = np.random.multivariate_normal(np.arange(8), np.eye(8,8)*var, N)

# Estimating the mean vector.
muVector = np.mean(Xtrain, axis=0)

# Creating the estimated covariance matrix and its inverse.
cov = np.eye(M,M)*var
inv_cov = np.linalg.inv(cov)  

# Normalization factor from the pdf.
norm_factor = 1/np.sqrt((2*np.pi)**M * np.linalg.det(cov))

# Estimating the pdf.
Phi = np.ones((N,1))
for row in range(N):
    temp = Xtrain[row,:] - muVector
    temp.shape = (1,M)
    temp = np.dot(-0.5*temp, inv_cov)
    temp = np.dot(temp, (Xtrain[row,:] - muVector))
    Phi[row] = norm_factor*np.exp(temp)

或者，您可以使用 scipy.stats.multivariate_normal 中的 pdf 方法:

# -*- coding: utf-8 -*-

import numpy as np
from scipy.stats import multivariate_normal

N = 1024
M = 8
var = 0.5

# Creating a Xtrain NxM observation matrix.
# Its muVector is [0, 1, 2, 3, 4, 5, 6, 7] and the variance for all
# independent random variables is 0.5.
Xtrain = np.random.multivariate_normal(np.arange(8), np.eye(8,8)*var, N)

# Estimating the mean vector.
muVector = np.mean(Xtrain, axis=0)

# Creating the estimated covariance matrix.
cov = np.eye(M,M)*var

Phi2 = multivariate_normal.pdf(Xtrain, mean=muVector, cov=cov)

Phi 和 Phi2 输出数组都将相等。