Contents

1. Statistics
2. Gaussian
3. Multivariate Gaussian
4. Gaussian Mixture Model
5. Multivariate Gaussian Mixture Model
6. Conditional Gaussian Mixture Model

Dependencies

The required dependencies are Python 3.8, Numpy, Pandas, Matplotlib, TensorFlow, and Tensorflow-Probability.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
import scipy
import tensorflow as tf
import tensorflow_probability as tfp
tfd = tfp.distributions

Statistics

The statistics required are: mean, covariance, diagonal, and standard deviation. We first generate X, a 2D array, then use the Numpy methods to compare statistics against the parameters used.

np.random.seed(0)  # random seed

mu = [0,1]
cov = [[2,0],
       [0,2]]
X = np.random.multivariate_normal(mu, cov, size=100)
X_mean = np.mean(X, axis=0)
X_cov = np.cov(X, rowvar=0)
X_diag = np.diag(X_cov)
X_stddev = np.sqrt(X_diag)
# X_mean
[-9.57681805e-04  1.14277867e+00]
# X_cov
[[ 1.05494742 -0.02517201]
 [-0.02517201  1.04230397]]
# X_diag
[1.05494742 1.04230397]
# X_stddev
[1.02710633 1.02093289]

Notice that the values of mean and covariance computed from X are comparable to the parameters specified to generate X. np.cov uses the parameter rowvar=0 to convert rows of samples into rows of variables to compute the covariance matrix. np.diag obtains the diagonal, which is the variances from a covariance matrix. np.sqrt will obtain the standard deviations of the diagonal.

#tensorflow