Multivariate Gaussian distributions are widely used in machine learning. However, that distributions are not easily understood. This post covers how to visualize 2d multivariate distributions with python. 3D Gaussian Distribution can help you to understand that easily. Case I (independent) \begin{align}Let \, \mu_x= \begin{bmatrix}0 \\ 0\\ \end{bmatrix}, cov =R= \begin{bmatrix}1 & 0\\ 0 & 1\\ \end{bmatrix}\end {align} In this case we know multivariate Gaussian distribution is given by p(x)=\frac{1}{\sqrt{(2\pi)^n}det R} exp(-\frac{1}{2}(x-\mu_x)^TR^{-1}(x-\mu_x)) . The result represents the result when both x_1 and x_2 are independent probabilities. The shape of a circle indicates that the probabilities are randomly distributed. The shape relates to off-diagonal matrix elements. 3d surface indicates probability of combination of two variables such as (0,1), (0,0)-Very high, or (2,2)-very low. Let’s think second case (off-diagonal elements is not zero) Case II The def...
