The Trivial Intro

The Gaussian distribution is one of the most widely used continuous distribution with applications in many fields. It has several other names like normal distribution, bell curve. The density function with mean $\mu$ and variance $\sigma^2$ is given by: $$ f(x\vert \mu,\sigma^2)= \frac{1}{\sqrt{2\pi \sigma^2}}\exp^{\frac{-(x-\mu)^2}{2\sigma^2}} $$

Assume we are given some dataset X with n features or variables and N number of data points. Letters in bold (x) denote vectors and the others are scalars.

This post considers only the approximate inference algorithms that are based on optimization.This is only an overview of such algorithms.