EM Algorithm Explained: Estimating Parameters in Gaussian Mixture Models (with Python)

In this video, we break down the Expectation-Maximization (EM) algorithm by solving a specific two-step experiment. We start with a uniform discrete random variable $y$ and a Gaussian random variable $x$ dependent on $y$, where the mean parameter $\mu$ is unknown. What we cover:The Theory: Understanding the Latent Variable ($y$) and the Observed Data ($x$).E-Step (Expectation): How to calculate the posterior probability of the latent variables given our current estimate of $\mu$.M-Step (Maximization): How to update $\mu$ to maximize the expected log-likelihood.Python Implementation: A full walkthrough of the code to estimate $\mu$ from $n$ independent samples using an iterative approach. Problem Statement:Sample $y \in \{1, 2, 3\}$ uniformly.Sample $x \sim N(y\mu, 1)$.Goal: Estimate $\mu$ from samples $x_1, \dots, x_n$.This is a classic example of a Gaussian Mixture Model (GMM) simplified for learning. Whether you are studying for a Data Science interview or a Machine Learning exam, this walkthrough will help clarify how EM converges to a solution.