How to code Gaussian Mixture Models from scratch in Python

In the realm of unsupervised learning algorithms, Gaussian Mixture Models or GMMs are special citizens. GMMs are based on the assumption that all data points come from a fine mixture of Gaussian distributions with unknown parameters. They are parametric generative models that attempt to learn the true data distribution. Hence, once we learn the Gaussian parameters, we can generate data from the same distribution as the source. We can think of GMMs as the soft generalization of the K-Means clustering algorithm.