8 Probability 2: Maximum Likelihood, Gaussian Mixture Models and Expectation Maximization (MLVU2019)
Channel: MLVU
Date: 2019-03-01

slides: https://mlvu.github.io/lectures/42.ProbabilisticModels2.annotated.pdf
course materials: https://mlvu.github.io

We return to the subject of probability, focusing this time on density estimation: how do we fit a probability distribution to our data. We show how the complicated functions defining the probability density functions of normal distributions come about, and how to work out maximum likelihood estimators for their parameters. We also introduce the Gaussian Mixture Model, a distribution that is the sum of multiple normals. Since the parameters of this model cannot be fit analytically, we discuss, the Expectation Maximization algorithm, which will help us search for a good fit.

Errors: 
- slide 12 is missing a minus in the exponent.
- In slide 40, the weights should sum to 1.