Bayesian Methods for Machine Learning

Welcome to first week of our course! Today we will discuss what bayesian methods are and what are probabilistic models. We will see how they can be used to model real-life situations and how to make conclusions from them. We will also learn about conjugate priors — a class of models where all math becomes really simple.

This week we will about the central topic in probabilistic modeling: the Latent Variable Models and how to train them, namely the Expectation Maximization algorithm. We will see models for clustering and dimensionality reduction where Expectation Maximization algorithm can be applied as is. In the following weeks, we will spend weeks 3, 4, and 5 discussing numerous extensions to this algorithm to make it work for more complicated models and scale to large datasets.

This week we will move on to approximate inference methods. We will see why we care about approximating distributions and see variational inference — one of the most powerful methods for this task. We will also see mean-field approximation in details. And apply it to text-mining algorithm called Latent Dirichlet Allocation.

This week we will learn how to approximate training and inference with sampling and how to sample from complicated distributions. This will allow us to build simple method to deal with LDA and with Bayesian Neural Networks — Neural Networks which weights are random variables themselves and instead of training (finding the best value for the weights) we will sample from the posterior distributions on weights.

Welcome to the fifth week of the course! This week we will combine many ideas from the previous weeks and add some new to build Variational Autoencoder -- a model that can learn a distribution over structured data (like photographs or molecules) and then sample new data points from the learned distribution, hallucinating new photographs of non-existing people. We will also the same techniques to Bayesian Neural Networks and will see how this can greatly compress the weights of the network without reducing the accuracy.

Welcome to the final week of our course! This time we will see nonparametric Bayesian methods. Specifically, we will learn about Gaussian processes and their application to Bayesian optimization that allows one to perform optimization for scenarios in which each function evaluation is very expensive: oil probe, drug discovery and neural network architecture tuning.