Bayesian Models for Machine Learning (in English)

• 26 hrs lectures
• 13 hrs exercises
• 13 hrs projects

• 51 pts final exam
• 24 pts mid-term test
• 25 pts projects

To demonstrate the limitations of Deep Neural Nets (DNN) that have become a very popular machine learning tool successful in many areas, but that excel only when sufficient amount of well annotated training data is available. To present Bayesian models (BMs) allowing to make robust decisions even in cases of scarce training data as they take into account the uncertainty in the model parameter estimates. To introduce the concept of latent variables making BMs modular (i.e. more complex models can be built out of simpler ones) and well suitable for cases with missing data (e.g. unsupervised learning when annotations are missing). To introduce basic skills and intuitions about the BMs and to develop more advanced topics such as: approximate inference methods necessary for more complex models, infinite mixture models based on non-parametric BMs, or Auto-Encoding Variational Bayes. The course is taught in English.

Nothing in life is given for sure. The uncertainty is accompanying us also in machine learning, classification and recognition - in the basic courses, youll learn how to train parameters of Gaussian models or neural networks. But are they correct? Can we be sure about the result? How about if the model is deployed on data different from the training ones? The BAY course will teach you not to trust anything and express everything as probability distributions rather than hard numbers. You will enjoy lots of maths, but if you are serious about machine learning, you cant consider it just as "connecting black boxes". You need a solid mathematical background.

• C. Bishop: Pattern Recognition and Machine Learning, Springer, 2006
• P Orbanz: Tutorials on Bayesian Nonparametrics: http://stat.columbia.edu/~porbanz/npb-tutorial.html

1. Probability theory and probability distributions 
2. Inference in Bayesian Networks
3. Markov Random Fields, Factor graphs, Belief Propagation
4. Expectation-Maximization algorithm (with application to Gaussian Mixture Model) 
5. Bayesian Inference (priors, uncertainty of the parameter estimates, posterior predictive probability) 
6. Inference in Bayesian models with conjugate priors
7. Variational Bayes inference, Mean-field approximation
8. Approximate inference in Bayesian models using Gibbs sampling 
9. Collapsed Gibbs sampling based inference for Bayesian Gaussian Mixture Model
10. Infinite mixture models, Dirichlet Process, Chinese Restaurant Process
11. Pitman-Yor Process for Language modeling

Lectures will be immediately followed by demonstration exercises where examples in Python will be presented. Code and data of all demonstrations will be made available to the students and will constitute the basis for the project.

The project will follow on the demonstration exercises and will make the student work on provided (simulated or real) data. The students will work in teams in "evaluation" mode and present their results at the final lecture/exercise.

• Half-semestral exam (24pts)  
• Submission and presentation of project (25pts) 
• Semestral exam, 51pts.