Title:  Bayesian Models for Machine Learning (in English) 

Code:  BAYa 

Ac.Year:  2019/2020 

Sem:  Winter 

Curriculums:  

Language of Instruction:  English 

News:  Em., 20190717, an information for Erasmus+ students: BAYa is a highly demanding, mathematicallyoriented course. Solid
background knowledge in the basics of machine learning (at least at the
level of FIT's IKR course, see http://www.fit.vutbr.cz/study/coursel.php.en?id=12754) and statistics is required
for its successful completion. 

Credits:  5 

Completion:  examination 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  26  13  0  0  13 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  51  24  0  0  25 



Guarantor:  Burget Lukáš, doc. Ing., Ph.D. (DCGM) 

Deputy guarantor:  Černocký Jan, doc. Dr. Ing. (DCGM) 

Lecturer:  Burget Lukáš, doc. Ing., Ph.D. (DCGM) 
Instructor:  Baskar Murali K. (DCGM) Diez Sánchez Mireia, M.Sc., Ph.D. (DCGM) Ondel Lucas, Mgr. (DCGM) 

Faculty:  Faculty of Information Technology BUT 

Department:  Department of Computer Graphics and Multimedia FIT BUT 

Schedule: 



Learning objectives: 

  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 nonparametric BMs, or AutoEncoding Variational Bayes. The course is taught in English. 
Description: 

  Probability theory and probability distributions, Bayesian Inference, Inference in Bayesian models with conjugate priors, Inference in Bayesian Networks, ExpectationMaximization algorithm, Approximate inference in Bayesian models using Gibbs sampling, Variational Bayes inference, Stochastic VB, Infinite mixture models, Dirichlet Process, Chinese Restaurant Process, PitmanYor Process for Language modeling, Expectation propagation, Gaussian Process, AutoEncoding Variational Bayes, Practical applications of Bayesian inference 
Why is the course taught: 

  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. 
Syllabus of lectures: 

  Probability theory and probability distributions
 Bayesian Inference (priors, uncertainty of the parameter estimates, posterior predictive probability)
 Inference in Bayesian models with conjugate priors
 Inference in Bayesian Networks (loopy belief propagation)
 ExpectationMaximization algorithm (with application to Gaussian Mixture Model)
 Approximate inference in Bayesian models using Gibbs sampling
 Variational Bayes inference, Stochastic VB
 Infinite mixture models, Dirichlet Process, Chinese Restaurant Process
 PitmanYor Process for Language modeling
 Expectation propagation
 Gaussian Process
 AutoEncoding Variational Bayes
 Practical applications of Bayesian inference

Syllabus of numerical exercises: 

 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. 
Syllabus  others, projects and individual work of students: 

 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. 
Fundamental literature: 

  C. Bishop: Pattern Recognition and Machine Learning, Springer, 2006
 S. J. Gershman and D.M. Blei: A tutorial on Bayesian nonparametric models, Journal of Mathematical Psychology, 2012.
 P Orbanz: Tutorials on Bayesian Nonparametrics: http://stat.columbia.edu/~porbanz/npbtutorial.html
 D.P. Kingma, M. Welling: AutoEncoding Variational Bayes, ICLR, Banff, 2014

Study literature: 

  C. Bishop: Pattern Recognition and Machine Learning, Springer, 2006
 S. J. Gershman and D.M. Blei: A tutorial on Bayesian nonparametric models, Journal of Mathematical Psychology, 2012.
 P Orbanz: Tutorials on Bayesian Nonparametrics: http://stat.columbia.edu/~porbanz/npbtutorial.html
 D.P. Kingma, M. Welling: AutoEncoding Variational Bayes, ICLR, Banff, 2014

Progress assessment: 

   Halfsemestral exam (24pts)
 Submission and presentation of project (25pts)
 Semestral exam, 51pts.

