= Lecture “Bayesian Learning” =


== General Information ==

|| Lecture || Thursdays 14-16 ('''22.10, 29.10, 5.11.2015, 7.1, 14.1, 21.1.2016''') ||
|| Room || MAR 4.062 ||
|| Teachers || Shinichi Nakajima ||
|| Contact || nakajima@tu-berlin.de ||
|| Language || English ||
|| Credits || 3 ECTS, Elective Course in Machine Learning Module I (computer science M.Sc.)||


== Topics ==

Bayesian learning is a category of machine learning methods, which are based on a basic law of probability, called Bayes’ theorem.  As advantages, Bayesian learning offers assessment of the estimation quality and model selection functionality in a single framework, while as disadvantages, it requires “integral” computation, which often is a bottleneck.  In this course, we introduce Bayesian learning, discuss pros and cons, how to perform the integral computation based on “conjugacy”, and how to approximate Bayesian learning when it is intractable.

The course covers
 * Bayesian modeling and model selection.
 * Bayesian learning in conjugate cases.
 * Approximate Bayesian learning in conditionally conjugate cases:
  * Gibbs sampling
  * variational Bayesian learning.
 * Approximate Bayesian learning in non-conjugate cases:
  * Metropolis-Hastings algorithm.
  * local variational approximation.
  * expectation propagation.

The lecture will be given on a blackboard.

Introduction[[attachment:BayesianLearningIntroduction.pdf]].

Variational Bayesian learning [[attachment:VariationalBayes.pdf]].

Markov chain Monte Carlo [[attachment:MCMC_short.pdf]].

Summary [[attachment:Summary.pdf]].

== Homeworks ==

The students who need credits must do homeworks by the due dates.

 * Homework 1 '''(modified on 9.12.2015)''': [[attachment:BayesianLearning_HW1.pdf]]  [[attachment:data.txt]] (due date: '''7.1.2016''')
 * Homework 2: [[attachment:BayesianLearning_HW2.pdf]]  [[attachment:data2.txt]]  [[attachment:initial.txt]] (due date: '''18.2.2016''')