Probabilistic Models

Algoritmit ja koneoppiminen
Syventävät opinnot
This course provides an introduction to probabilistic modeling from a computer scientist"s perspective. Many of the research issues in Artificial Intelligence, Computational Intelligence and Machine Learning/Data Mining can be viewed as topics in the "science of uncertainty," which addresses the problem of optimal processing of incomplete information, i.e., plausible inference, and this course shows how the probabilistic modeling framework forms a theoretically elegant and practically useful solution to this problem. The course focuses on the "degree-of-belief" interpretation of probability and illustrates the use of Bayes" Theorem as a general rule of belief-updating. As a concrete example of methodological tools based on this approach, we will study probabilistic graphical models focusing in particular on (discrete) Bayesian networks, and on their applications in different probabilistic modeling tasks.


02.03.2015 16.00 B123
Vuosi Lukukausi Päivämäärä Periodi Kieli Vastuuhenkilö
2015 kevät 13.01-26.02. 3-3 Englanti Sotiris Tasoulis


Aika Huone Luennoija Päivämäärä
Ti 16-18 D122 Sotiris Tasoulis 13.01.2015-26.02.2015
To 16-18 D122 Sotiris Tasoulis 13.01.2015-26.02.2015


Group: 1
Aika Huone Ohjaaja Päivämäärä Huomioitavaa
Ke 16-18 B222 Quan Nguyen 19.01.2015—27.02.2015





You may use one A4 sheet of handwritten notes.

You may use a calculator, but you may not use a cell phone, laptop, etc.



Please see the course syllabus.


The course learning objectives are available here.


A (tentative) detailed description of the lectures is available here.


A (tentative) set of objectives for each of the exercise sets is available here.


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Kirjallisuus ja materiaali

Materials for Class

Tuesday, January 13: Introduction to Probabilistic Models, Slides

Thursday, January 15: Refresher on Probability Theory, Slides

Note: Kevin deLaplante ( has many more introductory videos that may be helpful.


Tuesday, January 20: Bayesian Networks, Slides, Handout


Thursday, January 22: Special Models (Naive Bayes), Slides

Tuesday, January 27 - Thursday, January 29 : Special Models (Hidden Markov Models), Slides

Tuesday,  February 3 - Thursday, February 5 : Inference by Factors Elimination, Slides1, Slides2

Thursday, February 12: Multinomial Parameter Estimation, Slides


Tuesday, February 17: Learning with incomplete data, Slides


Thursday, February 19 - Tuesday, February 24: Scoring Functions for Structure Learning, Lecture Notes, Slides


Lab Exercises

Exercise grades

Wednesday, January 21: Foundations of Probability

Wednesday, January 28: Bayesian Networks

Wednesday, February 4: Naive Bayes Classifiers and Hidden Markov Models

Wednesday, February 11: Inference by Factors Elimination

Wednesday, February 18: Inference with Jointrees and Parameter Estimation with Complete Data

LaTex References

The Wikibook on LaTex is quite thorough and well organized.  In particular, the Mathematics section may be helpful.

Stack Overflow and the relevant section in Stack Exchange are also good resources, although it is often easiest to search using Google.

Additional Material