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.


27.02.2012 16.00 B123
Vuosi Lukukausi Päivämäärä Periodi Kieli Vastuuhenkilö
2012 kevät 17.01-23.02. 3-3 Englanti Pekka Parviainen


Aika Huone Luennoija Päivämäärä
Ti 16-18 D122 Pekka Parviainen 17.01.2012-23.02.2012
To 16-18 D122 Pekka Parviainen 17.01.2012-23.02.2012


Group: 1
Aika Huone Ohjaaja Päivämäärä Huomioitavaa
To 14-16 B119 Teppo Niinimäki 23.01.2012—24.02.2012

Information for international students

The course will be held in English.


This course belongs to the Algorithms and Machine Learning sub-pogramme in the Master's programme of the department, and together with 582637 Project in Probabilistic Models (2 cr), it forms one of the three optional courses of the sub-programme.

For students in the old Intelligent Systems specialisation area: this course replaces, together with the project work 582637 Project in Probabilistic Models  (2 cr), the course Three Concepts: Probability (6 cr).

The format of the course in Spring 2012 follows roughly the format of the course in 2011.

The course is an introductory course, and only elementary knowledge on probability theory is required as a prerequisite. Different parts of the course, however, have different requirements with respect to the mathematical machinery needed to apply the concepts in question. Typically some analysis and elementary mathematical statistics is required. At the very least we assume that the participants are familiar with topics covered in the courses 582630 Design and analysis of algorithms (4 cr) and 582631 Introduction to machine learning (4 cr).

Kurssin suorittaminen

There will be weekly exercises and a final exam. Solutions to the weekly exercises need to be delivered to the course assistant before each exercise session (by paper or by email).

The maximum number of points that can be earned from the exercises is 12 and from the course exam 48, so the total maximum is 60 points (and you need 30 points in total and 24 points from the exam to pass the course). The course exam will be held on 27.2. 16.00-18.30 (a calculator is allowed but no other electronic devices or written material).

Grades are now available.

Please give feedback (especially verbal comments are welcome).


Lecture Schedule

Tue 17.1. Overview of the course, administrative issues. Lecture notes I: 1-40.

Thu 19.1. Refresher in probability. Lecture notes II: 1-28.

Tue 24.1. Bayesian inference. Lecture notes III:1-46.

Thu 26.1. Bayesian inference continues (Lecture notes III:47-53). The Bayesian network representation. Lecture notes IV:1-19 (updated 2.2.)

Tue 31.1. The Bayesian network representation (Lecture notes IV:20-37) .

Thu 2.2. The Bayesian network representation (Lecture notes IV:38-55).

Tue 7.2. Inference in Bayesian networks. Lecture notes V: 1-27 (updated 15.2.).

Thu 9.2. Inference in Bayesian networks. Lecture notes V:28-47, Lecture notes VI:1-3 (updated 15.2.).

Tue 14.2. Inference in Bayesian networks continues (Lecture notes VI:4-24).

Thu 16.2. Inference in Bayesian networks continues; Lecture notes VII:1-16.  Learning Bayesian networks; Lecture notes VIII:1-21 (updated 23.2.).

Tue 21.2. Learning Bayesian networks continues. Lecture notes IX:1-22 (updated 23.2.).

Thu 23.2. Learning Bayesian networks continues (Lecture notes IX:23-39).



Thu 26.1. Exercises and solutions (fixed 30.1.)

Thu 2.2. Exercises and solutions

Thu 9.2. Exercises and solutions

Thu 16.2. Exercises and solutions

Thu 23.2. Exercises and solutions (problem 5 fixed 27.2.)



Kirjallisuus ja materiaali

The primary material is the lectures notes. All lecture notes in one file.

Additional material: