## 582636 Probabilistic Models (4 cr) / Todennäköisyysmallit (4 op), Spring 2009

**N.B. Lectures in Finnish this year!**Luennoidaan suomeksi, materiaali on englanniksi.

### News

- 25.02.2009: Solution to Exercise 12 CORRECTED.
- 24.02.2009: Example solutions to exercises 8-12 are out.
- 23.02.2009: The script "auto-bcourse.py" was modified to make it work properly on Windows. Thanks to Davin Wong for pointing this out.
- 22.02.2009: The deadline of the home assignment was extended to the morning of Tue March 3rd.

### Lectures

13.01.-19.02.: Tue, Thu 16-18 in B222

Course instructor: Prof. Petri Myllymäki

### Introduction

This is a new course belonging to the new Algorithms and Machine Learning sub-pogramme in the Master's programme of the department, and together with*582637 Project in probability 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 Todennäköisyysmallien harjoitustyö (2 cr), the course Three Concepts: Probability (6 cr).

### Course Description

This course provides an introduction to issues in probability theory from a computer scientist's perspective. Many of the research issues in Artificial Intelligence, Computational Intelligence and Data Mining can be actually viewed as topics in the "science of uncertainty," which addresses the problem of optimal processing of incomplete information, i.e., plausible inference. The first part of the course introduces the use of probability for plausible inference. After a brief introduction to frequentist inference, 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. The theoretical framework will be applied for simple probabilistic modeling example tasks taken from examples in machine learning or data mining. The second part of the course is an introduction to graphical models (in particular Bayesian networks) used in such modeling tasks, and also introduces some of the software available for probabilistic modeling.### Exercises

There will be exercises that will be discussed in connection with the lectures (no separate meeting times for this). A larger home assignment is to be delivered after the course exam.In the next period there will be a separate project work course 582637 Todennäköisyysmallien harjoitustyö (2 cr) with more involved hands-on empirical work on the subject.

### Prerequisites

The course is an introductory course, and only elementary knowledge on probability theory is required. 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. 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)*.

### Course schedule

Tue 13.01.2009, 16-18: | First meeting, administrative issues, introduction of the course |

Thu 15.01.2009, 16-18: | First set of lecture notes. |

Tue 20.01.2009, 16-18: | Second set of lecture notes, introduction to exercises 1-3. |

Thu 22.01.2009, 16-18: | Exercises 1-3 (session supervised by Dr. Teemu Roos) |

Tue 27.01.2009, 16-18: | Third set of lecture notes. |

Thu 29.01.2009, 16-18: | Third set of lecture notes continued. Fourth set of lecture notes started. |

Tue 03.02.2009, 16-18: | The fourth set continued. |

Thu 05.02.2009, 16-18: | The fourth set continued, the fifth set started |

Tue 10.02.2009, 16-18: | Fifth set continued. |

Thu 12.02.2009, 16-18: | Exercises 4-7. |

Tue 17.02.2009, 16-18: | Fifth set continued. |

Thu 19.02.2009, 16-18: | Exercises 8-12 |

Fri 27.02.2009, 9-12: | Course exam. |

Tue 03.03.2009, 8:00: | Deadline for the home assignment |

### Material

The primary material is the lectures notes (not available yet, but check out the notes of the Three concepts: probability course in 2008 and 2007).- First set of lecture notes.
- Second set of lecture notes.
- Third set of lecture notes.
- Fourth set of lecture notes.
- Fifth set of lecture notes

- B-Course
- Stuart Russell and Peter Norvig, Artificial Intelligence: A Modern Approach. Chapters 13, 14, (15, optional), 20.1-20.3
- Myllymäki & Tirri, Bayes-verkkojen mahdollisuudet.
- Bishop: Pattern Recognition and Machine Learning, Chapter 8.
- B-Course: Bayesian software and on-line tutorial.
- Loredo, From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics.
- Mackay, Information Theory, Inference, and Learning Algorithms: Chapter IV
- Heckerman, A Tutorial on Learning Bayesian Networks.
- Buntine, Operations for Learning with Graphical Models.
- Jeffrey, Probabilistic thinking
- Jaynes, Probability Theory: The Logic of Science.

### Course exam

Friday, 27.02. at 9-12 in A111.

*
Petri Myllymäki
*