Postgraduate Course: Probabilistic Modelling and Reasoning (INFR11050)
Course Outline
School  School of Informatics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Credits  10 
Home subject area  Informatics 
Other subject area  None 
Course website 
http://www.inf.ed.ac.uk/teaching/courses/pmr 
Taught in Gaelic?  No 
Course description  When dealing with real world data, we often need to deal with uncertainty. For example, short segments of a speech signal are ambiguous, and we need to take into account context in order to make sense of an utterance. Probability theory provides a rigorous method for representing and reasoning with uncertain knowledge. The course covers two main areas (i) the process of inference in probabilistic reasoning systems and (ii) learning probabilistic models from data. Its aim is to provide a firm grounding in probabilistic modelling and reasoning, and to give a basis which will allow students to go on to develop their interests in more specific areas, such as dataintensive linguistics, automatic speech recognition, probabilistic expert systems, statistical theories of vision etc. 
Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  This course has the following mathematics prerequisites:
1  Probability theory: Discrete and continuous univariate random variables. Expectation, variance. Univariate Gaussian distribution. Joint and conditional distributions. (At the level taught in MfI 1&4).
2  Linear algebra: Vectors and matrices: definitions, addition. Matrix multiplication, matrix inversion. Eigenvectors, determinants, quadratic forms. (At the level taught in MfI 2&3).
3  Calculus: Functions of several variables. Partial differentiation. Multivariate maxima and minima. Integration: need to know definitions, including multivariate integration. (At the level taught in MfI 1&2)
4  Special functions: Log, exp are fundamental. (At the level taught in MfI 1)
5  Geometry: Basics of lines, planes and hyperplanes. Coordinate geometry of circle, sphere, ellipse, ellipsoid and ndimensional generalizations. (At level taught in MfI 1&4) 
Additional Costs  None 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  Yes 
Course Delivery Information

Delivery period: 2012/13 Semester 1, Available to all students (SV1)

Learn enabled: No 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Central  Lecture   111      10:00  10:50  Central  Lecture   111   10:00  10:50    
First Class 
Week 1, Tuesday, 10:00  10:50, Zone: Central. LT2 Appleton Tower 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S1 (December)   2:00   
Summary of Intended Learning Outcomes
1  Define the joint distribution implied by directed and undirected probabilistic graphical models.
2  Carry out inference ingraphical models from first principles by hand, and by using the junction tree algorithm.
3  Demonstrate understanding of maximum likelihood and Bayesian methods for parameter estimation by hand derivation of estimation equations for specific problems.
4  Critically discuss differences between various latent variable models for data.
5  Derive EM updates for various latent variable models (e.g. mixture models).
6  Define entropy, joint entropy, conditional entropy, mutual information, expected code length.
7  Demonstrate ability to design, assess and evaluate belief network models.
8  Use matlab code implementing probabilistic graphic models.
9  Demonstrate ability to conduct experimental investigations and draw conclusions from them. 
Assessment Information
Written Examination 80
Assessed Assignments 20
Oral Presentations 0
Assessment
One assignment, mainly focussing on learning probabilistic models of data.
If delivered in semester 1, this course will have an option for semester 1 only visiting undergraduate students, providing assessment prior to the end of the calendar year. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
*Introduction
* Probability
o events, discrete variables
o joint, conditional probability
* Discrete belief networks, inference
* Continuous distributions, graphical Gaussian models
* Learning: Maximum Likelihood parameter estimation
* Decision theory
* Hidden variable models
o mixture models and the EM algorithm
o factor analysis
o ICA, nonlinear factor analysis
* Dynamic hidden variable models
o Hidden Markov models
o Kalman filters (and extensions)
* Undirected graphical models
o Markov Random Fields
o Boltzmann machines
* Information theory
o entropy, mutual information
o source coding, KullbackLeibler divergence
* Bayesian methods for
o Inference on parameters
o Model comparison
Relevant QAA Computing Curriculum Sections: Artificial Intelligence 
Transferable skills 
Not entered 
Reading list 
* The course text is "Pattern Recognition and Machine Learning" by C. M. Bishop (Springer, 2006).
* In addition, David MacKay's book "Information Theory, Inference and Learning Algorithms" (CUP, 2003) is highly recommended.

Study Abroad 
Not entered 
Study Pattern 
Lectures 20
Tutorials 7
Timetabled Laboratories 0
Nontimetabled assessed assignments 20
Private Study/Other 53
Total 100 
Keywords  Not entered 
Contacts
Course organiser  Dr Iain Murray
Tel: (0131 6)51 9078
Email: I.Murray@ed.ac.uk 
Course secretary  Miss Kate Weston
Tel: (0131 6)50 2701
Email: Kate.Weston@ed.ac.uk 

