Postgraduate Course: Probabilistic Modelling and Reasoning (INFR11050)
Course Outline
School  School of Informatics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  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. 
Course description 
*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

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  This course is open to all Informatics students including those on joint degrees. For external students where this course is not listed in your DPT, please seek special permission from the course organiser.
Mathematics prerequisites:
1  Probability theory: Discrete and continuous univariate random variables. Expectation, variance. Joint and conditional distributions.
2  Linear algebra: Vectors and matrices: definitions, addition. Matrix multiplication, matrix inversion. Eigenvectors, determinants, quadratic forms.
3  Calculus: Functions of several variables. Partial differentiation. Multivariate maxima and minima. Integration: need to know definitions, including multivariate integration.
4  Special functions: Log, exp are fundamental.
5  Geometry: Basics of lines, planes and hyperplanes. Coordinate geometry of circle, sphere, ellipse, ellipsoid and ndimensional generalizations.
6  Graph theory: Basic concepts and definitions: vertices and edges, directed and undirected graphs, trees, paths and cycles, cliques.
Programming prerequisite: A basic level of programming is assumed and not covered in lect  