Postgraduate Course: Probabilistic Modelling and Reasoning (INFR11134)
|School||School of Informatics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|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 data-intensive linguistics, automatic speech recognition, probabilistic expert systems, statistical theories of vision etc.
This 20 credit course replaces INFR11050 Probabilistic Modelling and Reasoning - 10 credit version.
The course will cover the most important topics in probabilistic modelling and unsupervised learning, and provide a thorough basis for understanding other extensions developments and applications.
- events, discrete variables
- joint, conditional probability
* Discrete belief networks, inference
* Continuous distributions, graphical Gaussian models
* Learning: Maximum Likelihood parameter estimation
* Decision theory
* Hidden variable models
- mixture models and the EM algorithm
- factor analysis
- ICA, non-linear factor analysis
* Dynamic hidden variable models
- Hidden Markov models
- Kalman filters (and extensions)
* Undirected graphical models
- Markov Random Fields
- Boltzmann machines
* Information theory
- entropy, mutual information
- source coding, Kullback-Leibler divergence
* Approximate Inference: MCMC, Variational Methods
* Bayesian methods for
- Inference on parameters
- Model comparison
Entry Requirements (not applicable to Visiting Students)
|Prohibited Combinations|| Students MUST NOT also be taking
Probabilistic Modelling and Reasoning (INFR11050)
||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
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 n-dimensional 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 lectures. The assessed assignment will involve some programming.
Previously taking and being happy with MLPR is highly recommended for this course. There will be some assumption that people are familiar with machine learning concepts such as those taught on MLPR or an equivalent course.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 30,
Seminar/Tutorial Hours 10,
Feedback/Feedforward Hours 2,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Exam 80%, Coursework 20%.
||The extra time that a 20 point course provides will allow much more room for feedback, including online questions and feedback from those questions within core lecture time. This will enhance the current feedback arrangements. The marked assignment will provide additional feedback. Finally exam like questions will be provided for each lecture, or pair of lectures that help students see what they would need to do with what they have learnt in an exam setting. The coursework will be returned before the end of the lecture period allowing within lecture feedback.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||2:00|
On completion of this course, the student will be able to:
- Define the joint distribution implied by directed and undirected probabilistic graphical models, and carry out inference in graphical models from first principles by hand; convert between different graphical models.
- Demonstrate understanding of maximum likelihood and Bayesian methods for parameter estimation by hand derivation of estimation equations for specific problems.
- Critically discuss differences between various latent variable models for data and derive EM updates for various latent variable models (e.g. mixture models). Implement, and perform computations of approximate inference methods.
- Demonstrate ability to design, assess and evaluate belief network models, and use code implementing probabilistic graphic models.
- Demonstrate ability to conduct experimental investigations and draw conclusions from them.
|Graduate Attributes and Skills
||The student will be able to reason about uncertainty, an important transferable skill.
In addition the student will be able to:
- Undertake critical evaluations of a wide range of numerical and graphical data.
- Apply critical analysis, evaluation and synthesis to forefront issues, or issues that are informed by forefront developments in the subject/discipline/sector.
- Identify, conceptualise and define new and abstract problems and issues.
- Develop original and creative responses to problems and issues.
- Critically review, consolidate and extend knowledge, skills, practices and thinking in a subject/discipline/sector.
- Deal with complex issues and make informed judgements in situations in the absence of complete or consistent data/information.
|Keywords||Bayesian Statistics,Unsupervised Learning,Probabilistic Models
|Course organiser||Dr Michael Urs Gutmann
Tel: (0131 6)50 5190
|Course secretary||Mrs Sam Stewart
Tel: (0131 6)51 3266