Unsupervised Learning 2003 Course Web Page (OLD)

Gatsby Computational Neuroscience Unit
University College London

MSc Intelligent Systems

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Code: COMP GI02 / COMP 4c51 / Gatsby

Year: MSc in Intelligent Systems, Gatsby Unit Core Course

Prerequisites: A good background in statistics, calculus, linear algebra, and computer science. You should thoroughly review the maths in the following cribsheet [pdf] [ps] before the start of the course. You must either know Matlab or Octave, be taking a class on Matlab/Octave, or be willing to learn it on your own. Any student or researcher at UCL meeting these requirements is welcome to attend the lectures. Students wishing to take it for credit should consult with the course lecturer (email:

Term: 1, 2003

Time: 11.00 to 13.00 Mondays and Thursdays

Location: Gatsby Unit, 17 Queen Square

Taught By: Zoubin Ghahramani

Teaching Assistants: Iain Murray and Ed Snelson.

Homework Assignments: all assignments for this course are to be handed in to the Gatsby Unit, not to the CS department. Please hand in all assignments at the beginning of lecture on the due date to either Zoubin, Iain, or Ed. Late assignments will be penalised. If you are unable to come to class, you can also hand in assignments to Alexandra Boss, Room 408, Gatsby Unit.

Late Assignment Policy: Assignments that are handed in late will be penalised as follows: 10% penalty per day for every weekday late, until the answers are discussed in a review session. NO CREDIT will be given for assignments that are handed in after answers are discussed in the review session.

Textbook: There is no required textbook. However, I recommend the following recently published textbook as an excellent source for many of the topics here, and I will be occasionally assigning reading from it:

David J.C. MacKay (2003) Information Theory, Inference, and Learning Algorithms, Cambridge University Press. (also available online)

Dates and Title Topics Materials
Sep 29, Oct 6, Oct 9
Introduction and Statistical Foundations
  • Maximum Likelihood
  • Bayesian learning
  • The relation to coding  length
  • Supervised vs Unsupervised vs Reinforcement Learning
Lecture Slides
Assignment 1 (due Oct 9)
Readings: Nuances of Probability Theory by Tom Minka.
Probability Theory: The Logic of Science by ET Jaynes
Sam Roweis' notes on matrix algebra
Tom Minka's notes on matrix algebra
Probability and Statistics Online Reference
Oct 2
Oct 13 and Oct 16
Latent Variable Models
  • Mixture of Gaussians (MoG) and k-means
  • Factor Analysis (FA) and PCA
Lecture Slides
Assignment 2 (NEW: due Thurs Oct 23)
Suggested Readings:
* Cribsheet [pdf] [ps]of Basic Maths Needed for Machine Learning
* David MacKay's Book, Chapters 20, 22 and 23 on k-means and MoG
* Max Welling's Class Notes on PCA and FA [pdf] [ps]
Oct 20 and 23
The EM Algorithm
  • General Theory
  • Application to MoG and to FA
  • Extensions
Lecture Slides
Assignment 3
Oct 27 and 30
Latent Variable Time Series Models
  • Hidden Markov Models (HMMs)
  • Forward-Backward and Viterbi
  • Linear Dynamical Systems
  • Kalman Filtering (KF) and Extended KF
  • Hybrid and Nonlinear Time Series Models
Lecture Slides
Suggested Further Readings:
Ghahramani, Z. and Hinton, G.E. (1996) Parameter estimation for linear dynamical systems.
Minka, T. (1999) From Hidden Markov Models to Linear Dynamical Systems
Welling (2002) The Kalman Filter (class notes).
Nov 3 and 6
Reading Week
Nov 10
Introduction to Graphical Models I
  • Conditional Independence
  • Undirected Graphs (Markov Networks)
  • Hammersley-Clifford Theorem
  • Directed Graphs (Bayesian Networks)
  • Factor Graphs
Lecture Slides
Assignment 4 (due Nov 19, deadline extended)
Data Sets: geyser.txt, data1.txt
Suggested Further Readings:
The following three related articles will appear in Arbib (ed): The Handbook of Brain Theory and Neural Networks (2nd edition)
Jordan and Weiss (2002) Probabilistic Inference in Graphical Models
Ghahramani (2002) Graphical Models: Parameter Learning
Heckerman (2002) Graphical Models: Structure Learning
Shachter (1998) Bayes Ball
Nov 13
Introduction to Graphical Models II
  • Belief Propagation
Belief Propagation Demo: Fluffy and Moby
Factor Graph Propagation
Nov 17 and 20
Hierarchical and Nonlinear Models
  • Independent Components Analysis (ICA)
  • Sigmoid Belief Networks
  • Boltzmann Machines
Lecture Slides
Suggested Readings: Max Welling's Notes on ICA
David MacKay's Book, Ch 34 on ICA
Nov 24 and Nov 27
Sampling Methods
  • Monte Carlo:
    • simple Monte Carlo,
    • Rejection Sampling,
    • Importance Sampling
  • Markov chain Monte Carlo (MCMC):
    • Gibbs Sampling
    • Metropolis 
    • Hybrid Monte Carlo and other methods
Lecture Slides (MCMC)
Assignment 5 (due Dec 4)
Suggested Readings: David MacKay's Book, Ch 29 and 30 on Monte Carlo methods;
A more in-depth treatment of Monte Carlo methods is in Radford Neal's Technical Report;
Dec 1
Variational Approximations
  • Review of EM
  • Variational lower bounds and mean field methods
  • The Binary Latent Factor Model
Lecture Slides (Variational)
Suggested Readings: David MacKay's Book, Ch 33 on variational methods;
Jordan et al's Introduction to Variational Methods [ps.gz] [pdf]
Dec 4
Bayesian Model Selection
  • Occam's Razor
  • Model selection and averaging
  • BIC and Laplace approximations
  • Variational Bayesian EM algorithm
Lecture Slides (Bayesian Model Selection)
Assignment 6 (due End of Term)
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Code: genimages.m ,
Dec 8 and 11

Aims: This course provides students with an in-depth introduction to unsupervised learning techniques. It presents probabilistic approaches to modelling and their relation to coding theory and Bayesian statistics. A variety of latent variable models will be covered including mixture models (used for clustering), dimensionality reduction methods, time series models such as hidden Markov models which are used in speech recognition and bioinformatics, independent components analysis, hierarchical models, and nonlinear models.  The course will  present the foundations of probabilistic graphical models (e.g. Bayesian networks and Markov networks) as an overarching framework for unsupervised modelling. We will cover Markov chain Monte Carlo sampling methods and variational approximations for inference. Time permitting, students will also learn about Gaussian processes and the fundamentals of Bayesian decision theory/reinforcement learning/optimal control.

Learning Outcomes:  To be able to understand the theory of unsupervised learning systems; to have in-depth knowledge of the main models used in UL; to understand the methods of exact and approximate inference in probabilistic models; to be able to recognise which models are appropriate for different real-world applications of machine learning methods.

Method: Lecture presentations with associated class problems.


Course Location:

Gatsby Unit
17 Queen Square [map]
Mondays and Thursdays 11:00 - 13:00


Zoubin   020 7679 1199


Information here was last updated Sep 2003.