Supervised Learning

Keywords: Machine learning,
probabilistic modelling, Neural Networks, Bayesian Statistics, Learning
Theory, Support Vector Machines, Kernel Methods and Reinforcement Learning.

Code: COMP GI01 / COMP 4c55

Year: MSc in Intelligent Systems, PhD course at the Gatsby Unit

Prerequisites: A good background in statistics, calculus, linear algebra, and computer science. You should know some programming language (Matlab/Octave, C, Java, ...). It is preferable to be competent in either Matlab or 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.

Term: 1, 2004

Time: 14.00 to 17.00 Mondays

Location: 305 Pearson Building UCL

Coordinated By: Fernando Pérez-Cruz (fernando-at-gatsby.ucl.ac.uk)

Lecturers: Nathaniel Daw, David
J. C. MacKay, Iain Murray, Fernando Pérez-Cruz, Edward Snelson.

Homework Assignments: all assignments (coursework) 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 Fernando Perez-Cruz or the lecturer on that date. Late assignments will be penalised. If you are unable to come to class, you can also hand in assignments to Fernando Pérez-Cruz in its Office, Room 402, Gatsby Unit (Alexandra House 17 Queen Square).

Late Assignment Policy: Assignments that are handed in late will be penalised as follows: 10% penalty per day for every weekday late.

Recommended textbooks:

Cristhopher M. Bishop (1995)
*Neural
Networks for Pattern Recognition*. Claredom Press.

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

Bernhard Schölkopf and
Alexander J. Smola (2002) *Learning with Kernels*. MIT Press. (partially
available online)

Tom M. Mitchell (1997) *Machine
Learning*. McGraw-Hill.

Lectures

**October 6th: Intorudction
to Supervised Learning**

- Topics: Machine Learning, why and what for. Supervised, unsupervised and reinforcement learning. Risk Minimization. Bayes theorem. Least Sqaure Regression. Nonlinear Regression. Curse of Dimensionality. Overfitting and underfitting.

- Lecturer: Fernando Pérez-Cruz

- Material:

Readings: Chapter 1 in Bishop's book.

**October 11th: Math and Matlab
Review. Basic Optimization**

- Topics: Review of maths and Matlab concepts that are necessary for supervised Learning. Introduction to optimization: gradient descent, Newton method, conjugate gradient descent and Lagrange multipliers.

- Lecturers: Iain Murray, Fernando Pérez-Cruz and Edward Snelson.

- Material:

Readings: Cribsheet of Basic Maths Needed for Machine Learning.

Readings: Chapter 6 in Schölkopf and Smola's Book.

**October 18th: Multilayered
Perceptrons and Bayesian Learning.**

- Topics: Single Layer and Multilayered Perceptron and Bayesian Learnign.

- Lecturer: David MacKay.

- Material:

Assignment1: Due on the 25th of October (2pm).

**October 25th: Optimisation.
Basic tools in Machine Learning**

- Topics: Cover conjugate gradient descent and Lagrange Multipliers. Regularisation and cross-validation. Bayesian Learning and Naïve Bayes.

- Lecturer: Fernando Pérez-Cruz.

- Material:

Readings: Chapter 6 in Schölkopf and Smola's Book. Sections 9.2 and
9.8 in Bishop's book.

Chapter 6 in Mitchell's book.

Assignment2: Due on Friday the 5th of November
(2pm). Assignment2a Due on Monday the 22nd of
November.

**November 1st: Approximation
and Sampling**

- Topics: Laplace approximation. Monte Carlo Methods: Rejection sampling, Importance sampling and Metropolis-Hasting MCMC.

- Lecturer: Iain Murray.

- Material:

**November 15th: Gaussian
Processes for Regression**

- Topics: Gaussian Processes. Covariance Matrices. Regression estimation using Gaussian Processes

- Lecturer: Edward Snelson.

- Material:

Assignment3: Due on Monday the 29th of November
(2pm). Data for the last 2 questions GPdata

**November 22nd: Introduction
to Learning Theory**

- Topics: Loss-Functions and Risk Minimization. Basics results in Learning Theory. Introduction to Kernels. Regularization and Representer Theorem.

- Lecturer: Fernando Perez-Cruz.

- Material:

Further Readings: Kernel Methods and their Potential Use in Signal Processing.

**November 29th: Support Vector
Machines for Classification**

- Topics: Maximum margin solution. Changing the dot product using the kernel trick. Support Vector Machines. Multiclass problems.

- Lecturer: Fernando Perez-Cruz.

- Material:

Code: SVM 2D demo.

Assignment4: Due on Monday the 6th of December
(2pm). Data for the last questions: data.

Hint for Q3: Good values for C range from 5 to 20 and for sigma between
1 and 10.

**December 6th: Extensions
to kernel methods**

- Topics: Support Vector Machine for Regression. One-class SVM. Relevance Vector Machine.

- Lecturer: Fernando Perez-Cruz.

- Material:

Sections 3.1-4 Mitchell's book

Assignment5: Due on Wednesday the 15th of December
(2pm). data and kpca.m.

**December 10th: Reinforcement
Learning (B10 Gatsby Unit)**

- Topics: MPD, Reinforcement Learning, Q-Learning.

- Lecturer: Nathaniel Daw

- Material:

Slides: Reinforcement Learning.