Probabilistic Modelling and Reasoning
Course homepage
This is a course for MSc level students. The course descriptor can
be found
here.
The
introductory
handout for the course is available.
MATHS PREREQUSITES: To do PMR you need a
reasonable background in statistics, calculus, linear algebra.
Please check the
course descriptor.
You should also thoroughly review the maths in the following
cribsheet (from Iain Murray)
before the start of the course, and attempt the
tut0.pdf sheet.
A handout on
Mathematical
Preliminaries which used to be used for the course LfD1 is also
useful for PMR; all material is relevant.
Lectures
PMR lectures will be Lecture Theatre 2,
Appleton Tower
on Tuesdays and Fridays 1000-1050.
Information taken from
Informatics
2012/13 lecture timetable.
Resources
-
Books. The course textbook is Pattern
Recognition and Machine Learning by Christopher M. Bishop,
Springer (2006).
- Other useful texts for some of the material are
Information Theory, Inference and Learning Algorithms by
David J. C. MacKay (Cambridge University Press, 2003; free online
version available),
Bayesian
Reasoning and Machine Learning by David Barber (Cambridge
University Press, 2012; free online version available), and
Artificial
Intelligence: A Modern Approach by S. Russell and P. Norvig (Prentice Hall,
third edition, 2010).
-
A web
page giving details of some books with maths background,
and some web-based resources
-
Links
to more advanced mathematical material.
-
A handout Introduction
to MATLAB giving an introduction to MATLAB and the NETLAB neural networks
toolbox. Further MATLAB tutorials are available at
UNH
Matlab Tutorial, US
Navy Matlab Tutorial and MTU
Introduction to Matlab
-
A Brief
Introduction to Graphical Models and Bayesian Networks by Kevin Murphy.
-
Thomas Minka's excellent
Statistical
Learning/Pattern Recognition Glossary
-
Max Welling's Classnotes in Machine Learning
-
The Association for Uncertainty in Artificial
Intelligence homepage is a good place to start looking for interesting
material.
-
The Kalman Filter
website.
-
List
of Public Domain Belief Network Tools from a course on Belief Networks
at Duke University.
- Zoubin Ghahramani's tutorial/overview paper
Unsupervised Learning (original
link), in Bousquet, O., Raetsch, G. and von Luxburg, U. (eds) Advanced Lectures on Machine Learning LNAI 3176, Springer-Verlag (2004).
Assignments
There will be one assignment in this course, worth 20%
of the overall mark for the course.
Handout date: 19 October, due date Fri 16 Nov (4pm).
Feedback after 2 weeks (approx).
-
Assignment 1 is due in on
Fri 16 Nov by 4pm by manual submission to the ITO.
Here is the a12.zip file obtaining data and
matlab functions.
The NETLAB software is available via the downloads page from
via this
link. Use version 3.3, you will also need foptions.m.
Tutorial groups
Tutorials will start in week 3.
Tutorial groups listing from ITO. This may only be visible
from within .ed.ac.uk. In case of problems with the
assignment to specific groups
contact the ISS via the
support form .
Course Rep
Sergey Dudoladov s1233200
Software
We will be using the program JavaBayes, you can find more details
here. We will also be using some MATLAB code.
Office hour
Friday 11-12, starting in week 2.
It is probably best to catch me
after the lecture. I will then walk over to my office in IF 2.27.
Examination Information
PMR will be examined in the December 2012 exam diet.
Week-by-Week listing
Will build up here ...
Week 1
Lectures
Introduction
slides
slides4up,
Belief networks
slides
slides4up
Self-check maths sheet Check if you can do the
questions on
tut0.pdf
Tutorials No tutorials in week 1 (nor week 2)
Week 2
Lectures Belief networks continued,
Elimination algorithm
slides,
slides4up,
Gaussian distribution
slides,
slides4up
Tutorials No tutorials in week 2, but see sheet below for
the tutorial in week 3
Handout
Worked example for Holmes/Watson
network
JavaBayes example
sprinkler.bif (Bayes net for the
Holmes-Watson-Rain-Sprinkler problem)
Week 3
Lectures Gaussian distribution ctd,
Maximum likelihood estimation
slides,
slides4up,
Bayesian parameter estimation
slides
slides4up
Tutorials tut1.pdf,
answer sheet
ans1.pdf,
wikipedia
on Monty Hall problem
Handout on
Inference
with Gaussian Random Variables
Matlab code cointoss.m,
matlab code to illustrate posterior distribution under Beta prior
Web resource The
technical
report by David Heckerman entitled "A tutorial on Learning Bayesian
Networks". (
original
link)
Week 4
NO LECTURE ON FRI 12 OCT
Lectures
Decision theory
slides,
slides4up,
Mixture models
slides,
slides4up
Handout
Working for Gaussian
classifier
Tutorials tut2.pdf,
answer sheet
ans2.pdf
Week 5
Lectures
Mixture models continued,
Factor analysis and beyond
slides,
slides4up
Handout
Working for EM for
Mixture of Gaussians
Handout Working for PCA
solution as principal eigenvector
Handout on
Factor Analysis and Beyond
Tutorials tut3_1213.pdf,
matlab code
plotquad.m,
answer sheet
ans3_1213.pdf
Week 6
Lectures Factor analysis and beyond ctd,
Bayesian Model Selection
slides,
slides4up,
Hidden Markov models
slides
slides4up
Tutorials tut4_1213.pdf,
answer sheet
ans4_1213.pdf
Web resource
Te-Won
Lee's Blind source separation demo
Web resource Short explanation
of blind source separation from Helsinki
Optional reading
Paper on
GTM
by C. M. Bishop, M. Svensen and C. K. I. Williams (
original
link)
Web resource
chapter
28 from David MacKay's book Information Theory, Inference and
Learning Algorithms. See sections 28.1, 28.2 on model comparison
Week 7
Lectures
Hidden Markov Models continued,
Time Series Modelling and Kalman Filters
slides,
slides4up
Tutorials tut5_1213.pdf,
answer sheet
ans5_1213.pdf
Handout
Working for alpha and beta
recursions for HMMs
Web resource L Rabiner tutorial on HMMs from Proceedings of the
IEEE 77(2) 1989 is available from the IEL electonic library
here.
Optional reading
A Gentle Tutorial on the EM Algorithm and its Application to Parameter
Estimation for Gaussian Mixture and Hidden Markov Models by Jeff A. Bilmes
pdf
(
original
link)
Web resource
Harmonising chorales in the style of Johann Sebastian Bach, work
by Moray Allan using a HMM (MSc, School of Informatics, Edinburgh,
2002). See also
HMM Bach demo.
Handout on
Time Series Modelling
Web resource Movie
clips from Prof Andrew Blake's group illustrating tracking with non-linear
Kalman filters
Week 8
Lectures
Time Series Modelling and Kalman Filters ctd,
Junction tree algorithm
slides
slides4up
Tutorials tut6_1112.pdf,
answer sheet
ans6_1112.pdf
Handout Worked example of
inference in a junction tree
Handout
Worked example for c->b->a network
Week 9
NO LECTURE ON FRIDAY 16 NOV
Lectures
Undirected graphical models
slides,
slides4up
Tutorials tut7_1112.pdf,
answer sheet
ans7_1112.pdf
Handouts
Working for local Markov
property,
Working for Boltzmann machine
conditional distribution,
Working for derivative of a
log-linear model
Web resource
Information
about GrabCut from MSR Cambridge
Week 10
Lectures Last lecture on Tues 20 Nov.
Finish off Undirected graphical models, followed by
question and answer session. If there is time I will then
discuss Coding and Information Theory
(not examinable)
slides,
slides4up
Tutorials tut8_1112.pdf,
answer sheet
ans8_1112.pdf
Revision Session
I will hold a revision session on Thurs 6 Dec 10-11am in the
Hugh Robson Building Lecture Theatre.
This will be a question and answer format, not a lecture.
This page is maintained by Chris
Williams
