Learning in Graphical Models – spring 2006

ICS: 274B
Instructor: Max Welling
 

Code

Typ

Sec

Unt

Instructor

Time

Place

36745

Lec

A

4

WELLING, M.

TuTh   2:00- 3:20p

CS 213


Prerequisites

ICS 274A  Probabilistic Learning: Theory
and Algorithms, or with consent of instructor.


Goals

Many modern approaches to probabilistic modeling of real world
data sets can be formulated in the unifying framework of graphical
models. Graphical models provide a common language to think and
communicate about probabilistic models and makes explicit the
underlying assumptions. Moreover, it provides the appropriate
structure for computations necessary for inference and learning in
these models.

It is the primary goal of this course to familiarize the student
with the concepts of graphical models, and in particular with
learning these models from data. A student who has successfully
completed the course should be able to understand a wide variety
of well known models in terms of this unifying framework and feel
comfortable using it to design new models. The course will contain
1) formal mathematical sections necessary for the development of
the theory, 2) examples of probabilistic models (re)formulated in
the language of graphical models and 3) examples of successful
applications to real data.

This secondary goal of this class is to give the
students hands on experience in solving real world problems.
For that purpose I have negotiated a deal with SciTech, a San Diego based company:
if we improve their (naive Bayes) classifier on a particular classification problem
(prediction of activity levels of chemical compounds - for data, see below) then they
will provide a $300 bonus for the student who will come down and present this work.
In addition, provided their goals are met one student can implement this algorithm into
their software package as a summer intern.


Homework : (slides serve to give you an impression what was done last time, but I expect
                     that we will significantly deviate from that. Also, homework will be updated as we go.)

Book: Book-chapters can be found in this password protected directory

week 1: ROC
- read sections 2.1, 2.2, 2.3 from chapter 2 of David MacKay's book.
- read chapter 2, 5 (until "plates") & 13 from Mike Jordan's book.
- read classnotes
- Excercises HW1

week 2:
- read chapter 6, 7 from Mike Jordan's book.
- Excercises HW2
(only the relevant ones on topics we have treated in class)
- Project 1 (due May 4)

 week 3:
- read chapter 9, 19, 20 from Mike Jordan's book.
- Excercises HW3 ,  Excercises HW4  
(only the relevant ones on topics we have treated in class. At this point homework is optional but instructive. )

week 4,5,6:
- read chapters 10,11,14 from Jordan’s book.
- read the following classnotes: classnotes (EM) , classnotes (PPCA, FA, ICA)
- start on Project 2 (due Tu June 6)

--------------------------------------------------------------------------------------
(stuff below this line is not updated)

 week 7: belief propagation, junction trees.

  week 8: classnote (Sampling)

 week 9: classnotes(HMM) classnotes(KF)

week 10:
- presentation projects:

 week 11: final exam:

 


MATLAB Demos:

week 1: demo_Bayes, demo_MAP, demo_ML, plotGauss1D, plotGauss2D, ginput2
week 2: demo_LinReg, demo_LogReg
week5: demo_EM
week6: MoG_demo, plotGauss_color, randMean, randCovariance, kmeans, dist2, randvec, gaussian
week7: demo_pca, FA
week8: demo_gibbs, demo_mcmc
week9: demo_HMM demo_KF, demo_KF2


SciTech Dataset:

training_data.mat  This files includes:

Training labels: 0: inactive compound, 1: medium active compound, 2: active compound, sparse format.

Continuous attributes: 2 continuous attributes: AlogP and Molecular_Weight

Discrete attributes: 3 discrete attributes: Num_H_Acceptors,  Num_H_Donors, Num_RotatableBonds.

Binary finger print: very sparse binary matrix where  1’s code for the presence of certain substructures, sparse format.

Using all the available attributes we wish to predict the activity level of the compound.
Background Reading: paper1,  paper2,  SciTech powerpoint slides.


Syllabus:

The course will primarily be lecture-based with homework and
exams. Most homework will revolve around the implementation of various
classification algorithms on the SciTech dataset provided above.
It is required that you use MATLAB for this coding work.

The following is a rough syllabus subject to change.

1. Review of Statistical Concepts

Random variables, probability distributions and
probability densities. The multivariate Gaussian distribution.
Marginal and conditional independence. Bayes' rule. Estimation:
maximum likelihood, MAP-estimates, Bayesian inference,
bias-variance tradeoff. Model selection and averaging,
over-fitting.

2. Graphical Models.

Markov random fields and undirected
graphical models. Bayesian networks and directed acyclic graphical
models. Semantics of graphical models: independence assumptions,
Markov properties, Markov blanket, separability. Factor graphs,
chain graphs. Plates.

3. Hidden Variables and Exact Inference.

Observed and hidden random variables. Bayes' ball algorithm. Exact inference:
junction tree propagation and cut-set conditioning.

4. Learning in Graphical Models.

The expectation
maximization algorithm and free energy minimization. Iterative
conditional modes. Iterative scaling.

5. Unsupervised Learning - Directed Graphical Models.

Mixture of Gaussians, K-means, principal components analysis,
probabilistic principal components analysis, factor analysis,
independent components analysis, latent Dirichlet allocation.

6. Unsupervised Learning - Undirected Graphical Models.

Boltzmann machines, products of experts, additive random field
models. Examples in vision and text.

7. Supervised Learning - Directed and Undirected Graphical Models.

Naive Bayes as a graphical model,
logistic regression, linear regression.
Conditional mixture models, mixtures of experts. Conditional
random fields.

8. Graphical Models of Time Series.

State space models, autoregressive models.
Hidden Markov Models. The Baum-Welch and Viterbi algorithm. The
Kalman filter and smoother. Dynamic Bayes nets. Examples in speech
and biological sequence data.

9. Approximate Inference.

Mean field methods and
structured variational inference. Loopy belief propagation. Region
graphs and generalized belief propagation. Sampling: rejection
sampling, importance sampling, particle filters, Markov chain
Monte Carlo sampling, Gibbs sampling, Hybrid Monte Carlo sampling.

10. Bayesian Learning and Structure Learning in Graphical Models.

Conjugate priors.
Fully observed Bayes' nets. Variational Bayes algorithm. Sampling
from the posterior. Laplace approximation. Chow-Liu's algorithm
for trees. Structure learning in fully observed Bayes' nets.
Structure learning in the presence of hidden variables: structural
EM.


Grading Criteria


Grading will be based on a combination of weekly homework and a project (40%
of the grade), a midterm exam (30%) and a final exam (30%) .


Textbook


The textbook that will be used for this course has not been
published yet, but copies will distributed during class.

1. M.I. Jordan: An Introduction to Graphical Models.


Optional side readings are:

2. D. MacKay: Information Theory, Inference and Learning
Algorithms
3. M.I. Jordan: Learning in Graphical Models
4. B. Frey: Graphical Models for Machine Learning and Digital
Communication
5. J. Pearl: Probabilistic Reasoning in Intelligent
Systems
6. R.O. Duda, P.E. Hart, D. Stork: Pattern
Classification
7. C.M. Bishop: Neural Networks for Pattern Recognition
8. T. Hastie, R. Tibshirani, J.H, Friedman: The Elements of
Statistical Learning
9. B.D. Ripley: Pattern Recognition and Neural Networks