Pattern Analysis and Machine Intelligence

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The following are last minute news you should be aware of ;-) 

07/10/2013: a new edition of the course starts today!

Course Aim & Organization

The objective of this course is to give an advanced presentation of the techniques most used in artificial intelligence and machine learning for pattern recognition, knowledge discovery, and data analysis/modeling.

Teachers

The course is composed by a blending of lectures and exercises by the course teacher and some teaching assistants.

Course Program

Techniques from machine and statistical learning are presented from a theoretical (i.e., statistics and information theory) and practical perspective through the descriptions of algorithms, the theory behind them, their implementation issues, and few examples from real applications. The course follows, at least partially, the outline of The Elements of Statistical Learning book (by Trevor Hastie, Robert Tibshirani, and Jerome Friedman):

  • Machine Learning and Pattern Classification: in this part of the course the general concepts of Machine Learning and Patter Recognition are introduced with a brief review of statistics and information theory;
  • Unsupervised Learning Techniques: the most common approaches to unsupervised learning are described mostly focusing on clustering techniques, rule induction, Bayesian networks and density estimators using mixure models;
  • Supervised Learning Techniques: in this part of the course the most common techniques for Supervised Learning are described: decision trees, decision rules, Bayesian classifiers, hidden markov models, lazy learners, etc.
  • Feature Selection and Reduction: techniques for data rediction and feature selection will be presented with theory and applications
  • Model Validation and Selection: model validation and selection are orthogonal issues to previous technique; during the course the fundamentals are described and discussed (e.g., AIC, BIC, cross-validation, etc. ).

Detailed course schedule

A detailed schedule of the course can be found here; topics are just indicative while days and teachers are correct up to some last minute change (I will notify you by email). Please note that not all days we have lectures!! 

Note: Lecture timetable interpretation
* On Mondays lectures start at 13:15 SHARP
* On Fridays lectures start at 10:30 (quarto d'ora accademico)
Date Day Time Room Teacher Topic
07/10/2013 Monday 13:15 - 15:00 V.08 Matteo Matteucci Course Introduction (Ch. 1)
11/10/2013 Friday 10:30 - 15:15 V.08 Matteo Matteucci Two examples from classification (Ch. 2)
14/10/2013 Monday 13:15 - 15:00 V.08 Matteo Matteucci Statistical Decision Theory and Bias-Variance trade off (Ch. 2)
18/10/2013 Friday 10:30 - 13:15 V.08 Matteo Matteucci Model Selection (Ch. 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.10,)
21/10/2013 Monday 13:15 - 15:00 V.08 Matteo Matteucci Discriminating functions, decision boundary and Linear Regression (Ch.4.1, Ch. 4.2)
25/10/2013 Friday 10:30 - 13:15 V.08 Matteo Matteucci Linear Discriminant Analysis (Ch. 4.3)
28/10/2013 Monday 13:15 - 15:00 V.08 Matteo Matteucci Linear Discriminant Analysis (Ch. 4.3)
04/11/2013 Monday 13:15 - 15:15 V.08 Matteo Matteucci Logistic Regression (Ch. 4.4)
08/11/2013 Friday 10:30 - 13:15 V.08 Matteo Matteucci Logistic Regression (Ch.4.4)
11/11/2013 Monday 13:15 - 15:00 V.08 Luigi Malagò Linear Regression Methods (Ch. 2, Ch. 3, (*))
15/11/2013 Friday 10:30 - 13:15 V.08 Luigi Malagò Linear Regression Methods (Ch. 2, Ch. 3, (*))
18/11/2013 Monday 13:15 - 15:00 V.08 Luigi Malagò Linear Regression Methods (Ch. 2, Ch. 3, (*))
22/11/2013 Friday 10:30 - 13:15 V.08 Luigi Malagò Linear Regression Methods (Ch. 2, Ch. 3, (*))
25/11/2013 Monday 13:15 - 15:00 V.08 Davide Eynard Clustering I: Introduction and K-Means
29/11/2013 Friday 10:30 - 13:15 V.08 Davide Eynard Clustering II: K-Means Alternatives, Hierarchical, SOM
02/12/2013 Monday 13:15 - 15:00 V.08 Davide Eynard Clustering III: Mixture of Gaussians, DBSCAN, Jarvis-Patrick
06/12/2013 Friday 10:30 - 13:15 V.08 Davide Eynard Clustering IV: Spectral Clustering and Evaluation Measures


(*) Linear regression methods (Ch 2.1, 2.2, 2.3 and 2.3.1, 2.4, 2.6 and 2.6.1, 2.7 and 2.7.1, 2.8 and 2.8.1, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.9, see paper "Least Angle Regression" linked below, pages 1-16)

Course Evaluation

The course evaluation is composed by two parts:

  • A homework with exercises covering the whole program that counts for 30% of the course grade
  • A written examination covering the whole program that count for 70% of the course grade

The homework is just one per year, it will be published at the end of the course and you will have 15 days to turn it in. It is not mandatory, however if you do not turn it in you loose 30% of the course grade. There is the option of repeat the homework after the end of the course, but this has to be discussed and agreed with the course professor.

Teaching Material (the textbook)

Lectures will be based on material taken from the aforementioned slides and from the following book.

Some additional material that could be used to prepare the oral examination will be provided together with the past homeworks.

Teacher Slides

In the following you can find the lecture slides used by the teacher and the teaching assistants during classes:

  • Course introduction: introductory slides of the course with useful information about the grading, and the course logistics. Some examples from supervised learning and two algorithms for classification (taken from The Elements of Statistical Learning book).
  • Probability Basics: Slides on probability basics used to introduce Statistical Decision Theory.
  • Model Selection: slides presenting images, tables and examples about model selection (taken from The Elements of Statistical Learning book).
  • Linear Classification Examples: slides presenting images, tables and examples about (generalized) linear methods for classification (taken from The Elements of Statistical Learning book).
  • Kernel Smoothing Examples: slides presenting images, tables and examples about Kernel Smoothing, Kernel Density Estimation and Gaussian Mixture Models (taken from The Elements of Statistical Learning book).
  • Support Vector Machines: these slides have been used to present Support Vector Machines (taken from The Elements of Statistical Learning book).

Additional Papers

Papers used to integrate the textbook

Clustering Slides

These are the slides used to present clustering algorithms during lectures

  • Lesson 3: Mixture of Gaussians, DBSCAN, Jarvis-Patrick (slides, handouts)

Past Exams and Sample Questions

These are the text of past exams to give and idea on what to expect during the class exam:

2013 Homework

The 2013 Homework (alike the 2012 one) is organized as an octave series of tutorials. You are requested to go through the tutorials and practice with the algorithms that have been presented in class. To prove us you have done it and that you have understood the code you will be requested to solve few exercises and provide us a pdf report by email

Part 1: Regression

  • Homework 2013 Regression: this is the text of the first part of the homework; it has been intentionally edited not to allow cut and paste. This part of the homework will contribute to the 10% of the grade and the deadline to submit the solution by email to matteucci@elet.polimi.it and malago@di.unimi.it is Sunday 09/06 23:59
    • prostate.data: the dataset used for the homework
    • prostate.info: the dataset used for the homework
    • diabete.mat: the dataset used for the homework
    • textread.m: (optional) function which might be useful depending on your octave version
    • strread.m: (optional) function which might be useful depending on your octave version

For any question or doubt please sen us an email as soon as possible.


Note 1: for some strange reason the CSM of the website has decided to rename the files with capitals, please save them in lower case :-(

Note 2: rename the file Diabete.data into diabete.mat ... still fighting with the CSM :-)

Note 3: the code has been tested with octave under linux, we suggest to use it not to spend too much time with installing it under windows or using matlab. If you do not have linux installed, try using a live CD as the ubuntu 13.04 live distro ;-)

Part 2: Classification

  • Homework 2013 Classification: this is the text of the second part of the homework; it has been intentionally edited not to allow cut and paste. This part of the homework will contribute to the 10% of the grade and the deadline to submit the solution by Sunday 23/06 23:59

Note 1: Submit the solution by loading it on www.dropitto.me/matteucci (pwd is dropittome)

Note 2: please name your pdf as pami_SURNAME_STUDENTID_classification.pdf; if you submit a homework for different people, please pick one of the names for the file but PUT ALL THE NAMES IN THE COVER PAGE!!

Errata Corrige: there were a few bugs in the homework text. I have updated the pdf and they were:

In the computation of feature projection, the code for the maximization of a'B*a via SVD should be changed as it follows 

% maximization of a'*B*a / a'*w*a via SVD
[Vw, Dw, Vw] = svd(W);
Whalf = Vw * sqrt(Dw) * Vw'; % Whalf'*Whalf == W
Wminushalf = inv(Whalf);
Mstar = M*Wminushalf;
   % Add this variable for computing Mstar mean
   meanMstar = mean(Mstar);
for i=1:size(M,1)
   % Remove the mean saved before the loop
   Mstar(i,:) = Mstar(i,:)-meanMstar;
end
Bstar = Mstar'*Mstar;
[Vstar, Db, Vstar] = svd(Bstar);

In the Fisher projection it is more correct to use only the training data to learn the projection and then we can train and test on the corresponding subsets 

a = FisherProjection(X(training,:),Y(training,:));
reducedX = X*a(:,1);
[mu_0, mu_1, sigma, p_0, p_1] = linearDiscriminantAnalysis_train(reducedX(training), Y(training))

I forgot to filter for just the training samples when performing Quadratic Discriminant Analysis 

quadX = expandToQuadraticSpace(X);
%check this out!
size(quadX)
beta = linearRegression_train(quadX(training), Y(training));

And in general you should always train on the training data and test on the testing data ;-).

Part 3: Clustering

The code and the text of the third part of the homework are available online at these posts

As usual, this part of the homework will contribute to the 10% of the grade; the deadline to submit the solution is before the you take the exam sending it to davide.eynard_at_gmail.com.


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