Course: 2019/2020

Machine Learning

(12994)

Students are expected to have completed

This is a first term course, so no other courses of the Master programme are key for this course. However, it is highly desirable that students are familiarized with basic concepts from statistics.

After this course students will understand the principles of estimation, decision, and grouping problems, and will become familiarized with the different approaches for dealing with them. Students will understand that, for the correct understanding of these problems, it is necessary to master three basic probability theory elements: 1) the likelihood, 2) the difference between a priori and a posteriori uncertainty, and 3) Bayes' Theorem.
From a practical point of view, students will be presented different approaches for learning from data to solve these problems: non-parametric techniques, methods based on empirical risk minimization, or those that follow Bayesian principles.
More specifically, the followint list summarizes the main objectives of this course, enumerated as competences to be acquired by the students:
- knowledge of the theoretic principles underlying several of the most important techniques for learning from data.
- ability to apply such techniques on real problems, and to extract results and conclusions.
- understanding of clasic methods for estimation and clasifications, and skills for their correct application.
- ability to use machine learning tools: neural networks, support vector machines, etc.
- knowledge of last generation approaches, including those based on machine ensembles

Description of contents: programme

Unit 0: Introduction to data processing
Unit 1: Bayes' Estimation and Decision Theory
1.1. General overview of the estimation and decision problems
1.2. Bayes' Theorem
1.3. Bayes Estimation Theory. MSE, MAD, and MAP estimators
1.4. ML Estimation
1.5. Optimum Bayes' classifier for the binary and multiclass cases
1.6. Characterization of binary classifiers
Unit 2: Regression
2.1. The regression problem
2.2. Non-parametric regression: k-NN
2.3. Linear and polynomial least squares regression
2.4. Bayesian regression
2.5. Gaussian processes
Unit 3: Classification
3.1. Classification problema
3.2. Non-parametric methods: k-NN
3.3. Logistic regression
3.4. Support vector machines
Unit 4: Data clustering
4.1. k-means clustering
4.2. Spectral clustering

Learning activities and methodology

LECTURES AND PRACTICAL SESSIONS
Theory sessions consist of lectures in which the basic concepts of the course will be introduced, illustrating them with a large number of examples. Exercises and problems similar to those to be proposed in the exam will also be solved along the course.
LAB SESSIONS
Sessions in which students will apply the concepts presented in the course with the help of a computer. Students will deal with estimation and classification problems with real data, and will have to evaluate the performance of the implemented systems
RESEARCH PROJECT AND DISCUSSIONS
Students will be given a list of topics related to the research areas of the course, so that they can prepare a project on one of them. The work will be presented to the class on specific sessions.

Assessment System

- % end-of-term-examination 25
- % of continuous assessment (assigments, laboratory, practicals...) 75

Basic Bibliography

- C. E. Rasmussen. Gaussian Processes for Machine Learning. MIT Press. 2006
- R. O. Duda, P. E. Hart, D. G. Stork. Pattern Classification (2nd ed.). Wiley Interscience. 2001

Additional Bibliography

- C. M. Bishop. Pattern Recognition and Machine Learning. Springer. 2006