Mathematics Fundations in Machine Learning    

Recommended Prerequisites

 Álgebra linear, Análise em R^n.

Teaching Methods

Theoretical classes with exercises and applications.

Learning Outcomes

Machine learning involves an important set of mathematical concepts which are fundamental to understand with deep insights the algorithms and discuss or discover new technologies. The object of this Unit is to train students on the technology of artificial intelligence with a particular focus on the theoretical aspects, namely:

- understand the mathematical nature of the data;

- upgrade the notion of metric between data or cluster of data;

- introduce the concept of representatives of a cluster as a minimization of a custom function;

- be able to achieve complex operations on the data such as the dimensional reduction and understand the mathematical issues;

- be able to construct and justify mathematically clustering algorithms or classifiers.

Work Placement(s)

No

Syllabus

The syllabus content is

1) data and its characterization

2) Punctual metric and metric for clusters, notion of representatives

3) The mathematics of the Clustering

4) The mathematics of the classifiers

5) Dimentional reduction and its mathematical analysis.

Head Lecturer(s)

Stéphane Louis Clain

Assessment Methods

Continuous Assessment
Frequency: 100.0%

Final Assessment
Exam: 100.0%

Bibliography

1) Charles Bouveyron, Gilles Celeux, T. Brendan Murphy, Adrian E. Raftery. Model-Based Clustering and Classification for Data Science With Applications in R. Cambridge University Press (2019), ISBN 9781108644181, DOI: https://doi.org/10.1017/9781108644181

2) Ethem Alpaydin. Introduction to Machine Learning, 4th edition (Adaptive Computation and Machine Learning series), The MIT Press (2020), ISBN-13 978-0262043793

3) Andriy Burkov. The Hundred-Page Machine Learning Book. freecomputerbooks.com (2019), ISBN-13 978-1999579500

4) Deisenroth, M.P., Faisal, A.A. and Ong, C.S. Mathematics for Machine Learning. Cambridge: Cambridge University Press (2020), ISBN: 9781108470049

5) Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Jonathan Taylor. An Introduction to Statistical Learning: with Applications in Python (Springer Texts in Statistics) (2023), ISBN-13 978-3031387463.