Modelling and Optimization

Code:

M3023

Acronym:

M3023

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Artificial Intelligence and Data Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:IACD	63	study plan from 2021/22	3	-	6	48	162

Teaching language

Suitable for English-speaking students

Objectives

1. Learn to formulate an optimization problem mathematically;
2. Study the main relevant optimization problems;
3. Gain sensitivity to the theoretical and practical (computational) difficulty in solving these problems;
4. Study of optimization models underlying the operation of machine learning methods.

Learning outcomes and competences

Knowledge of the optimization models underlying the main machine learning methods.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Prerequisites: only the knowledge provided by the curricular units of the first two years.
Corequisites: none.

Program

1. Optimization on different types of Learning
2. Statistical learning, empirical risk minimization
3. Formal optimization models for learning
4. Optimization for linear predictors
5. Convex learning problems
6. Gradient descent and variants
7. Optimization for margin maximization
8. Optimization in kernel methods
9. Integer optimization models for optimal trees

Mandatory literature

Shai Shalev-Shwartz and Shai Ben-David; Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, 2014. ISBN: 978-1-107-05713-5 (Available in http://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning)

Teaching methods and learning activities

Lectures: presentation of the program topics and discussion of aplications in machine learning.
Labs: problem solving.

Software

python

keywords

Physical sciences > Computer science > Cybernetics > Artificial intelligence
Physical sciences > Mathematics > Applied mathematics > Numerical analysis
Physical sciences > Mathematics > Applied mathematics > Operations research

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Teste	75,00
Exame	25,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Mandatory attendance at classes, in accordance with U.P. rules.

Calculation formula of final grade

Final classification = T1 + T2 + E
T1 = classification of the 1st test, with a score of 7.5 values
T2 = classification of the 2nd test, with a score of 7.5 values
E = classification of the final exam, with a score of 5 values

Note: Students who average 75% or higher on the tests are exempt from the final exam.

Examinations or Special Assignments

n/a

Internship work/project

n/a

Special assessment (TE, DA, ...)

The same evaluation criteria is used for all students.

Classification improvement

Final exam.