Numerical Analysis Laboratory
A.Y. 2024/2025
Learning objectives
The course aims to provide the theoretical and implementation foundations of Machine Learning, with particular reference to modern deep neural networks (Deep Learning). Notions of approximation theory, optimization theory and statistical theory of learning related to neural networks will be provided. The link of neural network-based algorithms with classical numerical methods and their properties will be emphasized. During the course, some significant applications will also be presented, relating in particular to image and signal processing.
Expected learning outcomes
At the end of the course students will possess basic knowledge relating to the structure of modern deep neural networks, they will be able to recognize the fundamental typologies and will possess knowledge of the main training algorithms. They will be able to understand the approximation properties of the networks in question.
Students will also be able to implement some relevant types of neural networks in Python/Pytorch in their completeness
Students will also be able to implement some relevant types of neural networks in Python/Pytorch in their completeness
Lesson period: Second semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Fundamentals of Machine learning theory; learning tasks; measure of generalization ability
Elements of optimization theory, optimization algorithms
Introduction to neural networks: fully connected feed-forward networks, back-propagation, cost functions
Neural networks and approximation theory; universal approximation theorem
Optimization and regularization
Convolutional neural networks: application to image processing
Advanced elements of Machine Learning: autoencoder networks, generative networks; neural networks and inverse problems; elements of Explainable AI
Elements of optimization theory, optimization algorithms
Introduction to neural networks: fully connected feed-forward networks, back-propagation, cost functions
Neural networks and approximation theory; universal approximation theorem
Optimization and regularization
Convolutional neural networks: application to image processing
Advanced elements of Machine Learning: autoencoder networks, generative networks; neural networks and inverse problems; elements of Explainable AI
Prerequisites for admission
Calculus xx, Foundations of Numerical Analysis, Probability
Teaching methods
The topics will be treated from a theoretical point of view and constantly accompanied by the computer implementation of the algorithms and architectures studied, both starting from scratch and using widely used dedicated libraries (in particular pytorch) on the Colab environment. A few hours will be dedicated to initial literacy in the Python language
Teaching Resources
notes during lessons
Assessment methods and Criteria
The exam will consist of the creation of a hands-on project (APPROVED/NOT APPROVED)
MAT/08 - NUMERICAL ANALYSIS - University credits: 3
Laboratories: 36 hours
Professors:
Causin Paola, Naldi Giovanni
Shifts:
Professor(s)