Machine Learning
A.Y. 2026/2027
Learning objectives
The course provides the basic concepts of machine learning, developing an understanding of its theoretical and methodological aspects, and offering an overview of the concepts and terminology commonly used in disciplines that rely on these methods. Particular emphasis is placed on the aspects of machine learning that are most closely connected to physics.
Expected learning outcomes
By the end of the course, students will be able to critically select the most appropriate method for a given machine learning problem; discuss machine learning methods within the conceptual frameworks that underpin them; independently read contemporary research papers in the field; and explain the role of physics in understanding the underlying principles of machine learning and in developing new models and paradigms.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
INTRODUCTION
- Fundamental concepts and terminology
- Curse of dimensionality and data geometry
- A paradigmatic problem: polynomial fitting
- Foundations of statistical learning theory
- Bayesian inference
SIMPLE MODELS
- Unsupervised learning techniques (PCA, clustering, density estimation, )
- Linear regression
- Learning rules
- The perceptron (storage capacity and teacher-student setting)
- Neural networks and the universal approximation theorem
- Logistic regression
KERNEL METHODS
- Kernel regression
- Support vector machines
- Gaussian processes
- Kernel methods as a conceptual framework for deep learning
GENERATIVE AND ENERGY-BASED MODELS [optional]
- Associative memories and the Hopfield model
- Restricted Boltzmann machines
- Diffusion models
- Fundamental concepts and terminology
- Curse of dimensionality and data geometry
- A paradigmatic problem: polynomial fitting
- Foundations of statistical learning theory
- Bayesian inference
SIMPLE MODELS
- Unsupervised learning techniques (PCA, clustering, density estimation, )
- Linear regression
- Learning rules
- The perceptron (storage capacity and teacher-student setting)
- Neural networks and the universal approximation theorem
- Logistic regression
KERNEL METHODS
- Kernel regression
- Support vector machines
- Gaussian processes
- Kernel methods as a conceptual framework for deep learning
GENERATIVE AND ENERGY-BASED MODELS [optional]
- Associative memories and the Hopfield model
- Restricted Boltzmann machines
- Diffusion models
Prerequisites for admission
Basic knowledge of probability, statistics, and linear algebra.
Teaching methods
The course is delivered through classroom lectures. Part of the lectures will be devoted to exercises and in-depth discussions on selected topics, during which students will actively participate. At the instructor's discretion, a computer laboratory session may be organized.
Teaching Resources
(1)
Christopher M. Bishop
Pattern recognition and machine learning
Springer New York, 2006
Freely available here:
https://www.microsoft.com/en-us/research/wp-content/uploads/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf
(2)
A. Engel, C. Van den Broeck
Statistical mechanics of learning
Cambridge University Press, 2012
Christopher M. Bishop
Pattern recognition and machine learning
Springer New York, 2006
Freely available here:
https://www.microsoft.com/en-us/research/wp-content/uploads/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf
(2)
A. Engel, C. Van den Broeck
Statistical mechanics of learning
Cambridge University Press, 2012
Assessment methods and Criteria
An oral examination of approximately 30 minutes aimed at assessing the expected learning outcomes.
PHYS-02/A - Theoretical Physics of Fundamental Interactions, Models, Mathematical Methods and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
PHYS-04/A - Theoretical Physics of Matter, Models, Mathematical Methods and Applications - University credits: 3
Lessons: 42 hours
Professor:
Gherardi Marco
Professor(s)