This short course will give an introduction to data science for physicists. The course will introduce the basics of data science problems, and introduce students to Bayesian techniques for inference, unsupervised learning methods for exploratory data analysis, and neural networks. On the theoretical side, students will learn fundamentals of random matrix theory and of the theory of neural networks.

After this course, students will 1. Understand the fundamental ingredients of a data science problems 2. Be able to apply the basics of Bayesian inference problems to inference problems 3. Know the basics of random matrix theory, including the Wigner and Wishart ensembles as well as their spectra 4. Know basic unsupervised learning techniques 5. Know the basics of neural network architectures and neural learning dynamics in supervised learning.

Pre-requisites are probability, linear algebra and analysis at the level obtained after successful completion of a Bachelor degree in Physics, Mathematics, Mathematical Engineering, Computer science, or a similar course. The course does not assume any knowledge of data science.

I Basics of Bayesian inference [R. Trotta] Introduction to inference: what is it? Why do we need it? Frequentist probability vs bayesian probability Confidence levels, posterior distributions, priors and the difference between all those If time allows: classical hypothesis testing vs Bayesian model comparison II An introduction to random matrix theory [J. Barbier] The Wigner ensemble and the semi-circular law Wishart Ensemble and Marchenko–Pastur law Spiked matrix models and the BBP transition III Introduction to unsupervised learning and dimensional reduction [A. Laio] Principal Component Analysis Multidimensional scaling and kernel methods Intrinsic dimension estimates IV Neural networks [S. Goldt] Neural networks 101: types and applications + some open theoretical problems Learning dynamics: empirical phenomena and theoretical predictions The impact of data structure Unsupervised learning: from Hebbian learning to independent components

This is an entirely taught course.

As an introduction to the course, chapters 1-3, 20-21, 38-39, 41, and 44 of the book “Information Theory, Inference, and Learning Algorithms” by David MacKay are recommended reading.

Dispense;

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... The course will be assessed by a written exam of two hours, covering all four topics of the course.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.