Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Type D and Type F activities

I semestre From 10/1/20 To 1/29/21
years Modules TAF Teacher
1° 2° Algorithms D Roberto Segala (Coordinator)
1° 2° Scientific knowledge and active learning strategies F Francesca Monti (Coordinator)
1° 2° Genetics D Massimo Delledonne (Coordinator)
1° 2° History and Didactics of Geology D Guido Gonzato (Coordinator)
II semestre From 3/1/21 To 6/11/21
years Modules TAF Teacher
1° 2° Advanced topics in financial engineering F Luca Di Persio (Coordinator)
1° 2° Algorithms D Roberto Segala (Coordinator)
1° 2° Python programming language D Vittoria Cozza (Coordinator)
1° 2° Organization Studies D Giuseppe Favretto (Coordinator)
List of courses with unassigned period
years Modules TAF Teacher
1° 2° ECMI modelling week F Not yet assigned
1° 2° ESA Summer of code in space (SOCIS) F Not yet assigned
1° 2° Google summer of code (GSOC) F Not yet assigned
1° 2° Introduzione all'analisi non standard F Sisto Baldo
1° 2° C Programming Language D Pietro Sala (Coordinator)
1° 2° LaTeX Language D Enrico Gregorio (Coordinator)
1° 2° Mathematics mini courses F Marco Caliari (Coordinator)

Teaching code

4S008279

Credits

3

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Period

I semestre dal Oct 1, 2020 al Jan 29, 2021.

To show the organization of the course that includes this module, follow this link:  Course organization

Learning outcomes

The objective is to introduce statistical modelling and exploratory data analysis. The mathematical foundations of Statistical Learning (supervised and unsupervised learning, deep learning) are developed with emphasis on the underlying abstract mathematical framework, aiming to provide a rigorous, self-contained derivation and theoretical analysis of the main models currently used in applications.

Program

The entire course will be available online. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held in-class.

1. Linear regression
Normal random vectors and their properties. Linear regression models. Least squares and
projections. Parameter estimators and their optimality (Gauss-Markov Theorem, with
proof). Distribution of the estimators. Testing predictors’ significance. Best subset selection
and its formulation as Mixed Integer Optimization problem. Ridge regression.
Interpretation of ridge regression with the singular value decomposition (with proof).
LASSO.

2. Linear methods for classification
Bayes classifier and its optimality (with proof). Linear regression after binary coding. Linear
discriminant analysis. Separating hyperplanes. The perceptron algorithm (with proof of
termination)

3. Model selection and assessment.
Loss function; training and prediction error. Cross validation. Explicit expression of cross
validation for linear regression (with proof). Bootstrap and application to model
assessment.

4. Clustering.
Center based clustering. K-center clustering; K-median clustering; K-means clustering.
Lloyd’s algorithm for K-means. Ward’s algorithm. Spectral clustering: graph Laplacian. The
multiplicity of the eigenvalue 0 of the graph Laplacian equals the number of connected
components (with proof). Unnormalized and normalized spectral clustering algorithms.
Relation of spectral clustering with graph-cut.

5. Introduction to Neural Networks.
Single layer neural networks. Cybenko’s density theorem (with proof). Multilayer neural
networks. Training a neural network: the gradient descent algorithm.

Reference texts
Author Title Publishing house Year ISBN Notes
T. Hastie, R. Tibshirani, J. Friedman. The elements of statistical learning. Data mining, inference, and prediction. (Edizione 2) Springer 2009

Examination Methods

Oral exam

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE