Statistics

This course provides a study of the fundamentals of statistical inference such as probability distribution, point estimation, interval estimation, and hypothesis testing. Other topics include: sampling distributions; parameter estimation; confidence intervals; parametric hypothesis testing; ANOVA and nonparametric contrasts; Bayesian inference.

This course covers generalized linear models, some major statistical learning tools, and models for complex causal relationships, mainly in the context of social sciences. Lectures are combined with practical computer lab tutorials in order to illustrate the applications of the theoretical tools. The analysis is carried out using the statistical software environment R, which is freely available under the GNU General Public License.

This course provides an introduction to different methods for supervised learning (regression and classification). The course contains both model- and algorithm-based approaches. The main focus is supervised learning, but unsupervised methods like clustering are briefly discussed. The course also deals with issues connected to large amounts of data (i.e. "big data"). The course gives a good basis for further studies in statistics or data science, but is also useful for students who need to perform data analysis in other fields.

The course provides an elementary introduction to probability and statistics with applications. It covers statistical methods often used by decision makers to present and describe data and how to draw conclusions about populations and make reliable forecasts. In addition, since many statistical calculations are only feasible when one uses computers, students will also learn how to use Microsoft Excel to perform statistical analyses. 

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. This course provides students with the advanced knowledge to the field of network analysis and its usages in other fields of research. At the end of the course, students gain knowledge on the Web as a socio-technical system involving specific processes, entities, and behaviors, using interdisciplinary methods that blend computer science, sociology, ethnography, economics, linguistics, etc. The students are able to analyze the Web phenomena similarly to typical objects from natural sciences, distinguishing between data and applications, agents from computationally generated profiles, and addressing the characteristics of networks of entities emerging from the informational, physical, social, and conceptual spaces constituting the Web.

This course is a basic introduction to the dynamics of time-dependent data. The course starts by discussing the type of data to be analyzed. Apart from typical single number time series such as temperatures or stock prices, students also consider the evolution of geospatial variables, 3D, and text data. This is followed by the basic Exploratory Data Analysis in the context of time-dependent data. The course will then provide insights on how time-dependent data can be analyzed based on real world examples and applications. Areas of applications that might be considered are speech, stock market evolution, music, geospatial data such as MRI scans, and medical time series data used in diagnostics.

This course covers the basic concepts and applications of linear optimization, convex optimization, and non-linear & combinatorial optimization. Topics include introduction to optimization, intro to convex optimization, linear programming (LP), least squares (LS), quadratic programming (QP), second-order cone programming (SOCP), semi-definite programming (SDP), duality: connecting convex optimization with non-convex optimization, strong/weak duality, gradient descent ascent (GDA), interior point method (IPM), Lagrange relaxation, applications: unsupervised learning (GAN, Wasserstein GAN), and applications: sparse/low-rank recovery (compressed sensing, matrix completion). 

Prerequisites: Calculus, Linear Algebra 

The course equips students with practical skills in data analysis and visualization techniques essential for extracting actionable insights from complex datasets. Lab sessions and projects help students learn about exploratory data analysis, geospatial visualization, and interactive dashboard development. Students gain skills that are highly valued across a wide set of academic and business fields. 

This course introduces the mathematical theory of probability, starting with the definition of probability spaces to the fundamental limit theorems, namely the law of large numbers and the central limit theorem. The following concepts are covered: measurement theory, probability spaces; conditional probability and independence; random variables, discrete random variables; density random variables; discrete random vectors; density random vectors; notions of convergence for sequences of random variables; limit theorems; Gaussian vectors. 

This course explores basic statistical concepts and tools to analyze real world data, understand concepts of of uncertainty and probability, and apply distribution models to solve relevant problems. Topics include: analysis of univariate data; analysis of bivariate data; introduction to probability; random variables; distribution models; linear regression.