Obiettivi formativi Learning goals
Statistical Machine Learning provides a rigorous introduction to the statistical and probabilistic principles that underpin modern artificial intelligence, including predictive and generative AI, and data-driven decision making. The course presents machine learning as a statistical discipline, where learning algorithms are viewed as methods for inference from data under uncertainty.
The course combines theoretical foundations with methodological and computational aspects. Students will develop an understanding of probabilistic modelling, statistical inference, optimization and generalization theory, together with the practical skills required to implement, evaluate and compare modern learning algorithms. Representative methodologies include kernel methods, deep neural networks, probabilistic generative models such as denoising diffusion probabilistic models (DDPMs), and modern uncertainty quantification techniques including conformal prediction. Throughout the course, particular emphasis is placed on principled model assessment, uncertainty quantification, and the interpretation of predictive models.
Theoretical results are complemented by programming assignments and a substantial project based on real datasets, allowing students to connect statistical principles with computational implementation using modern open-source scientific computing environments.
Knowledge and understanding
Upon successful completion of the course, students will understand the statistical principles underlying modern machine learning and their role in predictive and generative artificial intelligence. They will be able to interpret learning algorithms within a unified probabilistic framework, understanding how statistical modelling, inference, optimization and regularization jointly determine predictive performance and generalization.
Students will understand the assumptions, mathematical foundations and computational characteristics of the principal supervised and unsupervised learning methodologies, including kernel methods, (deep) neural networks and probabilistic generative models. They will also understand the theoretical principles governing model selection, validation, complexity control/regularization, and uncertainty quantification, together with the statistical tools used to assess and compare learning algorithms.
Finally, students will acquire familiarity with modern scientific computing environments for implementing, analysing and experimentally evaluating statistical machine learning methods.
Applying knowledge and understanding
Upon successful completion of the course, students will be able to formulate complex data analysis problems within an appropriate statistical learning framework and identify suitable modelling strategies based on the characteristics of the data and the objectives of the analysis.
They will acquire the practical skills required to implement, train and compare modern machine learning methods, integrating statistical modelling with computational techniques to build complete data analysis pipelines. Students will learn to assess predictive performance using principled statistical methodologies, quantify predictive uncertainty, and interpret the results in light of the assumptions and limitations of the adopted models.
Programming assignments and a final project will provide hands-on experience with real-world datasets, enabling students to bridge theoretical concepts with practical implementation and to develop reproducible machine learning solutions.
Making judgements
Upon successful completion of the course, students will have developed the ability to critically evaluate statistical learning methodologies from both theoretical and empirical perspectives. They will be able to assess whether the assumptions underlying a learning model are appropriate for a given application, compare competing modelling approaches, and interpret empirical results in light of statistical evidence.
Particular emphasis is placed on understanding the role of uncertainty in statistical learning, enabling students to distinguish between predictive performance, statistical significance, and confidence in model outputs. Students will develop the ability to critically assess the reliability, robustness and limitations of learning algorithms when applied to complex real-world data.
Communication skills
Students will develop the ability to communicate statistical and machine learning methodologies effectively through written reports and oral presentations. They will learn to present methodological choices, experimental results, and quantitative evidence in a clear, rigorous and reproducible manner, adapting the level of technical detail to both specialist and non-specialist audiences.
The final project will also foster the ability to discuss modelling decisions, interpret experimental findings, and provide constructive scientific feedback on the work of peers.
Learning Skill
The course aims to develop the independent learning skills required for continued study and research in statistical machine learning and artificial intelligence. By combining theoretical analysis with computational practice, students will acquire the ability to understand new methodologies from the scientific literature, critically evaluate their statistical foundations, and adapt them to novel application domains.
Particular emphasis is placed on developing a probabilistic mindset for reasoning under uncertainty, enabling students to understand emerging machine learning methodologies, integrate advances from the rapidly evolving AI landscape, and pursue lifelong learning with methodological rigour and intellectual independence.
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Obiettivi formativi General objectives
The primary objective is to study algorithms and data structures that efficiently solve problems whose solution, using trivial approaches, would require very high resources. The algorithms studied will be implemented in Java language.
Specific objectives
Knowledge and ability to understand
Basic data structures and their use in solving sorting, searching, and graph problems will be shown. It will be shown how the data structures described are made available in Java language. The student will be able to determine the computational complexity of algorithms, and associate them with the appropriate complexity class.
Ability to apply knowledge and understanding
At the end of the course the students will be able to determine algorithms to efficiently solve complex problems, in particular problems on graphs, and choose the most suitable data structures to obtain an efficient implementation of the algorithm. They will also be able to use the Java classes that implement the data structures studied.
Autonomy of judgment
Students will be able to distinguish the computational complexity of problems and algorithms, and to identify the computationally more costly steps in solving a problem.
Communication skills
Students will be able to describe, in appropriate terms, the characteristics of the main data structures, and identify the primitives needed to efficiently implement an algorithm.
Learning ability
Students who pass the exam will be able to take advanced courses, of an applicative nature, that require the use of sophisticated algorithms. They will also be able to appreciate software engineering and computational complexity theory teachings.
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Obiettivi formativi Learning goals.
The different techniques existing for Big Data management will be illustrated, with a particular emphasis on NoSQL databases.
The course will also deal with the problem of collecting Big Data from various sources such as from the web or from the online social networks.
This will require also the introduction of the different formats that are commonly used to encode unstructured, semi-structured and structured data and of the different techniques that can be used to automate their processing.
Successively, pre-processing techniques, including denoising and imputation of missing data, will be considered.
Then, the course will treat dimensionality reduction techniques, based on feature extraction and feature selection.
Finally, some statistical learning models, supervised and unsupervised, for the analysis of Big Data, will be presented.
Real-world problems will be addressed during the course using suitable software.
Knowledge and understanding.
The student will learn as to apply some statistical learning techniques for dimensionality reduction, based on feature extraction and feature selection.
Moreover, he will know and understand some powerful statistical learning models, supervised and unsupervised, to analyse Big Data.
Applying knowledge and understanding.
The student will be able to manage Big Data collected from various sources.
He will learn as to apply dimensionality reduction techniques, based on feature extraction and feature selection.
Moreover, he will be able to choose and apply some powerful statistical learning models to analyse Big Data.
Making judgements.
Students will develop critical skills through the application of a wide range of machine learning and statistical models.
They also will develop the critical sense through the comparison between alternative solutions to the same problem obtained using different learning logics.
They will learn to critically interpret the results obtained by applying the procedures to real data sets.
Communication skills.
Students, through the study and execution of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the intermediate and final written tests and in the oral tests.
Communication skills are also developed through group activities.
Learning skills.
Students who pass the exam will have learned an analytical approach that allows them to tackle Big Data analysis with statistical models and machine learning methods.
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Obiettivi formativi Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.
Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.
Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.
Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.
Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test.
Communication skills will be also developed through group activities.
Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.
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Obiettivi formativi General
Managers worldwide, beyond their personal experience, rely more and more on the use of
quantitative decision models which allow to take advantage of today’s data availability. Morover,
new computational tools, including algorithms, cloud computing and distributed processing, make
it possible to both develop and compute analytical models in a very short time, meeting the
requirement of practical applications and often using real time data. Data Driven Decision Making
is the new paradigm for managers to make better, evidence based, more rational, transparent and
reliable decisions.
In this context, the primary educational objective of the course is students' learning of the main
decision problems that arise in real world and the quantitative methods to model them and to
feed them with adequate data. Students must also be able to correctly use, for decision-making
and management purposes, computer tools to analyze data generated by real problems in
different contexts (e.g. service management, marketing, transportation, operations management
and production, and finance) through the analysis of several case studies.
Specific objectives
a) Knowledge and ability to understand
After attending the course the students know and classify the main decision problems arising in
real world organization and the main analytical methods (decision and optimization models and
algorithms) to be used to support a Manager during his/her decision process.
b) Ability to apply knowledge and understanding
At the end of the course the students are able to formalize real problems in terms of decision
problems and to apply the specific methods taught in the course to solve them. They are also able
to classify the type of problem to it the most appropriate quantitative method, experimenting the
effectiveness for decisional purposes also on real problems.
c) Autonomy of judgment
Students develop critical skills through the application of modeling, decision analysis and multi
objective optimization methodologies to a broad set of practical problems. They also develop the
critical sense through the comparison between alternative solutions to the same problem
obtained using methods of analysis and realistic scenarios different from each other. They learn to
critically interpret the results obtained by applying the procedures to real data sets.
d) Communication skills
Students, through the study and the carrying out of practical exercises, acquire the technical-
scientific language of the course, which must be properly used both in the intermediate and final
written tests and in the oral tests. Communication skills are also developed through group
activities.
e) Learning ability
Students who pass the exam have learned methods of decision analysis and multiobjective
optimization that allow them to face, decision-making problems and optimization on complex
organizations.
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Obiettivi formativi General Targets:
Prior educational teaching concern is the students’ understanding of the main (Economic Statistics Modeling) problems and methods for Panel Data making use of parametric estimation. Here the empirical focus is on individuals represented by Decisional Making Units (DMU). More specifically, these are banks typically involved in the European (and also international) banking system. The course will focus on managerial problems of these firms by studying equations such as cost (mostly) and profit functions which are relevant to asses on the Efficiency of banks. Furthermore, students should know both how to solve analytical problems, in order to apply the appropriate methodology, and to interpret results obtained from empirical applications to actual data.
Specific Targets:
a) Knowledge and capability in understanding.
After attending the course, students know and understand main problems of Panel Data. In particular, the course will account for the logic for building empirical models, related to the underlying economic theory (and the consequent subdivisions in endogenous and exogenous variables), with one or more equations in order to evaluate the degree of efficiency of a typical Decisional Making Unit (here the bank and possibly the insurance company). We will study the main estimation methods of Panel Data for solving efficiency problems pertaining a firm traditionally operating in the private sector.
b) Capability of applying knowledge and comprehension
At the end of the course students are able to formalize and solve problems by means of specific methods as well as treating fundamental models of Panel Data to answer questions on the Efficiency and Productivity Analysis for the banking system. Finally, students will be able to apply the methods studied to real data and interpret results correctly also from a theoretical point of view.
c) Autonomy in assessment.
Students develop analytical skills and capacity of facing different alternative approaches for solving actual empirical problems.
d) Communication ability.
Students learn technical language which is appropriate for the subject studied and that will be used at the oral and written exam, by means of practical exercises.
e) Learning capacity.
Students passing the exam are capable to extend the methodology studied also to other fields and derive conclusions.
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Obiettivi formativi Learning goals
The main goal is acquiring advanced modelling techniques for mutivariate economic data. Students are expected to understand the theoretical foundations of the methods studied and to apply them to real datasets.
Knowledge and understanding
The focus of the course will on the Vector Autoregressive (VAR) model in stationary and non stationary settings, using both asymptotic and simulation (bootstrap) inference
Applying knowledge and understanding
After the course students will be able to specify a VAR model, evaluate if is adequate to the dataset of interest , use for estimating causal relationship and formatulate forecasts
Making judgements
Learning how to judging the adequacy of the models and assessing the uncertainty of the estimated relationships and forecasts will be an essential part of the course
Communication skills
Learning to communicate the results of the estimation process both in oral and written form will be an essential part of the course
Learning skills
The models object of the course are essential parts of the most advanced and complex models used in quantitative economic analysis, which the students will then be able to tackle.
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