Course Syllabus
Sustainable Development Goals
Aims
The aim of this course is to provide the theoretical foundations of Statistics and indicate how the theory sheds light on the properties of practical methods used in AI. The topics include estimation, prediction, testing, confidence sets, and the general approach to statistical modeling and learning, with some exposure to robust statistical inference.
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Knowledge and understanding
Students should acquire a thorough knowledge of the principles and techniques of statistical inference, from point estimates, confidence intervals, and hypothesis testing, up to statistcal modelling. They must understand how these methodologies allow reliable conclusions to be drawn from data, even in the presence of uncertainty or variability. -
Applied knowledge and understanding
Students will be able to apply statistical inference techniques to complex problems, using advanced statistical software. They will be able to design studies, analyze real data, interpret results and make informed decisions in research, economics, finance or other scientific disciplines. -
Autonomy of judgment
Students will develop the ability to critically evaluate inference methodologies, recognizing the limitations and assumptions of each method. They will be able to compare different approaches, interpret results in an informed manner and evaluate the reliability of statistical conclusions, even in the presence of complex data or limited samples. -
Communication skills
Students will learn to communicate the results of inferential analyses clearly and precisely, adapting language and graphic representations to different audiences, including colleagues, decision makers or non-specialists. They will be able to write technical reports and present their results with graphical representations in an effective and understandable way. -
Learning skills
Finally, students will be encouraged to work autonomously, taking responsibility for their own analyses and decisions based on data. They should be able to design statistical studies, choose the most appropriate techniques and critically evaluate the results, having acquired a professional attitude.
Contents
The course consists of a theoretical part, with applications on data using the R software environment. Statistical Inference and statistical modeling are presented, with a view on modern methods for supervised and unsupervised learning widely employed in AI.
Detailed program
- Crash course: Quick review of basic probability theory, and on Statistical inference to recall Interval estimation and Hypothesis testing.
- Simple linear regression: least squares estimation method
- Multiple linear regression: least squares estimation method, model adequacy measures, sampling distribution of OLS estimators, hypothesis tests and confidence intervals for the regression coefficients, analysis of variance, outliers and influential observations, robust linear regression.
- Linear models for regression and for classification
- Lasso and Ridge regression, with model selection
- Robust statistical modeling
- Unsupervised learning: model-based clustering, latent variables, PCA and factor analysis.
Prerequisites
Statistics background: basis of probability theory and knowledge of the most relevant continuous and discrete random variables.
Mathematics background: linear algebra, matrix theory and advanced calculus.
Teaching form
40 hourd of frontal lessons and 24 hours of interactive practical lessons in R language.
Attendance to lectures and interactive exercises is highly recommended.
Textbook and teaching resource
- Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. Cengage learning.
- James G., Witten D., Hastie T. and Tibshirani R. (2021). An Introduction to Statistical Learning, with applications in R (2nd edition). Springer Verlag.
- Hastie T. , Tibshirani R., Friedman J. (2021). The Elements of Statistical Learning (2nd edition). Springer Verlag.
Semester
First
Assessment method
The exam consists in a written exam with three open-ended questions to assess the student's knowledge and understanding of the subject, (1h30m) jointly with the development of an application in R on real data (1h). The exam is closed book. An additional oral discussion can be requested by the lecturer.
Office hours
Office: University of Milan-Bicocca,
Department of Statistics and Quantitative Methods, Via Bicocca degli Arcimboldi, 8
20125 MILANO
Building U7-Civitas, Floor 4, room 4021
Phone: +39-02-6448-3118
just drop me an email (francesca.greselin@unimib.it) and we will agree on how and when to meet
Sustainable Development Goals
Staff
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Francesca Greselin
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Giorgia Zaccaria
