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Statistics for Machine Learning A.Y. 2024/25
This is the home page of a Ph.D. level course offered at the National Ph.D. in AI - Society. The program covers the basic methodologies, techniques and tools of statistical analysis. This includes basic knowledge of probability theory, random variables, convergence theorems, statistical models, estimation theory, hypothesis testing, bayesian inference, causal reasoning. Other topics covered include bootstrap, expectation-maximization, and applications to machine learning problems.
The course is an extract of the M.Sc. level course Statistics for Data Science.
Instructors
- Andrea Pugnana
- Università di Pisa
- Salvatore Ruggieri
- Università di Pisa
Pre-requisites
Students should be comfortable with most of the topics on mathematical calculus covered in:
- [P] J. Ward, J. Abdey. Mathematics and Statistics. University of London, 2013. Chapters 1-8 of Part 1.
You can refresh such notions through this recording and slides.
Mandatory Teaching Material
The following is the mandatory text book:
- [T] F.M. Dekking C. Kraaikamp, H.P. Lopuha, L.E. Meester. A Modern Introduction to Probability and Statistics. Springer, 2005.
Software
Some running examples will be provided using the R programming language. However, knowledge of R is not required nor mandatory for the exam.
Exams
Ph.D. students may do an exam (on voluntary basis) in the form of a report and a presentation on an advanced topic/survey to be agreed upon. The topic is typically related/relevant to the objectives of the Ph.D. studies of the student.
Ph.D. students will receive an attendance statement if they attend at least 7 out of the 10+1 classes.
Class calendar
Please, subscribe to the course Teams channel to receive updates on the course.
Lessons will be both live-streamed (see Teams channel) and in presence at the Department of Computer Science, University of Pisa.
Teaching material might be updated after the classes to align with actual content and to correct typos. Be sure to download the updated versions.
| # | Date | Room | Topic | Teaching material |
|---|---|---|---|---|
| 01 | 17/3 11-13 | Sem. Est | Introduction. Probability and independence. Bayes' rule. Speaker: A. Pugnana | … |
| 02 | 20/3 14-16 | Sem. Est | Discrete and continuous random variables. Speaker: A. Pugnana | … |
| 03 | 24/3 11-13 | Sem. Est | Expectation and variance. Computations with random variables. Moments. Speaker: A. Pugnana | … |
| 04 | 27/3 14-16 | Sem. Est | Functions of random variables. Distances between distributions. Simulation. Speaker: A. Pugnana | … |
| 05 | 31/3 11-13 | Sem. Est | Law of large numbers. The central limit theorem. Graphical summaries. Kernel Density Estimation. Numerical summaries. Speaker: A. Pugnana | … |
| 06 | 10/4 16-18 | Sem. Est | Unbiased estimators. Efficiency and MSE. Maximum likelihood estimation. Speaker: S. Ruggieri. | … |
| 07 | 14/4 11-13 | Sem. Est | Statistical decision theory. Speaker: S. Ruggieri. | … |
| 08 | 28/4 11-13 | Sem. Ovest | Confidence intervals and Hypotheses testing. Fitting distributions. Testing independence/association. Speaker: S. Ruggieri. | … |
| 09 | 5/5 11-13 | Sem. Est | Bootstrap and resampling methods. Speaker: S. Ruggieri. | … |
| 10 | 8/5 16-18 | Sem. Ovest | Multiple-sample tests of the mean and applications to classifier comparison. Speaker: S. Ruggieri. | … |
| Extra | 12/05 14-16 | Fib-C | Seminar: Introduction to causal modeling and reasoning. Speakers: I. Beretta and M. Cinquini. | … |