====== 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 [[mds:sds:start|Statistics for Data Science]].

=====Instructors=====

  * **Andrea Pugnana**
    * Università di Pisa
    * [[https://andrepugni.github.io/]]
    * [[andrea.pugnana@di.unipi.it]]  

  * **Salvatore Ruggieri**
    * Università di Pisa
    * [[http://pages.di.unipi.it/ruggieri/]]
    * [[salvatore.ruggieri@unipi.it]]   


=====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 [[http://131.114.72.230/sds/video/sds06_20220225.mp4|recording]] and {{:mds:sds:s4ds06.pdf|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.

  * [[https://cran.r-project.org/|R]]
  * [[https://www.rstudio.com/|R Studio]]


=====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 [[https://teams.microsoft.com/l/team/19%3AWNufde35gV7296FvkTLCt7tHKShmbJQTqZT8h5lsPMA1%40thread.tacv2/conversations?groupId=914fe1d1-5fb2-4023-be47-e5a9e4eda8a8&tenantId=c7456b31-a220-47f5-be52-473828670aa1|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.  | ... |