Advanced topics in machine learning (CK0255) Probability and random variables (TIP8421)
The course overviews basic facts of probability and distribution theory, the mechanisms of basic inference, large-sample theory on convergence in probability and convergence in distribution, the central limit theorem, and complete inference based on maximum likelihood theory.
Introductory refresher: Probability theory and distribution theory;
Multivariate distributions: Distributions, expectations, transformations, correlation and dependence;
Common distributions: The binomial distribution and friends, the Poisson distribution, the gamma distribution and friends, the normal distribution, $t$ and $F$ distributions, mixtures;
Elementary inference: Sampling and statistics, confidence intervals, hypothesis testing;
Consistency and limiting distributions: Generalities about convergence in probability and distribution, the central limit theorem;
Maximum likelihood methods: Estimation and testing, Rao-Cramér lower bound, tests, expectation-maximization.
If time allows, selected topics related to sufficiency, completeness, uniqueness and independence will be discussed, too.
Physical location ♜: Wednesdays and Fridays 14:00-16:00, Bloco 951, Sala 10. Internet location ♖: Here! Or, here (CK0255/TIP8421) for mambojumbo related to administration.
Evaluation ✍: Approximately half a dozen theoretical and practical problem sets will be assigned as homework: Home assignments are for training but are not mandatory, they can be handed-in but they will not be evaluated. The actual evaluation will be based on three or four partial evaluations (APs) in class (weight 70%) and a final project (weight 30%). If needed a final evaluation (AF) will be arranged.
As we use problem set questions covered by books, papers and webpages, we expect you not to copy, refer to, or look at the solutions in preparing your answers. We expect you to want to learn and not google for answers: If you do happen to use other material, it must be acknowledged clearly with a citation on the submitted solution.
☯ The purpose of problem sets is to help you think about the material, not just give us the right answers.
Homeworks must be done individually: Each of you must hand in his/her own answers. In addition, each of you must write his/her own code when requested. It is acceptable, however, for you to collaborate in figuring out answers. We are assuming that you take the responsibility to make sure you personally understand the solution to any work arising from collaboration (though, you must indicate on each homework with whom you collaborated).
⚛ To typeset assignments, students are encouraged to use this LaTeX template: Source (PDF).