Department of Mathematics and Statistics

• An Introduction to viscosity solutions with applications in Economics by A. Davini: Friday September 12, 22 and 26 from 11am to 12:30pm in Auditorium 6, Monday September 15 and 22 from 11am to 12:30pm in Auditorium 6, Thursday September 18 from 2pm to 5pm in Auditorium 4, and Thursday September 25 from 2pm to 5pm in Auditorium 6, 2025
• Prophet Inequalities by B. Ziliotto : Thursday September 4 from 9:30am to 11am in Auditorium 5, Friday September 5, 12, 26 and October 3 from 9:30am to 11am in 335, Monday September 8 from 9:30am to 11am in 535, Monday September 15, 22, 29 from 9:30am to 11am in 335, 2025
• Diffusion Models in Generative AI by J. Chhor: in Semester 2 after first half of Stochastic Optimal Control in Economics
• Functional Data Analysis by Davy Paindaveine (Université Libre de Bruxelles)
• Strategic Aspects of Bandit Models by Eran Shmaya (Stony Brook University)

• Selected topics in nonsmooth optimization with G Li:  Monday September 16, 23, 30 and October 7, 2024 from 9h30 to 12h30.
• Bi-Level Optimization with D. Salas : Wednesday October 16 and 23 from 9h30 to 12h30; Wednesday November 6 from 8h to 11h; Wednesday November 13 and 27 from 9h30 to 12h30.
• Statistical Theory of Deep Learning from February 10 to 14, 2025
• Prophet Inequalities with B. Ziliotto : Tuesday October 1 and 8 from 15h30 to 18h30; Tuesday October 15, 22 and November 5 from 14h to 17h
• Online and Reinforcement Learning with J. Chhor : Semester 2.

Ingrid Van Keilegom (TSE Visitor) gave a short course on duration analysis with a review of the basics and some more specialized topics on the following dates:

• Class 1: Monday May 13 from 10 to 12 in T225
• Class 2: Tuesday May 14 from 1:30 to 3:30 in T225
• Class 3: Wednesday May 15 from 10 to 12:30 in T225

Title: Duration analysis: review of the basics and some more specialized topics

In this course we started by reviewing the basics of duration analysis (censoring, Kaplan-Meier estimator, Cox model, log-rank test,…) (class 1). Then, more specialized topics have been treated, namely the topic of cure models (class 2) and of dependent censoring (class 3). Cure models are used when the event of interest (e.g. finding a new job) never happens for a proportion of the population, leading to a survival function with a mass at infinity. It is then often of interest to model and estimate separately that mass at infinity and the survival function of those with finite event times, depending on a set of covariates. Dependent censoring means that the duration time and the censoring time are not stochastically independent, whereas usually in duration analysis it is assumed that they are independent. The survival function can in that case not be identified without additional assumptions. Several models will be discussed that lead to (partially) identified survival functions. It has also be seen how the presence of covariates can help to identify the survival function.

Professor Rik Lopuhaä (TSE Visitor) gave a course on February 2024.

Title: Robust estimation of multivariate location and scatter

Abstract: in this course, we discussed several popular methods for robust estimation of multivariate location and scatter including S-estimators and the minimum covariance determinant estimator. We introduced these methods, explain their relationship with M-estimators, and discussed their robustness and asymptotic properties. We also discussed the mathematical techniques that can be used to rigorously derive the properties and features of these methods, and illustrate their implementation in R and how to use them in practice.

Peter Takac (University of Rostock, Germany) gave a course at TSE on February 2023 "Semi-linear and quasi-linear Black-Scholes-type equations in Mathematical Finance: Analytical and numerical methods with some monotonicity"

-> Syllabus (PDF)

Pierre Alquier (Riken AIP) gave courses at TSE on November 2022 "PAC-Bayes and Information bounds, with Applications to Variational Inference"

-> Syllabus (PDF)