Probability & Statistics Seminar

Upcoming sessions :

• Thursday 23.10.2025, 13h30, MNO 1.020
  Marina Gomtsyan (Laboratoire de Probabilités, Statistique et Modélisation), TBA
  Abstract: TBA

• Thursday 13.11.2025, 12h00, MNO 1.050
  Søren Wengel Mogensen (Department of Finance, Copenhagen Business School), Graph learning using integer programming
  Abstract: Learning dependence structures among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data is known as graph learning or as causal discovery if the graphs are given a causal interpretation. Existing approaches typically rely on restrictive assumptions about the data-generating process, employ greedy oracle algorithms, or solve approximate formulations of the graph learning problem. As a result, they are either sensitive to violations of central assumptions or fail to guarantee globally optimal solutions. We address these limitations by introducing a nonparametric graph learning framework based on nonparametric conditional independence testing and integer programming. We encode the graph learning problem as an integer-programming problem, prove that our encoding is sound and complete, and that solving the integer-programming problem provides a globally optimal solution to the original graph learning problem. Our method leverages an efficient encoding of graphical separation criteria, enabling the exact recovery of larger graphs than was previously feasible. We provide an implementation in the openly available R package `glip’ which supports learning (acyclic) directed (mixed) graphs and LWF-chain graphs. From the resulting output one can compute representations of the corresponding Markov equivalence classes or weak equivalence classes. Empirically, we showcase that our approach achieves state-of-the-art performance on benchmark datasets for learning acyclic directed mixed graphs.

• Thursday 27.11.2025, 13h30, MNO 1.00
  Lorenzo Dello Schiavo (Università degli Studi di Roma “Tor Vergata”), TBA
  Abstract: TBA

• Thursday 4.12.2025, 13h30, MNO 1.020
  Petr Zamolodtchikov (Bielefeld University), TBA
  Abstract: TBA

• Thursday 19.02.2025, 13h30, MNO 1.020
  Eva Loecherbach (Université Paris 1), TBA
  Abstract: TBA

Past sessions :

• Tuesdat 14.10.2025, 13h30, MNO 0.020
  Diego Bolón (Université Libre de Bruxelles), A review on highest density region estimation
  Abstract: Highest density regions (HDRs in short) are sets where the density function of the data exceeds a given (and usually high) threshold. Estimating the HDRs of a population from a data sample is a useful tool for data visualisation, cluster analysis, outlier detection, and prediction. Due to its practical utility, HDR estimation for Euclidean data has been widely considered in the literature. However, HDR estimation in other contexts has only recently been addressed. In this talk, we begin by exploring the different techniques that have been developed for HDR estimation in the Euclidean context. This introduction allows us to highlight the particular issues of this specific topic, such as how to measure consistency in this context. Then, we explore the recent efforts to extend these techniques for populations supported on a manifold, including a novel approach that combines a density function estimator with some a priori geometric information.

• Thursday 18.09.2025, 14h30, MNO 1.040
  Zeev Rudnick (Tel-Aviv University), Number theory and spectral theory of the Laplacian
  Abstract: I will discuss some of the interactions between number theory and the spectral theory of the Laplacian. Some have very classical background, such as the connection with lattice point problems. Others are newer, including connections between random matrix theory, the zeros of the Riemann zeta function, and spectral statistics on the moduli space of hyperbolic surfaces. The talk is aimed at a general audience.

• Thursday 25.09.2025, 13h30, MNO 1.040
  Yuichi Goto (Kyushu University), Integrated copula spectrum with applications to tests for time-reversibility and tail symmetry
  Abstract: The spectral density plays a pivotal role in time series analysis. Since the classical spectral density is defined as the Fourier transform of autocovariance functions, it fails to capture the distributional features. To overcome this drawback, we consider the spectral density based on copula and show the weak convergence of integrated copula spectra. This result combined with the subsampling procedure enables us to construct uniform confidence bands, a test for time-reversibility, and a test for tail symmetry. This talk is based on joint work with T. Kley (Georg-August-Univ. Gottingen), R. Van Hecke (Ruhr-Univ. Bochum), S. Volgushev (Univ. of Toronto), H. Dette (Ruhr-Univ. Bochum), and M. Hallin (Univ. libre de Bruxelles).

• Thursday 2.10.2025, 14h30, MNO 1.020
  Alejandro David De La Concha Duarte (University of Luxembourg), Collaborative Likelihood-Ratio Estimation over Graphs
  Abstract: Density ratio estimation is an elegant approach for comparing two probability measures P and Q, relying solely on i.i.d. observations from these distributions and making minimal assumptions about P and Q. In the first part of the talk, we introduce a graph-based extension of this problem, where each node of a fixed graph is associated with two unknown node-specific probability measures, P_v and Q_v, from which we observe samples. Our goal is to estimate, for each node, the density ratio between the corresponding densities while leveraging the information provided by the graph structure. We develop this idea through a concrete non-parametric method called GRULSIF. A key feature of collaborative likelihood-ratio estimation is that it enables a straightforward derivation of test statistics to quantify differences between the node-level distributions P_v and Q_v. In the second part of the talk, we present a non-parametric, graph-structured multiple hypothesis testing framework named collaborative non-parametric two-sample testing, which has potential applications in spatial
  statistics and neuroscience.