Probability & Statistics Seminar

Upcoming sessions :

• Wednesday 11.03.2026, 13h30, MNO 1.010
  Donatien Hainaut (ISBA-LIDAM UCLouvain), European and American option pricing with constrained Gaussian process regressions
  Abstract: In this talk, we present a method for pricing European and American options using Gaussian processes. For European options, we reformulate the problem of solving the Feynman–Kac (FK) partial differential equation (PDE) as a model‑constrained regression task. Two training sets are constructed by sampling state variables from the PDE’s interior domain and from its terminal boundary. The regression function is then estimated so that it fits the option payoffs on the boundary samples while satisfying the FK PDE on the interior samples. Within a Bayesian framework, we model both the payoffs and the FK residuals as noisy observations. Assuming a Gaussian process prior for the regression function, we derive a closed‑form approximation of the option price. We illustrate the performance of the method on call options in the Heston model and on basket call options in a Black–Scholes setting. We then extend the approach to American options. The variational inequality governing American option prices is recast as a nonlinear penalized Feynman–Kac (PFK) equation. To handle the nonlinearity of the PFK operator, we propose an iterative algorithm in which the nonlinear term is frozen and evaluated using the price approximation from the previous iteration. At each iteration, we sample state variables from the PDE’s interior domain and its terminal boundary, and fit a constrained regression function that matches the boundary payoff and satisfies the PFK PDE in the interior. Under a Gaussian process prior, this again leads to a closed‑form approximation for the option price. In the numerical experiments, we evaluate American put options in the Heston and Black–Scholes models, as well as in the two‑factor Hull–White model.

• Thursday 19.03.2026, 13h30, MNO 1.050
  Tom Klose (University of Oxford), A Rough Functional Breuer–Major Theorem
  Abstract: We extend the functional Breuer-Major theorem by Nourdin and Nualart (2020) to the space of rough paths. The proof of tightness combines the multiplication formula for iterated Malliavin divergences, due to Furlan and Gubinelli (2019), with Meyer’s inequality and a Kolmogorov-type criterion for the r-variation of cadlag rough paths, due to Chevyrev et al. (2022). Since martingale techniques do not apply, we obtain the convergence of the finite-dimensional distributions through a bespoke version of Slutsky’s lemma: First, we overcome the lack of hypercontractivity by an iterated integration-by-parts scheme which reduces the remaining analysis to finite Wiener chaos; crucially, this argument relies on Malliavin differentiability of the nonlinearity but not on chaos decay and, as a consequence, encompasses the centred absolute value function. Second, in the spirit of the law of large numbers, we show that the diagonal of the second-order process converges to an explicit symmetric correction term. Finally, we compute all the moments of the remaining process and, through a fine combinatorial analysis, show that they converge to those of the Stratonovich Brownian rough path perturbed by an antisymmetric area correction, as computed by a suitable amendment of Fawcett’s theorem. All of these steps benefit from a major combinatorial reduction that is implied by the original argument of Breuer and Major (1983). This is joint work with Henri Elad Altman (Paris XIII) and Nicolas Perkowski (FU Berlin).

• Thursday 16.04.2026, 13h30, MNO 1.050
  Germain Van Bever (Université Libre de Bruxelles), TBA
  Abstract: TBA

• Thursday 21.05.2026, 13h30, MNO 1.050
  Olivier Lopez (ENSAE Paris), TBA
  Abstract: TBA

• Thursday 10.09.2026, time TBA, room TBA
  Fabrice Baudoin (Aarhus University), TBA
  Abstract: TBA

Past sessions :

• Thursday 26.02.2026, 13h30, MNO 1.050
  Richard Samworth (University of Cambridge), Learn the score
  Abstract: Score estimation has recently emerged as a key modern statistical challenge, due to its pivotal role in generative modelling via diffusion models.  Moreover, it is an essential ingredient in a new approach to linear regression via convex $M$-estimation, where the corresponding error densities are log-concave.  I will outline the antitonic score matching framework that underpins this latter application, and explain its advantages over ordinary least squares, for both estimation and inference (e.g. prediction intervals).  Motivated by both problems, I will then present new results on the minimax rates of score estimation over subclasses of log-concave densities.

• Thursday 29.01.2026, 13h30, MNO 1.040
  Linh Ha (University Of Luxembourg), Empirical Set-valued Expectiles- Convergence and Computational Framework
  Abstract: Expectiles have recently attracted increasing attention as M-quantile risk measures due to their coherency, law invariance, and elicitability. The expectile region, analogous to the Tukey depth region, characterizes the central confidence region of a multivariate distribution, while cone expectiles describe the “tail” of a multivariate distribution with respect to a cone-induced preorder. Together, the expectile region and cone expectiles form the family of set-valued expectiles, which can be applied to data clustering, multivariate data analysis and risk management. Consequently, the estimation of empirical set-valued expectiles arises as a natural research question. This paper investigates the convergence of the empirical expectile region and discusses the convergence rate of the empirical region under certain distributional assumptions on the random vector $X$. Furthermore, it proposes a general framework for computing set-valued expectiles in higher-dimensional settings via vector linear programming. Another optimization-based framework is also proposed for computing empirical expectile depth defined via the expectile (trimmed) region.

• Thursday 22.01.2026, 13h30, MNO 1.020
  Fabrice Wunderlich (University Of Luxembourg), ‘Skorokhod meets Itô. Again.’ — Weak Convergence of Stochastic Integrals on Skorokhod Space 
  Abstract: I will present a new, self-contained approach to the limit theory of stochastic integrals on Skorokhod space, based on a simple and tractable notion of good decompositions for semimartingale integrators. For integrators admitting such decompositions and converging weakly in the J1 or M1 Skorokhod topology, I give conditions under which Itô integration is continuous with respect to both the integrators and weakly convergent integrands. The results unify and streamline existing continuity theorems in the classical J1 setting and yield new conclusions in the M1 topology. Moreover, I will expose a fundamental relationship between the M1 and J1 topologies for families of local martingales, notably that their M1 tightness in fact implies their J1 tightness under a mild localised uniform integrability condition. I will conclude with applications, including models of anomalous diffusion arising as stochastic integrals with respect to continuous-time random walks.
  

• Thursday 4.12.2025, 13h30, MNO 1.020
  Petr Zamolodtchikov (Bielefeld University), Local convergence rates of the nonparametric least squares
  estimator with applications to transfer learning
  Abstract: Convergence properties of empirical risk minimisers can be conveniently expressed in terms of the associated population risk. To derive bounds on the estimator’s performance under covariate shift, however, pointwise convergence rates are required. Under weak assumptions on the design distribution, it is shown that least squares estimators (LSE) over 1-Lipschitz functions are also minimax rate optimal with respect to a weighted uniform norm, where the weighting accounts in a natural way for the non-uniformity of the design distribution.

• Thursday 27.11.2025, 13h30, MNO 1.020
  Lorenzo Dello Schiavo (Università degli Studi di Roma “Tor Vergata”), Massive Particle Systems, Wasserstein Brownian Motions, and the Dean–Kawasaki SPDE
  Abstract: Let W be a conservative, ergodic Markov diffusion on some arbitrary state space M, converging exponentially fast to equilibrium. We consider:
  (1) Systems of up to countably many massive particles in M, with finite total mass. Each particle is subject to an independent instance of the noise W, with volatility the inverse mass carried by the particle. We prove that the corresponding infinite system of SDEs has a unique solution, for every starting configuration and every distribution of the masses in the infinite simplex.
  (2) Solutions to the Dean–Kawasaki SPDE with singular drift, driven by the generator L of W. We prove that the equation may be given rigorous meaning on M, and that it has a unique `distributional’ solution. This extends Konarovskyi–Lehmann–von Renesse’s `ill-posedness vs. triviality’ to the case of infinitely many massive particles.
  (3) Diffusions with values in the space P of all probability measures on M, driven by the geometry induced by L.
  (4) In the case when M is a manifold, differential-geometric and metric-measure Brownian motions on P induced by the geometry of optimal transportation and reversible for a normalized completely random measure.
  We show that all these objects coincide.
  

• 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 23.10.2025, 13h30, MNO 1.020
  Marina Gomtsyan (Laboratoire de Probabilités, Statistique et Modélisation), Variable selection methods in sparse GLARMA models
  Abstract: We propose novel variable selection methods for sparse GLARMA (Generalised Linear Autoregressive Moving Average) models, which can be used for modelling discrete-valued time series. These models allow us to introduce some dependence in a Generalised Linear Model (GLM). The key idea behind our estimation procedure is first to estimate the coefficients of the ARMA part of the GLARMA model and then use a regularised approach, namely the Lasso, to estimate the regression coefficients of the GLM part of the model. Furthermore, we establish a sign-consistency result for the estimator of the regression coefficients in a sparse Poisson model without time dependence. The performance of our proposed methods was assessed on simulation studies in different frameworks and on several datasets in the field of molecular biology. Our approaches exhibit very good statistical performance, surpassing other methods in identifying non-null regression coefficients. Secondly, their low computational burden enables their application to relatively large datasets. Our proposed methods are implemented in R packages, which are publicly available on the Comprehensive R Archive Network (CRAN).

• 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 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.

• 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 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.