Tejas
Iyer
WIAS Berlin
When a branching process grows like its mean
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08. October
Tomorrow
09. October
Thu W40
Carlos
Soto
Differential Privacy over Manifolds and Shape Space
Abstract.
In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold. We present extensions of the Laplace and K-norm mechanisms that utilizes intrinsic distances and volumes on the manifold. We also consider in detail the specific case where the summary is the Fréchet mean of data residing on a manifold. We demonstrate that our mechanism is rate optimal and depends only on the dimension of the manifold, not on the dimension of any ambient space, while also showing how ignoring the manifold structure can decrease the utility of the sanitized summary. Lastly, we illustrate our framework in three examples of particular interest in statistics: the space of symmetric positive definite matrices, which is used for covariance matrices, the sphere, which can be used as a space for modeling discrete distributions, and Kendall's 2D planar shape space.
15. October
Wed W41
Carlos
Soto
University of Massachusetts Amherst
Differential Privacy over Manifolds and Shape Space
Abstract.
In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold. We present extensions of the Laplace and K-norm mechanisms that utilizes intrinsic distances and volumes on the manifold. We also consider in detail the specific case where the summary is the Fréchet mean of data residing on a manifold. We demonstrate that our mechanism is rate optimal and depends only on the dimension of the manifold, not on the dimension of any ambient space, while also showing how ignoring the manifold structure can decrease the utility of the sanitized summary. Lastly, we illustrate our framework in three examples of particular interest in statistics: the space of symmetric positive definite matrices, which is used for covariance matrices, the sphere, which can be used as a space for modeling discrete distributions, and Kendall's 2D planar shape space.
Fabian
Schaipp
INRIA
The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Training
Abstract.
We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for the constant schedule with linear cooldown; in particular, the practical benefit of cooldown is reflected in the bound due to the absence of logarithmic terms. Further, we show that this surprisingly close match between optimization theory and practice can be exploited for learning-rate tuning: we achieve noticeable improvements for training 124M and 210M Llama-type models by (i) extending the schedule for continued training with optimal learning-rate, and (ii) transferring the optimal learning-rate across schedules.
Annalaura
Rebucci
MPI Leipzig
On the De Giorgi--Nash--Moser regularity theory for kinetic hypoelliptic operators
Abstract
Markus
Pflaum
U Colorado
Dominic
Bunnett
TU Berlin
16. October
Thu W41
Julian
Kern
and
Guilherme
de Lima Feltes
preliminary discussion
21. October
Tue W42
Matijn
Francois
University of Geneva
22. October
Wed W42
Helia
Shafigh
WIAS Berlin
Responsive dormancy of a spatial population among a moving trap
Abstract.
In this talk, we study a spatial model for dormancy in a random environment via a two-type branching random walk in continuous-time, where individuals switch between dormant and active states depending on the current state of a fluctuating environment (responsive switching). The branching mechanism is governed by the same random environment, which is here taken to be a simple symmetric random walk. We will interpret the presence of this random walk as a trap which attempts to kill the individuals whenever it meets them. The responsive switching between the active and dormant state is defined so that active individuals become dormant only when a trap is present at their location and remain active otherwise. Conversely, dormant individuals can only wake up once the environment becomes trap-free again. We quantify the influence of dormancy on population survival by analyzing the long-time asymptotics of the expected population size. The starting point for our mathematical considerations and proofs is the Parabolic Anderson Model via the FeynmanâKac formula. In particular, we investigate the quantitative role of dormancy by extending the Parabolic Anderson Model to a two-type random walk framework. Joint work with Leo Tyrpak.
Jinhyung
Park
KAIST Daejeon
Annamaria
Massimini
CERMICS (ENPC) Paris, France
Finite volumes for a generalized Poisson--Nernst--Planck system with cross-diffusion
Abstract
24. October
Fri W42
Florian
Frick
CMU
28. October
Tue W43
Lasse
Merkens
HU
Renormalization group flows from defects in N = 1 minimal models
Abstract.
Leveraging the structure of non-invertible symmetries, we construct a family of renormalization group flows connecting N = 1 superconformal minimal models: SM(p, kp + I) â SM(p, kp â I). The triggering operator is Gâ1/2Ï(1,2k+1). A key element of our argument is that the topological defect lines of the bosonic coset theory persist in the fermionic case. These flows represent a supersymmetric generalization of the Virasoro flows discovered by Tanaka and Nakayama and include the previously known unitary flows (Pogossyan, k = 1, I = 2) as a special case. Furthermore, we demonstrate the completeness of this family; any flow between models SM(p, q) and SM(p, qâČ) can be obtained by composing these fundamental flows.
29. October
Wed W43
Ludger
Overbeck
UniversitĂ€t GieĂen
Bayesian Estimation with MCMC Methods for Stochastic Processes with Hidden States
Abstract.
Markov Modulated Stochastic Processes (MMSP) are a more flexible class of Stochastic Processes which capture phase changes arising in economies by allowing jumps in drift and volatility, linked to hidden states of a Markov chain. These models have been used to model option prices, renewable energy markets as well as for risk quantification. While Bayesian inference methods exists for simpler regime-switching models, we aim to extend it to more complex MMSPs. Our approach involves applying Bayesian estimation techniques to recover the hidden states and the parameters associated with each state of the Markov Chain. We propose Markov Chain Monte Carlo algorithms to perform Bayesian inference for MM-SPs. This will allow for a more data-driven analysis of asset returns with regime shifts and jumps. In the first part of the talk we review well-known estimation techniques for the CIR-process which is the solution of dXt = (a+ bXt)dt+ Ï X+ t dWt based on the paper Estimation in the CIR-Process (O. & RydĂ©n. Scand, Econometric Theory. 1997). Finally we want to extend this to a model with hidden variables, namely to dXt = a(Zt) + b(Zt)Xt dt + Ï(Zt) X+ s dWs where Z is a continuous-time Markov chain. This is a special case of a general regime switching stochastic process. dXt = ÎČ(Zt, Xt)dt + Ï(Zt, Xt)dWζ(Zt). We consider two special cases dXt = a(Zt) + b(Zt)Xt dt + Ï(Zt) X+ s dWs. For two special cases We formulate For parameter estimation we present a new version of the EM (Expectation Maximizer)-approach which was in a similar way used in the paper On the estimation of regime-switching LĂ©vy models (Chevalier & Goutte, Stud. Nonlinear Dyn. E. 2017). Finally, we discuss the potential modification of the EM-algorithm, if we consider conditional least square minimization instead of likelihood maximisation in the M-step of the EM-algorithm.
Hanna
Stange
UniversitĂ€t MĂŒnster
Pawel
Borowka
Jagiellonian University
Some questions about abelian surfaces
Abstract.
At the end of 19th century, Humbert characterised the locus of principally polarised abelian surfaces that contain elliptic curves. This locus has infinitely many irreducible components, called Humbert surfaces. The components can be indexed by natural numbers that are exponents of complementary elliptic curves. We would like to describe irreducible components for non-principally polarised abelian surfaces. In the talk, after a brief overview of principally polarised case, I will show some results based on a joint paper with R. Auffarth. I will restate some questions posed in the article and if time permits I will talk about a possible way to answer them.
Mohab
Safey El Din
Sorbonne
04. November
Tue W44
Xavier
Blot
Unversiteit van Amsterdam
05. November
Wed W44
Florian
Frick
Carnegie Mellon University
Zeros by symmetry: Chebyshev systems, cubature, and convex geometry
Abstract.
Iâll present a unified, equivariant-topological framework that controls the zero distribution of real-valued functions obtained by composing a fixed equivariant map with linear (or affine) functionals. This yields upper bounds on the topology of regions where multivariate trigonometric polynomials remain sign-constant, generalizing classical results. As special cases, we derive new restrictions on zero sets in Chebyshev spaces. Finally, Iâll show how these constraints translate into existence results for efficient cubature formulas for these functions. Joint work with Francesca Cantor, Julia D'Amico, Eric Myzelev
06. November
Thu W44
Rahul
Pandharipande
ETH ZĂŒrich
11. November
Tue W45
Taro
Kimura
Université Bourgogne Europe
Non-perturbative Schwinger-Dyson equation for DT/PT vertices
Abstract.
Non-perturbative Schwinger-Dyson (SD) equation is a discrete analog of the loop equation appearing in matrix models and related models. It was initially discussed for the gauge theory partition function and, as in the case of the matrix models, it has a close relation to the underlying infinite-dimensional symmetry of the system. In this talk, I'd like to discuss the non-perturbative SD equation for the higher-dimensional gauge theory partition function, interpreted as the generating function of the DT and PT invariants (DT/PT vertices) for CY3 and CY4 varieties, and address its underlying quantum algebraic structure, which is a consequence of geometric representation theory of the corresponding algebra.
12. November
Wed W45
Thomas
Kneib
UniversitÀt Göttingen
Demystifying Spatial Confounding
Abstract.
Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can lead to significant bias in covariate effect estimates. The problem is complex and has been the topic of extensive research with sometimes puzzling and seemingly contradictory results. We will give an introduction to spatial confounding and discuss some suggested solutions for dealing with it, including the formalisation as a structural equation model and spatial+, where spatial variation in the covariate of interest is regresssed away first and remaining residuals are then used to identify the relevant effect. In the second part of the presentation, we develop a broad theoretical framework that brings mathematical clarity to the mechanisms of spatial confounding, relying on an explicit analytical expression for the resulting bias. We see that the problem is directly linked to spatial smoothing and identify exactly how the size and occurrence of bias relate to the features of the spatial model as well as the underlying confounding scenario. Using our results, we can explain subtle and counter-intuitive behaviours. Finally, we propose a general approach for dealing with spatial confounding bias in practice, applicable for any spatial model specification. When a covariate has non-spatial information, we show that a general form of the so-called spatial+ method can be used to eliminate bias. When no such information is present, the situation is more challenging but, under the assumption of unconfounded high frequencies, we develop a procedure in which multiple capped versions of spatial+ are applied to assess the bias in this case. We illustrate our approach with an application to air temperature in Germany.
Sophia-Marie
Mellis
UniversitÀt Bielefeld
Nathan
Pflueger
Amherst College
Leonard
Kreutz
TU MĂŒnchen
18. November
Tue W46
Piotr
Sulkowski
Warsaw University
19. November
Wed W46
Alain
Celisse
Paris
Lutz
Recke
Humboldt-UniversitÀt zu Berlin
An H-convergence-based implicit function theorem and homogenization of nonlinear non-smooth elliptic systems
Abstract
Jinrong
Hu
TU Vienna
26. November
Wed W47
Alessandro
Palummo
Politecnico Milano
Physics-informed Functional Principal Component Analysis of Large-scale Datasets
Abstract.
Physics-informed statistical learning is an emerging area of spatial and functional data analysis that integrates observational data with prior physical knowledge encoded by partial differential equations (PDEs). We propose an iterative MajorizationâMinimization scheme for functional Principal Component Analysis of random fields in a general Hilbert space, formulated under the practically relevant assumption of partial observability of the data. By combining differential penalties with finite element discretizations, our approach recovers smooth principal component functions while preserving the geometric features of the spatial domain. The resulting estimation procedure involves solving a smoothing problem, which may become computationally demanding for large-scale datasets. After establishing the well-posedness of this smoothing problem under mild assumptions on the PDE parameters, we develop an efficient iterative algorithm for its solution. This framework enables the practical analysis of massive functional datasets at the population level, ranging from physics-informed fPCA to functional clustering, with applications to environmental and neuroimaging data.
Margherita
Lelli-Chiesa
Universita Roma Tre
Illia
Karabash
Institut fĂŒr Angewandte Mathematik, UniversitĂ€t Bonn
02. December
Tue W48
Nikolay
Barashkov
MiS Leipzig
03. December
Wed W48
Fanny
Seyzilles
Cambridge
Emanuele
Delucchi
SUPSI
10. December
Wed W49
Vladimir
Spokoiny
WIAS
17. December
Wed W50
Cesare
Miglioli
University of Pittsburgh
Incomplete U-Statistics of Equireplicate Designs: Berry-Esseen Bound and Efficient Construction.
Abstract.
U-statistics are a fundamental class of estimators that generalize the sample mean and underpin much of nonparametric statistics. Although extensively studied in both statistics and probability, key challenges remain. These include their inherently high computational costâaddressed partly through incomplete U-statisticsâand their non-standard asymptotic behavior in the degenerate case, which typically requires resampling methods for hypothesis testing. This talk presents a novel perspective on U-statistics, grounded in hypergraph theory and combinatorial designs. Our approach bypasses the traditional Hoeffding decomposition, which is the the main analytical tool in this literature but is highly sensitive to degeneracy. By fully characterizing the dependence structure of a U-statistic, we derive a new BerryâEsseen bound that applies to all incomplete U-statistics based on deterministic designs, yielding conditions under which Gaussian limiting distributions can be established even in the degenerate case and when the order diverges. Moreover, we introduce efficient algorithms to construct incomplete U-statistics of equireplicate designs, a subclass of deterministic designs that, in certain cases, enable to achieve minimum variance. To illustrate the power of this novel framework, we apply it to kernel-based testing, focusing on the widely used two-sample Maximum Mean Discrepancy (MMD) test. Our approach leads to a permutation-free variant of the MMD test that delivers substantial computational gains while retaining statistical validity.
13. January
Tue W02
Piotr
Sulkowski
University of Warsaw
14. January
Wed W02
Frank
Konietschke
Charité
27. January
Tue W04
Maciej
Dolega
Institute of Mathematics, Polish Academy of Sciences
28. January
Wed W04
Jakob
Runge
Uni Potsdam
11. February
Wed W06
Andrea
Poiatti
UniversitÀt Wien