194 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Laboratoire de Mathématiques d'OrsayFR12 papers
- Institut national de recherche en sciences et technologies du numériqueFR9 papers
- Centre Inria de SaclayFR7 papers
- Laboratoire de Probabilités, Statistique et ModélisationFR6 papers
- Centre National de la Recherche ScientifiqueFR4 papers
- Université Paris-SaclayFR4 papers
- Centre Inria d'Université Côte d'AzurFR3 papers
- École Polytechnique Fédérale de LausanneCH3 papers
- Institut de Mathématiques de ToulouseFR3 papers
- Institut National des Sciences Appliquées de ToulouseFR3 papers
- Université Toulouse III - Paul SabatierFR3 papers
- University of PotsdamDE3 papers
34 papers
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Multi-parameter Module Approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees
David Loiseaux, Mathieu Carrière, Andrew J. Blumberg
In this article, we introduce a new parameterized family of topological descriptors, taking the form of candidate decompositions, for multi-parameter persistence modules, and we id…
Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport
Alex Delalande
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of…
On the pathwidth of hyperbolic 3-manifolds
Kristóf Huszár
According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifold…
Estimation and Quantization of Expected Persistence Diagrams
Vincent Divol, Théo Lacombe
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series…
Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs
Théo Lacombe, Yuichi Ike, Mathieu Carriere +3
Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can…
Post hoc false discovery proportion inference under a Hidden Markov Model
Marie Perrot-Dockès, Gilles Blanchard, Pierre Neuvial +1
We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a Hidden Markov Model (HMM), which is recognized as a fundamental setting…
Quantitative Stability of Optimal Transport Maps under Variations of the Target Measure
Alex Delalande, Quentin Merigot
This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density and a probability measure on R^d , which we denote T…
Patchworking real algebraic hypersurfaces with asymptotically large Betti numbers
Charles Arnal
In this article, we describe a recursive method for constructing a family of real projective algebraic hypersurfaces in ambient dimension from families of such hypersurfaces in…
Generalized Penalty for Circular Coordinate Representation
Hengrui Luo, Alice Patania, Jisu Kim +1
Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA…
Computing persistent Stiefel-Whitney classes of line bundles
Raphaël Tinarrage
We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual Čech f…
PLLay: Efficient Topological Layer based on Persistence Landscapes
Kwangho Kim, Jisu Kim, Manzil Zaheer +3
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological feature…
Optimal quantization of the mean measure and applications to statistical learning
Frédéric Chazal, Clément Levrard, Martin Royer
This paper addresses the case where data come as point sets, or more generally as discrete measures. Our motivation is twofold: first we intend to approximate with a compactly supp…
Recovering the homology of immersed manifolds
Raphaël Tinarrage
Given a sample of an abstract manifold immersed in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its…
ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning
Martin Royer, Frédéric Chazal, Clément Levrard +2
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning framework…
Spectral Properties of Radial Kernels and Clustering in High Dimensions
David Cohen-Steiner, Alba Chiara de Vitis
In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in . Our approach focuses on high dimensions and relies sole…
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Mathieu Carrière, Frédéric Chazal, Yuichi Ike +3
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications…
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Abhishake Rastogi, Gilles Blanchard, Peter Mathé
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider t…
Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport
Vincent Divol, Théo Lacombe
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence dia…
On Order Types of Random Point Sets
Olivier Devillers, Philippe Duchon, Marc Glisse +1
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way…
Robust Bregman Clustering
Aurélie Fischer, Clément Levrard, Claire Brécheteau
Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman…
Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension
Jisu Kim, Jaehyeok Shin, Alessandro Rinaldo +1
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the se…
Strong Collapse for Persistence
Jean-Daniel Boissonnat, Siddharth Pritam, Divyansh Pareek
We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the…
Post hoc false positive control for spatially structured hypotheses
Guillermo Durand, Gilles Blanchard, Pierre Neuvial +1
In a high dimensional multiple testing framework, we present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. The coverage probabili…