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pro vyhledávání: '"Divol, Vincent"'
From the observation of a diffusion path $(X_t)_{t\in [0,T]}$ on a compact connected $d$-dimensional manifold $M$ without boundary, we consider the problem of estimating the stationary measure $\mu$ of the process. Wang and Zhu (2023) showed that for
Externí odkaz:
http://arxiv.org/abs/2410.11777
Autor:
Divol, Vincent, Gaucher, Solenne
This paper explores the theoretical foundations of fair regression under the constraint of demographic parity within the unawareness framework, where disparate treatment is prohibited, extending existing results where such treatment is permitted. Spe
Externí odkaz:
http://arxiv.org/abs/2409.02471
\v{C}ech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $OT_{p}$; however, the extent to which PDs are stable with respect
Externí odkaz:
http://arxiv.org/abs/2406.14919
Entropic Brenier maps are regularized analogues of Brenier maps (optimal transport maps) which converge to Brenier maps as the regularization parameter shrinks. In this work, we prove quantitative stability bounds between entropic Brenier maps under
Externí odkaz:
http://arxiv.org/abs/2404.02855
In general, the critical points of the distance function $d_{\mathsf{M}}$ to a compact submanifold $\mathsf{M} \subset \mathbb{R}^D$ can be poorly behaved. In this article, we show that this is generically not the case by listing regularity condition
Externí odkaz:
http://arxiv.org/abs/2312.13147
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the tra
Externí odkaz:
http://arxiv.org/abs/2301.11302
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the evolution of a
Externí odkaz:
http://arxiv.org/abs/2212.03722
Autor:
Divol, Vincent, Lacombe, Théo
Publikováno v:
International Conference on Machine Learning, Jul 2021, Virtual Conference, France
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 or point clouds sampled close to a manifold. Given random objects and
Externí odkaz:
http://arxiv.org/abs/2105.04852
Autor:
Divol, Vincent
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the sample. After re
Externí odkaz:
http://arxiv.org/abs/2102.07595
Autor:
Divol, Vincent
We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.
Externí odkaz:
http://arxiv.org/abs/2101.08126