Vacher, Adrien Vialard, François-Xavier
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples. In such situations, the goal is to find a transport map that has good generalization properties on unseen data, ideally the closest map to the ground truth, unknown in pr...
Dusson, Geneviève Ehrlacher, Virginie Nouaime, Nathalie
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [10] for mixtures of gaussian measures to other mixtures. We first prove in a general setting that for a set of at...
Gobet, Emmanuel Lage, Clara
Accounting for climate transition risks is one of the most important challenges in the transition to a low-carbon economy. Banks are encouraged to align their investment portfolios to CO2 trajectories fixed by international agreements, showing the necessity of a quantitative methodology to implement it. We propose a mathematical formulation for thi...
Lin, Chi-Heng
Augmentations and other transformations of data, either in the input or latent space, are a critical component of modern machine learning systems. While these techniques are widely used in practice and known to provide improved generalization in many cases, it is still unclear how data manipulation impacts learning and generalization. To take a ste...
Dumont, Théo Lacombe, Théo Vialard, François-Xavier
In this work, we study the structure of minimizers of the quadratic Gromov--Wasserstein (GW) problem on Euclidean spaces for two different costs. The first one is the scalar product for which we prove that it is always possible to find optimizers as Monge maps and we detail the structure of such optimal maps. The second cost is the squared Euclidea...
Gerber, Samuel Niethammer, Marc Ebrahim, Ebrahim Piven, Joseph Dager, Stephen R Styner, Martin Aylward, Stephen Enquobahrie, Andinet
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Medical image analysis
Brain pathologies often manifest as partial or complete loss of tissue. The goal of many neuroimaging studies is to capture the location and amount of tissue changes with respect to a clinical variable of interest, such as disease progression. Morphometric analysis approaches capture local differences in the distribution of tissue or other quantiti...
TORREGROSA, Sergio CHAMPANEY, Victor AMMAR, Amine HERBERT, Vincent CHINESTA, Francisco
Nowadays data is acquiring an indisputable importance in every field including engineering. In the past, experimental data was used to calibrate state-of-the art models. Once the model was optimally calibrated, numerical simulations were run. However, data can offer much more, playing a more important role than calibration or statistical analysis i...
Gallouët, Thomas Natale, Andrea Todeschi, Gabriele
We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the notion of geodesic extrapolation in the Wasserstein space, which in general is not uniquely defined. We propose several possible definitions for such an operation, and w...
Ito, Kaito
京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24263号 / 情博第807号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)准教授 加嶋 健司, 教授 太田 快人, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM
Jourdain, Benjamin Margheriti, William Pammer, Gudmund
Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. O...