Relevant bibliographies by topics / Distances de Wasserstein

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Distances de Wasserstein'

Author: Grafiati
Published: 18 May 2024
Last updated: 19 October 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Distances de Wasserstein.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Distances de Wasserstein"

1

Solomon, Justin, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas. "Convolutional wasserstein distances." ACM Transactions on Graphics 34, no. 4 (July 27, 2015): 1–11. http://dx.doi.org/10.1145/2766963.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Kindelan Nuñez, Rolando, Mircea Petrache, Mauricio Cerda, and Nancy Hitschfeld. "A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (March 24, 2024): 13202–10. http://dx.doi.org/10.1609/aaai.v38i12.29220.

Full text
Abstract:
Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing distances among large sets of PDs, with metrics which are accurate, theoretically sound, and fast to compute. Especially for denser multi-dimensional PDs, such comparison metrics are lacking. While on the one hand, Wasserstein-type distances have high accuracy and theoretical guarantees, they incur high computational cost. On the other hand, distances between vectorizations such as Persistence Statistics (PS)s have lower computational cost, but lack the accuracy guarantees and theoretical properties of a true distance over PD space. In this work we introduce a class of pseudodistances called Extended Topological Pseudodistances (ETD)s, which have tunable complexity, and can approximate Sliced and classical Wasserstein distances at the high-complexity extreme, while being computationally lighter and close to Persistence Statistics at the lower complexity extreme, and thus allow users to interpolate between the two metrics. We build theoretical comparisons to show how to fit our new distances at an intermediate level between persistence vectorizations and Wasserstein distances. We also experimentally verify that ETDs outperform PSs in terms of accuracy and outperform Wasserstein and Sliced Wasserstein distances in terms of computational complexity.
APA, Harvard, Vancouver, ISO, and other styles
3

Panaretos, Victor M., and Yoav Zemel. "Statistical Aspects of Wasserstein Distances." Annual Review of Statistics and Its Application 6, no. 1 (March 7, 2019): 405–31. http://dx.doi.org/10.1146/annurev-statistics-030718-104938.

Full text
Abstract:
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover the other distribution. They are ubiquitous in mathematics, with a long history that has seen them catalyze core developments in analysis, optimization, and probability. Beyond their intrinsic mathematical richness, they possess attractive features that make them a versatile tool for the statistician: They can be used to derive weak convergence and convergence of moments, and can be easily bounded; they are well-adapted to quantify a natural notion of perturbation of a probability distribution; and they seamlessly incorporate the geometry of the domain of the distributions in question, thus being useful for contrasting complex objects. Consequently, they frequently appear in the development of statistical theory and inferential methodology, and they have recently become an object of inference in themselves. In this review, we provide a snapshot of the main concepts involved in Wasserstein distances and optimal transportation, and a succinct overview of some of their many statistical aspects.
APA, Harvard, Vancouver, ISO, and other styles
4

Kelbert, Mark. "Survey of Distances between the Most Popular Distributions." Analytics 2, no. 1 (March 1, 2023): 225–45. http://dx.doi.org/10.3390/analytics2010012.

Full text
Abstract:
We present a number of upper and lower bounds for the total variation distances between the most popular probability distributions. In particular, some estimates of the total variation distances in the cases of multivariate Gaussian distributions, Poisson distributions, binomial distributions, between a binomial and a Poisson distribution, and also in the case of negative binomial distributions are given. Next, the estimations of Lévy–Prohorov distance in terms of Wasserstein metrics are discussed, and Fréchet, Wasserstein and Hellinger distances for multivariate Gaussian distributions are evaluated. Some novel context-sensitive distances are introduced and a number of bounds mimicking the classical results from the information theory are proved.
APA, Harvard, Vancouver, ISO, and other styles
5

Vayer, Titouan, Laetitia Chapel, Remi Flamary, Romain Tavenard, and Nicolas Courty. "Fused Gromov-Wasserstein Distance for Structured Objects." Algorithms 13, no. 9 (August 31, 2020): 212. http://dx.doi.org/10.3390/a13090212.

Full text
Abstract:
Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects, but treats them independently, whereas the Gromov–Wasserstein distance focuses on the relations between the elements, depicting the structure of the object, yet discarding its features. In this paper, we study the Fused Gromov-Wasserstein distance that extends the Wasserstein and Gromov–Wasserstein distances in order to encode simultaneously both the feature and structure information. We provide the mathematical framework for this distance in the continuous setting, prove its metric and interpolation properties, and provide a concentration result for the convergence of finite samples. We also illustrate and interpret its use in various applications, where structured objects are involved.
APA, Harvard, Vancouver, ISO, and other styles
6

Belili, Nacereddine, and Henri Heinich. "Distances de Wasserstein et de Zolotarev." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 330, no. 9 (May 2000): 811–14. http://dx.doi.org/10.1016/s0764-4442(00)00274-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Peyre, Rémi. "Comparison between W2 distance and Ḣ−1 norm, and Localization of Wasserstein distance." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 4 (October 2018): 1489–501. http://dx.doi.org/10.1051/cocv/2017050.

Full text
Abstract:
It is well known that the quadratic Wasserstein distance W2(⋅, ⋅) is formally equivalent, for infinitesimally small perturbations, to some weighted H−1 homogeneous Sobolev norm. In this article I show that this equivalence can be integrated to get non-asymptotic comparison results between these distances. Then I give an application of these results to prove that the W2 distance exhibits some localization phenomenon: if μ and ν are measures on ℝn and ϕ: ℝn → ℝ+ is some bump function with compact support, then under mild hypotheses, you can bound above the Wasserstein distance between ϕ ⋅ μ and ϕ ⋅ ν by an explicit multiple of W2(μ, ν).
APA, Harvard, Vancouver, ISO, and other styles
8

Tong, Qijun, and Kei Kobayashi. "Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions." Entropy 23, no. 3 (March 3, 2021): 302. http://dx.doi.org/10.3390/e23030302.

Full text
Abstract:
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.
APA, Harvard, Vancouver, ISO, and other styles
9

Beier, Florian, Robert Beinert, and Gabriele Steidl. "Multi-marginal Gromov–Wasserstein transport and barycentres." Information and Inference: A Journal of the IMA 12, no. 4 (September 18, 2023): 2720–52. http://dx.doi.org/10.1093/imaiai/iaad041.

Full text
Abstract:
Abstract Gromov–Wasserstein (GW) distances are combinations of Gromov–Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due to their invariance under measure- and distance-preserving transformations, they are well suited for many applications in graph and shape analysis. In this paper, we introduce the concept of multi-marginal GW transport between a set of mm-spaces as well as its regularized and unbalanced versions. As a special case, we discuss multi-marginal fused variants, which combine the structure information of an mm-space with label information from an additional label space. To tackle the new formulations numerically, we consider the bi-convex relaxation of the multi-marginal GW problem, which is tight in the balanced case if the cost function is conditionally negative definite. The relaxed model can be solved by an alternating minimization, where each step can be performed by a multi-marginal Sinkhorn scheme. We show relations of our multi-marginal GW problem to (unbalanced, fused) GW barycentres and present various numerical results, which indicate the potential of the concept.
APA, Harvard, Vancouver, ISO, and other styles
10

Zhang, Zhonghui, Huarui Jing, and Chihwa Kao. "High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection." Mathematics 11, no. 5 (March 6, 2023): 1272. http://dx.doi.org/10.3390/math11051272.

Full text
Abstract:
This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-dimensional data. Our simulation results show the robustness of the PRW-based estimator in the presence of noisy data and its ability to achieve a higher Sharpe ratio than regular Wasserstein distances when dealing with a large number of assets. Our empirical study also demonstrates that the proposed portfolio estimator outperforms classic “plug-in” methods using various covariance estimators in terms of risk when evaluated out of sample.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Distances de Wasserstein"

1

Boissard, Emmanuel. "Problèmes d'interaction discret-continu et distances de Wasserstein." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1389/.

Full text
Abstract:
On étudie dans ce manuscrit plusieurs problèmes d'approximation à l'aide des outils de la théorie du transport optimal. Les distances de Wasserstein fournissent des bornes d'erreur pour l'approximation particulaire des solutions de certaines équations aux dérivées partielles. Elles jouent également le rôle de mesures de distorsion naturelles dans les problèmes de quantification et de partitionnement ("clustering"). Un problème associé à ces questions est d'étudier la vitesse de convergence dans la loi des grands nombres empirique pour cette distorsion. La première partie de cette thèse établit des bornes non-asymptotiques, en particulier dans des espaces de Banach de dimension infinie, ainsi que dans les cas où les observations sont non-indépendantes. La seconde partie est consacrée à l'étude de deux modèles issus de la modélisation des déplacements de populations d'animaux. On introduit un nouveau modèle individu-centré de formation de pistes de fourmis, que l'on étudie expérimentalement à travers des simulations numériques et une représentation en terme d'équations cinétiques. On étudie également une variante du modèle de Cucker-Smale de mouvement d'une nuée d'oiseaux : on montre le caractère bien posé de l'équation de transport de type Vlasov associée, et on établit des résultats sur le comportement en temps long de cette équation. Enfin, dans une troisième partie, on étudie certaines applications statistiques de la notion de barycentre dans l'espace des mesures de probabilités muni de la distance de Wasserstein, récemment introduite par M. Agueh et G. Carlier
We study several problems of approximation using tools from Optimal Transportation theory. The family of Wasserstein metrics are used to provide error bounds for particular approximation of some Partial Differential Equations. They also come into play as natural measures of distorsion for quantization and clustering problems. A problem related to these questions is to estimate the speed of convergence in the empirical law of large numbers for these distorsions. The first part of this thesis provides non-asymptotic bounds, notably in infinite-dimensional Banach spaces, as well as in cases where independence is removed. The second part is dedicated to the study of two models from the modelling of animal displacement. A new individual-based model for ant trail formation is introduced, and studied through numerical simulations and kinetic formulation. We also study a variant of the Cucker-Smale model of bird flock motion : we establish well-posedness of the associated Vlasov-type transport equation as well as long-time behaviour results. In a third part, we study some statistical applications of the notion of barycenter in Wasserstein space recently introduced by M. Agueh and G. Carlier
APA, Harvard, Vancouver, ISO, and other styles
2

Fernandes, Montesuma Eduardo. "Multi-Source Domain Adaptation through Wasserstein Barycenters." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASG045.

Full text
Abstract:
Les systèmes d'apprentissage automatique fonctionnent sous l'hypothèse que les conditions d'entraînement et de test ne changent pas. Néanmoins, cette hypothèse est rarement vérifiée en pratique. En conséquence, le système est entraîné avec des données qui ne sont plus représentatives des données sur lesquelles il sera testé : la mesure de probabilité des données évolue entre les périodes d'entraînement et de test. Ce scénario est connu dans la littérature sous le nom de décalage de distribution entre deux domaines : une source et une cible. Une généralisation évidente de ce problème considère que les données d'entraînement présentent elles-mêmes plusieurs décalages intrinsèques. On parle, donc, d'adaptation de domaine à sources multiples (MSDA). Dans ce contexte, le transport optimal est un outil de mathématique utile. En particulier, qui sert pour comparer et manipuler des mesures de probabilité. Cette thèse étudie les contributions du transport optimal à l'adaptation de domaines à sources multiples. Nous le faisons à travers des barycentres de Wasserstein, un objet qui définit une moyenne pondérée, dans l'espace des mesures de probabilité, des multiples domaines en MSDA. Basé sur ce concept, nous proposons : (i) une nouvelle notion de barycentre lorsque les mesures en question sont étiquetées, (ii) un nouveau problème d'apprentissage de dictionnaire sur des mesures de probabilité empiriques et (iii) de nouveaux outils pour l'adaptation de domaines via le transport optimal de modèles de mélanges Gaussiens. Nos méthodes améliorent les performances de l'adaptation de domaines par rapport aux méthodes existantes utilisant le transport optimal sur des benchmarks d'images et de diagnostic de défauts inter-domaines. Notre travail ouvre une perspective de recherche intéressante sur l'apprentissage de l'enveloppe barycentrique de mesures de probabilité
Machine learning systems work under the assumption that training and test conditions are uniform, i.e., they do not change. However, this hypothesis is seldom met in practice. Hence, the system is trained with data that is no longer representative of the data it will be tested on. This case is represented by a shift in the probability measure generating the data. This scenario is known in the literature as distributional shift between two domains: a source, and a target. A straightforward generalization of this problem is when training data itself exhibit shifts on its own. In this case, one consider Multi Source Domain Adaptation (MSDA). In this context, optimal transport is an useful field of mathematics. Especially, optimal transport serves as a toolbox, for comparing and manipulating probability measures. This thesis studies the contributions of optimal transport to multi-source domain adaptation. We do so through Wasserstein barycenters, an object that defines a weighted average, in the space of probability measures, for the multiple domains in MSDA. Based on this concept, we propose: (i) a novel notion of barycenter, when the measures at hand are equipped with labels, (ii) a novel dictionary learning problem over empirical probability measures and (iii) new tools for domain adaptation through the optimal transport of Gaussian mixture models. Through our methods, we are able to improve domain adaptation performance in comparison with previous optimal transport-based methods on image, and cross-domain fault diagnosis benchmarks. Our work opens an interesting research direction, on learning the barycentric hull of probability measures
APA, Harvard, Vancouver, ISO, and other styles
3

Schrieber, Jörn [Verfasser], Dominic [Akademischer Betreuer] Schuhmacher, Dominic [Gutachter] Schuhmacher, and Anita [Gutachter] Schöbel. "Algorithms for Optimal Transport and Wasserstein Distances / Jörn Schrieber ; Gutachter: Dominic Schuhmacher, Anita Schöbel ; Betreuer: Dominic Schuhmacher." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2019. http://d-nb.info/1179449304/34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

SEGUY, Vivien Pierre François. "Measure Transport Approaches for Data Visualization and Learning." Kyoto University, 2018. http://hdl.handle.net/2433/233857.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Gairing, Jan, Michael Högele, Tetiana Kosenkova, and Alexei Kulik. "On the calibration of Lévy driven time series with coupling distances : an application in paleoclimate." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/6978/.

Full text
Abstract:
This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a Lévy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to Lévy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump Lévy component for some tail index greater than 2.
APA, Harvard, Vancouver, ISO, and other styles
6

Flenghi, Roberta. "Théorème de la limite centrale pour des fonctionnelles non linéaires de la mesure empirique et pour le rééchantillonnage stratifié." Electronic Thesis or Diss., Marne-la-vallée, ENPC, 2023. http://www.theses.fr/2023ENPC0051.

Full text
Abstract:
Cette thèse porte sur le théorème de la limite centrale, l'un des deux théorèmes limites fondamentaux de la théorie des probabilités avec la loi forte des grands nombres. Le théorème de la limite centrale usuel qui porte sur des fonctionnelles linéaires de la mesure empirique de vecteurs aléatoires indépendants et identiquement distribués a récemment été étendu à des fonctionnelles non linéaires par l'utilisation de la dérivée fonctionnelle linéaire sur l'espace de Wasserstein des mesures de probabilité. Nous généralisons cette extension à la mesure empirique de vecteurs aléatoires indépendants mais non identiquement distribués d'une part et à la mesure empirique des états successifs d'une chaîne de Markov ergodique d'autre part. Dans un second temps, nous nous intéressons au rééchantillonnage stratifié qui est couramment utilisé dans les filtres particulaires. Nous prouvons un théorème de la limite centrale pour le premier rééchantillonnage sous l'hypothèse que les positions initiales des particules sont indépendantes et identiquement distribuées et leurs poids sont proportionnels à une fonction positive des positions qui envoie leur loi commune sur une probabilité possédant une composante non nulle absolument continue par rapport à la mesure de Lebesgue. Ce résultat repose sur la convergence en loi de la partie fractionnaire des sommes partielles de poids normalisés vers une variable aléatoire uniforme sur [0,1]. Plus généralement, nous montrons la convergence en loi vers un vecteur aléatoire uniforme sur [dollar][0,1]^q[dollar] de q sommes partielles d'une suite de variables aléatoires i.i.d. de carré intégrable multipliées par une fonction de la moyenne empirique de cette suite. Pour traiter le couplage introduit par ce facteur commun, nous supposons que la loi commune a une composante non nulle absolument continue par rapport à la mesure de Lebesgue, ce qui assure la convergence en variation totale dans le théorème de la limite centrale pour cette suite. Sous l'hypothèse que la convergence en loi de la partie fractionnaire des poids normalisés reste vraie au étapes suivantes d'un filtre particulaire calculé en alternant des étapes de rééchantillonnage suivant le mécanisme stratifié et des mutations suivant des noyaux markoviens, nous obtenons une formule de récurrence pour la variance asymptotique des particules après n étapes. Nous vérifions la validité de cette formule au travers d'expériences numériques
This thesis is dedicated to the central limit theorem which is one of the two fundamental limit theorems in probability theory with the strong law of large numbers.The central limit theorem which is well known for linear functionals of the empirical measure of independent and identically distributed random vectors, has recently been extended to non-linear functionals. The main tool permitting this extension is the linear functional derivative, one of the notions of derivation on the Wasserstein space of probability measures.We generalize this extension by first relaxing the equal distribution assumptionand then the independence property to be able to deal with the successive values of an ergodic Markov chain.In the second place, we focus on the stratified resampling mechanism.This is one of the resampling schemes commonly used in particle filters. We prove a central limit theorem for the first resampling according to this mechanism under the assumption that the initial positions are independent and identically distributed and the weights proportional to a positive function of the positions such that the image of their common distribution by this function has a non zero component absolutely continuous with respect to the Lebesgue measure. This result relies on the convergence in distribution of the fractional part of partial sums of the normalized weights to some random variable uniformly distributed on [0,1]. More generally, we prove the joint convergence in distribution of q variables modulo one obtained as partial sums of a sequence of i.i.d. square integrable random variables multiplied by a common factor given by some function of an empirical mean of the same sequence. The limit is uniformly distributed over [dollar][0,1]^q[dollar]. To deal with the coupling introduced by the common factor, we assume that the common distribution of the random variables has a non zero component absolutely continuous with respect to the Lebesgue measure, so that the convergence in the central limit theorem for this sequence holds in total variation distance.Under the conjecture that the convergence in distribution of fractional parts to some uniform random variable remains valid at the next steps of a particle filter which alternates selections according to the stratified resampling mechanism and mutations according to Markov kernels, we provide an inductive formula for the asymptotic variance of the resampled population after n steps. We perform numerical experiments which support the validity of this formula
APA, Harvard, Vancouver, ISO, and other styles
7

Bobbia, Benjamin. "Régression quantile extrême : une approche par couplage et distance de Wasserstein." Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCD043.

Full text
Abstract:
Ces travaux concernent l'estimation de quantiles extrêmes conditionnels. Plus précisément, l'estimation de quantiles d'une distribution réelle en fonction d'une covariable de grande dimension. Pour effectuer une telle estimation, nous présentons un modèle, appelé modèle des queues proportionnelles. Ce modèle est étudié à l'aide de méthodes de couplage. La première est centré sur les processus empiriques, tendis que la seconde est basée sur le transport et le couplage optimal. Ces méthodes nous permettent de fournir et d'étudier les estimateurs des quantiles et des différents paramètres ainsi que de fournir une procédure de validation du modèle. La seconde approche est également développée dans le contexte général des extrêmes univariés
This work is related with the estimation of conditional extreme quantiles. More precisely, we estimate high quantiles of a real distribution conditionally to the value of a covariate, potentially in high dimension. A such estimation is made introducing the proportional tail model. This model is studied with coupling methods. The first is an empirical processes based method whereas the second is focused on transport and optimal coupling. We provide estimators of both quantiles and model parameters, we show their asymptotic normality with our coupling methods. We also provide a validation procedure for proportional tail model. Moreover, we develop the second approach in the general framework of univariate extreme value theory
APA, Harvard, Vancouver, ISO, and other styles
8

Nadjahi, Kimia. "Sliced-Wasserstein distance for large-scale machine learning : theory, methodology and extensions." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT050.

Full text
Abstract:
De nombreuses méthodes d'inférence statistique et de modélisation générative ont recours à une divergence pour pouvoir comparer de façon pertinente deux distributions de probabilité. La distance de Wasserstein, qui découle du transport optimal, est un choix intéressant, mais souffre de limites computationnelle et statistique à grande échelle. Plusieurs alternatives ont alors été proposées, notamment la distance de Sliced-Wasserstein (SW), une métrique de plus en plus utilisée en pratique en raison de ses avantages computationnels. Cependant, peu de travaux ont analysé ses propriétés théoriques. Cette thèse examine plus en profondeur l'utilisation de SW pour des problèmes modernes de statistique et d'apprentissage automatique, avec un double objectif : 1) apporter de nouvelles connaissances théoriques permettant une compréhension approfondie des algorithmes basés sur SW, et 2) concevoir de nouveaux outils inspirés de SW afin d'améliorer son application et sa scalabilité. Nous prouvons d'abord un ensemble de propriétés asymptotiques sur les estimateurs obtenus en minimisant SW, ainsi qu'un théorème central limite dont le taux de convergence est indépendant de la dimension. Nous développons également une nouvelle technique d'inférence basée sur SW qui n'utilise pas la vraisemblance, offre des garanties théoriques et s'adapte bien à la taille et à la dimension des données. Etant donné que SW est couramment estimée par une simple méthode de Monte Carlo, nous proposons ensuite deux approches pour atténuer les inefficacités dues à l'erreur d'approximation : d'une part, nous étendons la définition de SW pour introduire les distances de Sliced-Wasserstein généralisées, et illustrons leurs avantages sur des applications de modélisation générative ; d'autre part, nous tirons parti des résultats de concentration de la mesure pour formuler une nouvelle approximation déterministe de SW, qui est plus efficace à calculer que la technique de Monte Carlo et présente des garanties non asymptotiques sous une condition de dépendance faible. Enfin, nous définissons la classe générale de divergences "sliced" et étudions leurs propriétés topologiques et statistiques; en particulier, nous prouvons que l'erreur d'approximation de toute divergence sliced par des échantillons ne dépend pas de la dimension du problème
Many methods for statistical inference and generative modeling rely on a probability divergence to effectively compare two probability distributions. The Wasserstein distance, which emerges from optimal transport, has been an interesting choice, but suffers from computational and statistical limitations on large-scale settings. Several alternatives have then been proposed, including the Sliced-Wasserstein distance (SW), a metric that has been increasingly used in practice due to its computational benefits. However, there is little work regarding its theoretical properties. This thesis further explores the use of SW in modern statistical and machine learning problems, with a twofold objective: 1) provide new theoretical insights to understand in depth SW-based algorithms, and 2) design novel tools inspired by SW to improve its applicability and scalability. We first prove a set of asymptotic properties on the estimators obtained by minimizing SW, as well as a central limit theorem whose convergence rate is dimension-free. We also design a novel likelihood-free approximate inference method based on SW, which is theoretically grounded and scales well with the data size and dimension. Given that SW is commonly estimated with a simple Monte Carlo scheme, we then propose two approaches to alleviate the inefficiencies caused by the induced approximation error: on the one hand, we extend the definition of SW to introduce the Generalized Sliced-Wasserstein distances, and illustrate their advantages on generative modeling applications; on the other hand, we leverage concentration of measure results to formulate a new deterministic approximation for SW, which is computationally more efficient than the usual Monte Carlo technique and has nonasymptotical guarantees under a weak dependence condition. Finally, we define the general class of sliced probability divergences and investigate their topological and statistical properties; in particular, we establish that the sample complexity of any sliced divergence does not depend on the problem dimension
APA, Harvard, Vancouver, ISO, and other styles
9

Liu, Lu. "A Risk-Oriented Clustering Approach for Asset Categorization and Risk Measurement." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/39444.

Full text
Abstract:
When faced with market risk for investments and portfolios, people often calculate the risk measure, which is a real number mapping to each random payoff. There are many ways to quantify the potential risk, among which the most important input is the features from future performance. Future distributions are unknown and thus always estimated from historical Profit and Loss (P&L) distributions. However, past data may not be appropriate for estimating the future; risk measures generated from single historical distributions can be subject to error. To overcome these shortcomings, one natural way implemented is to identify and categorize similar assets whose Profit and Loss distributions can be used as alternative scenarios. In practice, one of the most common and intuitive categorizations is sector, based on industry. It is widely agreed that companies in the same sector share the same, or related, business types and operating characteristics. But in the field of risk management, sector-based categorization does not necessarily mean assets are grouped in terms of their risk profiles, and we show that risk measures in the same sector tend to have large variation. Although improved risk measures related to the distribution ambiguity has been discussed at length, we seek to develop a more risk-oriented categorization by providing a new clustering approach. Furthermore, our method can better inform us of the potential risk and the extreme worst-case scenario within the same category.
APA, Harvard, Vancouver, ISO, and other styles
10

Lescornel, Hélène. "Covariance estimation and study of models of deformations between distributions with the Wasserstein distance." Toulouse 3, 2014. http://www.theses.fr/2014TOU30045.

Full text
Abstract:
La première partie de cette thèse est consacrée à l'estimation de covariance de processus stochastiques non stationnaires. Le modèle étudié amène à estimer la covariance du processus dans différents espaces vectoriels de matrices. Nous étudions dans le chapitre 3 une méthode de sélection de modèle par minimisation d'un critère pénalisé en utilisant des inégalités de concentration, et le chapitre 4 présente une méthode basée sur l'estimation sans biais du risque. Dans les deux cas des inégalités oracles sont obtenues. La seconde partie de cette thèse concerne l'étude de modèles de déformations entre distributions. On suppose observer une quantité aléatoire epsilon à travers une fonction de déformation. C'est l'importance de la déformation, représentée par un paramètre theta, que l'on cherche à retrouver. Nous présentons plusieurs méthodes d'estimation basées sur la distance de Wasserstein en alignant les lois des observations pour retrouver le paramètre de déformation. Dans le cas où les variables aléatoires sont à valeurs réelles, le chapitre 7 donne des propriétés de consistance pour un M-estimateur et sa distribution asymptotique. On y utilise des techniques de Hadamard différentiabilité pour appliquer une Delta-Méthode fonctionnelle. Le chapitre 8 concerne l'étude d'un estimateur de type Robbins-Monro et présente des propriétés de convergence pour un estimateur à noyau de la densité de la variable epsilon obtenu à l'aide des observations. Le modèle est généralisé à des variables dans des espaces métriques complets dans le chapitre 9, puis, dans l'optique de créer un test d'adéquation, le chapitre 10 donne des résultats sur la distribution asymptotique d'une statistique de test
The first part of this thesis concerns the covariance estimation of non stationary processes. We are estimating the covariance in different vectorial spaces of matrices. In Chapter 3, we give a model selection procedure by minimizing a penalized criterion and using concentration inequalities, and Chapter 4 presents an Unbiased Risk Estimation method. In both cases we give oracle inequalities. The second part deals with the study of models of deformation between distributions. We assume that we observe a random quantity epsilon through a deformation function. The importance of the deformation is represented by a parameter theta that we aim to estimate. We present several methods of estimation based on the Wasserstein distance by aligning the distributions of the observations to recover the deformation parameter. In the case of real random variables, Chapter 7 presents properties of consistency for a M-estimator and its asymptotic distribution. We use Hadamard differentiability techniques to apply a functional Delta method. Chapter 8 concerns a Robbins-Monro estimator for the deformation parameter and presents properties of convergence for a kernel estimator of the density of the variable epsilon obtained with the observations. The model is generalized to random variables in complete metric spaces in Chapter 9. Then, in the aim to build a goodness of fit test, Chapter 10 gives results on the asymptotic distribution of a test statistic
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Distances de Wasserstein"

1

An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows. European Mathematical Society, 2021.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Computational Inversion with Wasserstein Distances and Neural Network Induced Loss Functions. [New York, N.Y.?]: [publisher not identified], 2022.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Distances de Wasserstein"

1

Bachmann, Fynn, Philipp Hennig, and Dmitry Kobak. "Wasserstein t-SNE." In Machine Learning and Knowledge Discovery in Databases, 104–20. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-26387-3_7.

Full text
Abstract:
AbstractScientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in exploring the structure on the unit level rather than on the sample level. Units can be compared based on the distance between their means, however this ignores the within-unit distribution of samples. Here we develop an approach for exploratory analysis of hierarchical datasets using the Wasserstein distance metric that takes into account the shapes of within-unit distributions. We use t-SNE to construct 2D embeddings of the units, based on the matrix of pairwise Wasserstein distances between them. The distance matrix can be efficiently computed by approximating each unit with a Gaussian distribution, but we also provide a scalable method to compute exact Wasserstein distances. We use synthetic data to demonstrate the effectiveness of our Wassersteint-SNE, and apply it to data from the 2017 German parliamentary election, considering polling stations as samples and voting districts as units. The resulting embedding uncovers meaningful structure in the data.
APA, Harvard, Vancouver, ISO, and other styles
2

Villani, Cédric. "The Wasserstein distances." In Grundlehren der mathematischen Wissenschaften, 93–111. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-71050-9_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Barbe, Amélie, Marc Sebban, Paulo Gonçalves, Pierre Borgnat, and Rémi Gribonval. "Graph Diffusion Wasserstein Distances." In Machine Learning and Knowledge Discovery in Databases, 577–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67661-2_34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Jacobs, Bart. "Drawing from an Urn is Isometric." In Lecture Notes in Computer Science, 101–20. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57228-9_6.

Full text
Abstract:
AbstractDrawing (a multiset of) coloured balls from an urn is one of the most basic models in discrete probability theory. Three modes of drawing are commonly distinguished: multinomial (draw-replace), hypergeometric (draw-delete), and Pólya (draw-add). These drawing operations are represented as maps from urns to distributions over multisets of draws. The set of urns is a metric space via the Wasserstein distance. The set of distributions over draws is also a metric space, using Wasserstein-over-Wasserstein. The main result of this paper is that the three draw operations are all isometries, that is, they preserve the Wasserstein distances.
APA, Harvard, Vancouver, ISO, and other styles
5

Santambrogio, Filippo. "Wasserstein distances and curves in the Wasserstein spaces." In Optimal Transport for Applied Mathematicians, 177–218. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20828-2_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Öcal, Kaan, Ramon Grima, and Guido Sanguinetti. "Wasserstein Distances for Estimating Parameters in Stochastic Reaction Networks." In Computational Methods in Systems Biology, 347–51. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31304-3_24.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Carrillo, José Antonio, Young-Pil Choi, and Maxime Hauray. "The derivation of swarming models: Mean-field limit and Wasserstein distances." In Collective Dynamics from Bacteria to Crowds, 1–46. Vienna: Springer Vienna, 2014. http://dx.doi.org/10.1007/978-3-7091-1785-9_1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Haeusler, Erich, and David M. Mason. "Asymptotic Distributions of Trimmed Wasserstein Distances Between the True and the Empirical Distribution Function." In Stochastic Inequalities and Applications, 279–98. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8069-5_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Walczak, Szymon M. "Wasserstein Distance." In SpringerBriefs in Mathematics, 1–10. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57517-9_1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Breiding, Paul, Kathlén Kohn, and Bernd Sturmfels. "Wasserstein Distance." In Oberwolfach Seminars, 53–66. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-51462-3_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Distances de Wasserstein"

1

Zhang, Xiaoxia, Chao Wang, Xusheng Hu, and Claude Delpha. "Incipient Cracks Characterization Based on Jensen-Shannon Divergence and Wasserstein Distance." In 2024 Prognostics and System Health Management Conference (PHM), 8–13. IEEE, 2024. http://dx.doi.org/10.1109/phm61473.2024.00010.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Lyu, Zihang, Jun Xiao, Cong Zhang, and Kin-Man Lam. "AI-Generated Image Detection With Wasserstein Distance Compression and Dynamic Aggregation." In 2024 IEEE International Conference on Image Processing (ICIP), 3827–33. IEEE, 2024. http://dx.doi.org/10.1109/icip51287.2024.10648186.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Malik, Vikrant, Taylan Kargin, Victoria Kostina, and Babak Hassibi. "A Distributionally Robust Approach to Shannon Limits using the Wasserstein Distance." In 2024 IEEE International Symposium on Information Theory (ISIT), 861–66. IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619597.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Lopez, Adrian Tovar, and Varun Jog. "Generalization error bounds using Wasserstein distances." In 2018 IEEE Information Theory Workshop (ITW). IEEE, 2018. http://dx.doi.org/10.1109/itw.2018.8613445.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Memoli, Facundo. "Spectral Gromov-Wasserstein distances for shape matching." In 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops. IEEE, 2009. http://dx.doi.org/10.1109/iccvw.2009.5457690.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Prossel, Dominik, and Uwe D. Hanebeck. "Dirac Mixture Reduction Using Wasserstein Distances on Projected Cumulative Distributions." In 2022 25th International Conference on Information Fusion (FUSION). IEEE, 2022. http://dx.doi.org/10.23919/fusion49751.2022.9841286.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Steuernagel, Simon, Aaron Kurda, and Marcus Baum. "Point Cloud Registration based on Gaussian Mixtures and Pairwise Wasserstein Distances." In 2023 IEEE Symposium Sensor Data Fusion and International Conference on Multisensor Fusion and Integration (SDF-MFI). IEEE, 2023. http://dx.doi.org/10.1109/sdf-mfi59545.2023.10361440.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Perkey, Scott, Ana Carvalho, and Alberto Krone-Martins. "Using Fourier Coefficients and Wasserstein Distances to Estimate Entropy in Time Series." In 2023 IEEE 19th International Conference on e-Science (e-Science). IEEE, 2023. http://dx.doi.org/10.1109/e-science58273.2023.10254949.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Barbe, Amelie, Paulo Goncalves, Marc Sebban, Pierre Borgnat, Remi Gribonval, and Titouan Vayer. "Optimization of the Diffusion Time in Graph Diffused-Wasserstein Distances: Application to Domain Adaptation." In 2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI). IEEE, 2021. http://dx.doi.org/10.1109/ictai52525.2021.00125.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Garcia Ramirez, Jesus. "Which Kernels to Transfer in Deep Q-Networks?" In LatinX in AI at Neural Information Processing Systems Conference 2019. Journal of LatinX in AI Research, 2019. http://dx.doi.org/10.52591/lxai201912087.

Full text
Abstract:
Deep Reinforcement Learning (DRL) combines the benefits of Deep Learning and Reinforcement Learning. However, it still requires long training times and a large number of instances to reach an acceptable performances. Transfer Learning (TL) offers an alternative to reduce the training time of DRL agents, using less instances and possibly improving performance. In this work, we propose a transfer learning formulation for DRL across tasks. Relevant source tasks are selected considering the action spaces and the Wasserstein distances of an output in a hidden layer of a convolutional neural network. Rather than transferring the whole source model, we propose a method for selecting only relevant kernels based on their entropy values, which results in smaller models that can produce better performances. In our experiments we use Deep QNetworks (DQN) with Atari games We evaluated the proposed method with dierent percentages of selected kernels and show that we can obtain similar performances than DQN in less nteractions and with smaller models.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Distances de Wasserstein' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography