Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Léger, Flavien"'
Nonnegative cross-curvature (NNCC) is a geometric property of a cost function defined on a product space that originates in optimal transportation and the Ma-Trudinger-Wang theory. Motivated by applications in optimization, gradient flows and mechani
Externí odkaz:
http://arxiv.org/abs/2409.18112
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth optimal maps
Externí odkaz:
http://arxiv.org/abs/2311.10208
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective function i
Externí odkaz:
http://arxiv.org/abs/2305.04917
Publikováno v:
Pure Appl. Analysis 5 (2023) 1041-1080
A classical tool for approximating integrals is the Laplace method. The first-order, as well as the higher-order Laplace formula is most often written in coordinates without any geometrical interpretation. In this article, motivated by a situation ar
Externí odkaz:
http://arxiv.org/abs/2212.04376
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman divergenc
Externí odkaz:
http://arxiv.org/abs/2206.08873
We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced by Jacobs and L\'eger to solve optimal transport problems. We evolve the gradient flow by s
Externí odkaz:
http://arxiv.org/abs/2011.08151
Publikováno v:
Neural Information Processing Systems, Dec 2020, Vancouver, Canada
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which can be solv
Externí odkaz:
http://arxiv.org/abs/2006.08172
Autor:
Léger, Flavien
We present a new perspective on the popular Sinkhorn algorithm, showing that it can be seen as a Bregman gradient descent (mirror descent) of a relative entropy (Kullback-Leibler divergence). This viewpoint implies a new sublinear convergence rate wi
Externí odkaz:
http://arxiv.org/abs/2002.03758
Akademický článek
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Autor:
Jacobs, Matt, Léger, Flavien
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n points, we comp
Externí odkaz:
http://arxiv.org/abs/1905.12154