Results 11 to 20 of about 6,516 (216)
Decorrelation using optimal transport
European Physical Journal C: Particles and FieldsBeing able to decorrelate a feature space from protected attributes is an area of active research and study in ethics, fairness, and also natural sciences.
Malte Algren +2 more
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Inverse Optimal Transport [PDF]
SIAM Journal on Applied Mathematics, 2020 Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal
Andrew M. Stuart, Marie-Therese Wolfram
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Metasurfaces and Optimal transport
The SMAI Journal of computational mathematics, 2022 This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numerical solution we study and implement a damped Newton algorithm to solve the semi discrete problem.
Cristian E. Gutiérrez +3 more
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Optimal Pricing for Optimal Transport [PDF]
Set-Valued and Variational Analysis, 2014 Suppose that $c(x,y)$ is the cost of transporting a unit of mass from $x\in X$ to $y\in Y$ and suppose that a mass distribution $μ$ on $X$ is transported optimally (so that the total cost of transportation is minimal) to the mass distribution $ν$ on $Y$.
Bartz, Sedi, Reich, Simeon
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SIAM Journal on Applied Mathematics, 2022 Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan which traditional optimal transport cannot enforce.
Zixuan Cang, Qing Nie, Yanxiang Zhao
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Unnormalized optimal transport [PDF]
Journal of Computational Physics, 2019 We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We obtain a one-parameter family of simple modifications of the formulation in [4].
Wilfrid Gangbo +3 more
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Proceedings of the AAAI Conference on Artificial Intelligence, 2022 Optimal Transport (OT) has become a popular tool in machine learning to align finite datasets typically lying in the same vector space. To expand the range of possible applications, Co-Optimal Transport (Co-OT) jointly estimates two distinct transport plans, one for the rows (points) and one for the columns (features), to match two data matrices that ...
Kerdoncuff, Tanguy +3 more
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Adaptive optimal transport [PDF]
Information and Inference: A Journal of the IMA, 2019 AbstractAn adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu $ and $\nu $, known only through a finite set of independent samples $(x_i)_{i=1..n}$ and $(y_j)_{j=1..m}$. The methodology automatically creates features that adapt to the data, thus avoiding reliance on a priori knowledge of the ...
Essid, Montacer +2 more
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CoRR, 2022 We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions.
Alexander Korotin +2 more
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