Results 21 to 30 of about 2,509,053 (235)
Hierarchical Sliced Wasserstein Distance [PDF]
International Conference on Learning Representations, 2022 Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality.
Khai Nguyen +5 more
semanticscholar +3 more sources
Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance [PDF]
Physical Review Research, 2021 We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L^{2}-Wasserstein distance ...
Muka Nakazato, Sosuke Ito
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Identifying critical States of complex diseases by local network Wasserstein distance [PDF]
Scientific ReportsComplex diseases often undergo abrupt transitions from pre-disease to disease states, with the pre-disease state is typically unstable but potentially reversible through timely intervention. Detecting these critical transitions is crucial.
Changchun Liu, Pingjun Hou, Lin Feng
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Hyperbolic Wasserstein Distance for Shape Indexing. [PDF]
IEEE Trans Pattern Anal Mach Intell, 2020 Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating ...
Shi J, Wang Y.
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Shape Analysis with Hyperbolic Wasserstein Distance. [PDF]
Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit, 2016 Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise.
Shi J, Zhang W, Wang Y.
europepmc +4 more sources
Detecting tiny objects in aerial images: A normalized Wasserstein distance and a new benchmark [PDF]
arXiv.org, 2022 Tiny object detection (TOD) in aerial images is challenging since a tiny object only contains a few pixels. State-of-the-art object detectors do not provide satisfactory results on tiny objects due to the lack of supervision from discriminative features.
Chang Xu +5 more
semanticscholar +1 more source
Asymptotics of Smoothed Wasserstein Distances [PDF]
Potential Analysis, 2021 We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive curvature; however, on flat Euclidean space---where the heat semigroup corresponds to smoothing the measures by ...
Hong-Bin Chen, Jonathan Niles-Weed
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Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance [PDF]
Neural Information Processing Systems, 2022 Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still incomplete. Recently,
Dohyun Kwon, Ying Fan, Kangwook Lee
semanticscholar +1 more source
Wasserstein distance to independence models [PDF]
Journal of Symbolic Computation, 2021 An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope.
Celik T. O. +4 more
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Energy-Based Sliced Wasserstein Distance [PDF]
Neural Information Processing Systems, 2023 The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution.
Khai Nguyen, Nhat Ho
semanticscholar +1 more source