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Showing 1 to 20 of 76 for “"Wasserstein"”.
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Learning and inference with Wasserstein metrics
… tools from the study of optimal transport (or Wasserstein) distances between probability distributions. Optimal transport distances capture an intuitive notion of similarity between distributions, by incorporating the underlying geometry of the domain of the distributions. Despite their …
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Vietoris–Rips metric thickenings and Wasserstein spaces
… then K can be interpreted as a subset of the Wasserstein space of probability measures on X. Such spaces are called simplicial metric thickenings, and a prominent example is the Vietoris–Rips metric thickening. In this work we study these spaces from three perspectives: metric geometry, …
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Distributionally robust binary classifier under Wasserstein distance
… with the radius calculated as per the Wasserstein distance. We derive the tractable formulation for the general problem. When focusing on the support vector machine (SVM), the general problem boils down to an easy-to-solve second- order cone programming problem. The robustified SVM is …
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Deep generative models via explicit Wasserstein minimization
… target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the “semi-discrete” setting), then the Wasserstein distance is realized by a …
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Generative modeling using the sliced Wasserstein distance
… to improve stability, for instance, by using the Wasserstein distance rather than the Jenson-Shannon divergence. Here, we consider an alternative formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddlepoint …
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Non-parametric threshold for smoothed empirical Wasserstein distance
… distribution P. We show that when 𝐾 < 𝜎, the Wasserstein distance 𝑊₂² (Pₙ*𝒩(0, 𝜎² 𝐼 subscript 𝑑), P*𝒩 (0, 𝜎² 𝐼 subscript 𝑑)) converges at the parametric rate 𝑂(1/𝑛), and when 𝐾 > 𝜎, there exists a 𝐾-subgaussian distribution P such that 𝑊₂² (Pₙ *𝒩 (0, 𝜎² 𝐼 subscript 𝑑), P* 𝒩 (0, 𝜎² 𝐼 subscript …
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Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space
… a non-smooth term (the entropy) over the Bures–Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when π is log-smooth and log-concave, as well as the first convergence guarantees to first-order …
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Advances in Gromov–Wasserstein optimal transport: linearization, multi-marginal generalization, barycenters and transfer operators
… models with a primary focus on the Gromov–Wasserstein (GW) transport problem. Figuratively, this transport problem offers a relaxed way of finding a correspondence that retains the geometry between given inputs, and evaluating how far they are from being isometric. After briefly introducing …
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Optimal transportation and barycenter problems via convex functions
… transportation problems and the associatedWasserstein distances in increasing levels of specificity. The first chapter introduces optimal transport problems and known properties characterizing optimal transport plans. The second chapter develops the Wasserstein distances, arising from …
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Diffusion Processes with Reflection
… Arbeit wird eine Partikelapproximation für die Wasserstein Diffusion bewiesen. Bei der Wasserstein Diffusion handelt es sich um einen reversiblen Markov Prozess mit Werten in der Menge von Wahrscheinlichkeitsmaßen auf dem Einheitsintervall. Das Ziel ist es, ein Partikelsystem zu definieren, so …
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Statistical problems in transport and alignment
… structure of this kind. First, we study the Wasserstein distance, a metric on the space of probability measures on an arbitrary metric space. We prove sharp rates of convergence for empirical measures in Wasserstein distance on sufficiently regular compact metric spaces, improving on a line …
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Generative adversarial networks for fine art generation
… been applied to the task of fine art generation. Wasserstein GANs and GANHack techniques have not been applied in GANs that generate fine art, despite their showing improved GAN results in other applications. This thesis investigates whether Wasserstein GANs and GANHack extensions to DCGANs can …
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An optimization perspective on log-concave sampling and beyond
… the main tools in this work—diffusions and Wasserstein gradient flows—through applications to functional inequalities, the entropic barrier, Wasserstein barycenters, variational inference, and diffusion models.
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Robust Inference via Optimal Transport Ambiguity Sets
… measures defined by distances such as the Wasserstein metric—and demonstrate that leveraging these ambiguity sets endows two widely used statistical algorithms with distributional robustness. The Kalman filter enables accurate, real-time tracking of latent states by assimilating noisy, …
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Interpolating Spline Curves of Measures
… which subsumes all of these problems: the Wasserstein space of measures with finite second moment. Works on point estimation, generalized means, and linear regression have appeared, as have some on smooth interpolation, greatly expanding the statistical toolkit for modern data. In this …
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Topics in Deep Generative Modelling Mathematical and Computational Aspects of Diffusion Models and Generative Adversarial Networks
… We establish a theoretical upper bound on the Wasserstein 2-distance between distributions induced by stochastic and deterministic dynamics, linking it to the Fokker-Planck equation and its residual. Furthermore, the thesis explores the interplay between diffusion models and data manifolds. We …
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Three essays on nonparametric estimation
… as the minimum of the entropy regularized Wasserstein metric provided by Cuturi (2013), which can be found with a nearly linear time complexity in the number of points in the mesh (Altschuler et al., 2017). It is also a common thread that links all three essays. After providing results on …
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Temporally Feathered Radiation Therapy under Uncertainty
… scenario generation techniques based on Wasserstein and fused Gromov-Wasserstein distances to approximate complex stochastic processes effectively. To solve the resulting models, we design block coordinate descent algorithms and demonstrate their performance across applications in …
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Robust Exact Algorithms for the Euclidean Bipartite Matching Problem
… of this problem is the computation of the p-Wasserstein distance which we define next. Given a complete bipartite graph with two disjoint sets of n points in d-dimensional Euclidean space and an integer p ≥ 1, let the cost of an edge be the p-th power of the Euclidean distance between its …
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Contributions to asymptotic theory in nonparametric statistics
… estimation on the d-dimensional torus, using Wasserstein distances as the loss function. We consider the question of constructing adaptive honest confidence sets, which have uniform coverage guarantees but also shrink at an optimal rate depending on the smoothness of the true parameter, …
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