Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 69 for “"Optimal Transport"”.
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Optimal transport strategies
… We here consider a number of natural fluid transport systems that may be framed in terms of constrained optimization problems. We first examine natural drinking strategies. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and …
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Statistical aspects of optimal transport
Optimal transport (OT) is a flexible framework for contrasting and interpolating probability measures which has recently been applied throughout science, including in machine learning, statistics, graphics, economics, biology, and more. In this thesis, we study several statistical problems at the …
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Optimal transport: theory, algorithms and applications
Optimal transport (OT), which deals with the matching of probability or positive measures, has been originally introduced by Monge in 1781. In particular its linear programming relaxation of Kantorovich in 1942 and the introduction of entropic regularization to OT by Léonard and Cuturi around a …
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Approximate Bayesian inference and optimal transport
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Riemannian Metric Learning via Optimal Transport
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using …
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Generative gradual domain adaptation with optimal transport
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01
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Robust Inference via Optimal Transport Ambiguity Sets
… shifts using ambiguity sets defined by two optimal transport-based metrics and propose two robust conformal prediction algorithms that preserves validity under these shifts. First, we consider ambiguity sets defined by a pseudo-divergence derived from the LévyProkhorov (LP) metric, which …
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Position-aware regularized optimal transport for network alignment
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01
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Topics in high-dimensional geometry and optimal transport
… part of this thesis involves topics related to optimal transport theory. The third chapter focuses on cost induced transforms. In particular, a family of order reversing isomorphisms $\mathcal{A}_t$, which are related to the polarity transform $\mathcal{A}$, is discussed. We prove that …
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Optimal transport in structured domains : algorithms and applications
Optimal transport provides a powerful mathematical framework for comparing probability distributions, and has found successful application in various problems in machine learning, including point cloud matching, generative modeling, and document comparison. However, some important limitations …
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Mechanism design : from optimal transport theory to revenue maximization
… the auctioneer's expected revenue. While optimal selling of a single item has been well-understood since the pioneering work of Myerson in 1981, extending his work to multi-item settings has remained a challenge. In this work, we obtain such extensions providing a mathematical framework …
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Scalable Combinatorial Algorithms for Optimal Transport Based Similarity Metrics
Optimal Transport (OT), also known as Wasserstein distance, is a valuable metric for comparing probability distributions. Owing to its appealing statistical properties, researchers in various fields, such as machine learning, use OT within applications. However, computing both exact and approximate …
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Warm Start Algorithms for Bipartite Matching and Optimal Transport
Minimum Cost Bipartite Matching and Optimal Transport are essential optimization challenges with applications in logistics, artificial intelligence, and multimodal data alignment. These problems involve finding efficient pairings while minimizing costs. Due to the combinatorial nature of …
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Geometric methods in computational optimal transport and high-dimensional inference
… advances the understanding of computational optimal transport and high-dimensional inference through four main contributions, each exploring fundamental connections between geometric structure and algorithmic efficiency. First, a refined analysis of the Sinkhorn algorithm’s convergence …
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Learning structured representations by embedding class hierarchy with fast optimal transport
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2027-05-01
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Robust Bayesian inference via optimal transport misfit measures: applications and algorithms
… Instrumental to our approach is the use of transport–Lagrangian (TL) distances as loss/misfit functions: such distances can be understood as “graph-space” optimal transport distances, and they naturally disregard certain features of the data that are more sensitive to time warping. We show …
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Minimax estimation with structured data : shape constraints, causal models, and optimal transport
… estimation, causal discovery, and optimal transport. In the area of shape-constrained estimation, we study the estimation of matrices, first under the assumption of bounded total-variation (TV) and second under the assumption that the underlying matrix is Monge, or supermodular. …
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Essays on Optimal Transport Theory and Causal Inference: A Theoretical and Empirical Approach
… perspective to identify the causal impact of transportation on air pollution. The first chapter explores identifying average treatment effects for the treated in the region where the covariate distributions across treatment and control groups have non-overlap support. We make a natural domain …
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Overcoming Computational Complexity Barriers for Optimal Transport in Discrete and Semi-Discrete Settings
… two probability distributions $mu$ and $nu$, Optimal Transport (OT) measures the minimum effort required to transport mass between $mu$ and $nu$. OT provides a meaningful distance between distributions and acts as a dissimilarity measure between them. Due to its useful statistical properties, …
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