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.
Results
Showing 1 to 12 of 12 for “"Optimal Transport Theory"”.
-
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 …
-
Mechanism design : from optimal transport theory to revenue maximization
… problem in Economics and Algorithmic Game Theory is the design of auctions that maximize 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 …
-
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 …
-
Distributionally robust optimization with marginals : theory and applications
… is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to be specified up to only the marginal distributions. We generalize the primal-dual formulations for this problem from the set of …
-
Geometry and Optimization of Relative Arbitrage
… 90s and the early 2000s, stochastic portfolio theory provides a novel mathematical framework to analyze this phenomenon. A major result of the theory is the construction of portfolio strategies that outperform the market portfolio under realistic conditions. These portfolios are called relative …
-
Interpretable Physics-informed Machine Learning Methods for Scientific Modeling and Data Analysis
… time-series data. Finally, we use tools from optimal transport theory and manifold learning to develop a robust non-parametric method for discovering conservation laws, showing the advantage of using geometric machine learning methods to solve scientific problems. By designing physics-informed …
-
A Minimax Approach for Learning Gaussian Mixtures
… of image, sound, and text data, they perform suboptimally in learning multi-modal distributionlearning benchmarks including Gaussian mixture models (GMMs). In this thesis, we propose Generative Adversarial Training for Gaussian Mixture Models (GATGMM), a minimax GAN framework for learning GMMs. …
-
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 …
-
A Mass Minimizing Flow for Real-Valued Flat Chains with Applications to Transport Networks
An oriented transportation network can be modeled by a 1-dimensional chain whose boundary is the difference between the demand and supply distributions, represented by weighted sums of point masses. To accommodate efficiencies of scale into the model, one uses a suitable Mα norm for transportation …
-
A concentration inequality based statistical methodology for inference on covariance matrices and operators
… from the concentration of measure literature–a theory that arose in the latter half of the 20th century from connections between geometry, probability, and functional analysis–to construct rigorous descriptive and inferential statistical methodology for covariance matrices and operators. A …
-
Wireless Communications and Networking with Unmanned Aerial Vehicles: Fundamentals, Deployment, and Optimization
… For deployment, using tools from optimization theory, holistic frameworks are developed for the optimal 3D placement of UAV base stations in uplink and downlink scenarios. The results show that the proposed deployment approaches significantly improve the downlink coverage for ground users, and …
-
Artificial General Intelligence (AGI)-Native Wireless Systems: Digital Twins and World Models for Beyond 6G Networks
… allocation. To solve this problem, we propose an optimal transport theory algorithm that ensures the optimal average synchronization time of the world models, while satisfying the synchronization intensity requirements of the DTs. Results show that synchronization delays can be reduced up to 25 % …