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Theoretical Guarantees for Bridging Metric Measure Embedding and Optimal Transport [article]

Mokhtar Z. Alaya, Maxime Bérar, Gilles Gasso, Alain Rakotomamonjy
2021 arXiv   pre-print
and compute an optimal transport (OT) on the embedded distributions.  ...  In addition to this novel proposal that generalizes several recent OT works, our contributions stand on several theoretical analyses: (i) we characterize the embedding spaces to define SERW distance for  ...  We consider two metric measure spaces (mm-space for short) (Gromov et al., 1999) is a compact metric space and µ is a probability measure with full support, i.e. µ(X) = 1 and supp[µ] = X.  ... 
arXiv:2002.08314v5 fatcat:4j3y2en4mrb33dfmwzarnxgoe4

Obtaining Dyadic Fairness by Optimal Transport [article]

Moyi Yang, Junjie Sheng, Xiangfeng Wang, Wenyan Liu, Bo Jin, Jun Wang, Hongyuan Zha
2022 arXiv   pre-print
The optimal transport-based dyadic fairness algorithm is proposed for graph link prediction.  ...  We aim to propose a pre-processing methodology to obtain dyadic fairness through data repairing and optimal transport.  ...  To bridge it with the optimal transport theory, we assume graph G 0 and G 1 form uniform distributions γ0 and γ1 . Then our goal can be explicitly described as min G W 1. = (γ 0 , γ1 ).  ... 
arXiv:2202.04520v1 fatcat:dl2ofav46jfq3mj4xpfenhayzu

Hilbert Sinkhorn Divergence for Optimal Transport

Qian Li, Zhichao Wang, Gang Li, Jun Pang, Guandong Xu
2021 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
We propose a theoretical and computational framework to bridge this gap.  ...  The Sinkhorn divergence has become a very popular metric to compare probability distributions in optimal transport.  ...  Another important reason is that the theoretical convergence of optimal transport in RKHS has not been well studied.  ... 
doi:10.1109/cvpr46437.2021.00383 fatcat:445micqmkrcjzpsvgaiyloswni

Robust ambulance allocation using risk-based metrics

Kaushik Krishnan, Lavanya Marla, Yisong Yue
2016 2016 8th International Conference on Communication Systems and Networks (COMSNETS)  
We show that optimizing based on risk measures can account for spatiotemporal patterns and prevent the extent of delay cascades that are typically seen in heavy-tailed arrival distributions.  ...  To address this, metrics other than average-case need to be used. We achieve robust location strategies by including risk metrics that account for tail behavior and not average performance alone.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their comments that greatly improved the presentation in this manuscript.  ... 
doi:10.1109/comsnets.2016.7439958 dblp:conf/comsnets/KrishnanMY16 fatcat:xdnn4pjfgncmtacsyvtakrooti

Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency [article]

Anish Chakrabarty, Swagatam Das
2021 arXiv   pre-print
The main result, consequently ensures the regeneration of the input distribution, harnessing the potential offered by Optimal Transport of measures under the Wasserstein metric.  ...  Similar examinations for Autoencoders, however, despite their diverse applicability and notable empirical performance, remain largely absent.  ...  Wasserstein Duality: A Brief Exposition The equivalence relation between Wasserstein Distance and Integral Probability Metrics (IPMs) [25] is a fairly wellstudied topic in optimal transport theory.  ... 
arXiv:2110.03995v1 fatcat:yon5dmn7b5esvjwnhjnytt4the

A Principled Approach for Learning Task Similarity in Multitask Learning [article]

Changjian Shui, Mahdieh Abbasi, Louis-Émile Robitaille, Boyu Wang, Christian Gagné
2019 arXiv   pre-print
We systematically derive the bounds based on two distinct task similarity metrics: H divergence and Wasserstein distance.  ...  However, the theoretical motivations for adding task similarity knowledge are often missing or incomplete.  ...  Optimal transport and Wasserstein distance We assume X the measurable space and denote P(X ) the set of all probability measures over X .  ... 
arXiv:1903.09109v1 fatcat:zjspozrvifegpgvisqacg75hj4

Feedback and Time are Essential for the Optimal Control of Computing Systems

Eric C. Kerrigan
2015 IFAC-PapersOnLine  
We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems.  ...  By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been  ...  input-output models and use the gap metric to provide guarantees on the closed-loop behavior.  ... 
doi:10.1016/j.ifacol.2015.11.309 fatcat:bdb2q7kfxrbjjkukkbqsyzvgma

Robust component: a robustness measure that incorporates access to critical facilities under disruptions

Shangjia Dong, Haizhong Wang, Ali Mostafavi, Jianxi Gao
2019 Journal of the Royal Society Interface  
To bridge this gap, this paper proposed the metric robust component and a probabilistic link-removal strategy to assess network robustness through a percolation-based simulation framework.  ...  This research can also be generalized to identify critical facilities and sites for future development.  ...  The authors are grateful for the insightful comments of the anonymous reviewers.  ... 
doi:10.1098/rsif.2019.0149 pmid:31387488 pmcid:PMC6731514 fatcat:plhbwy62i5hbtkx54exulxskae

Fair Mixup: Fairness via Interpolation [article]

Ching-Yao Chuang, Youssef Mroueh
2021 arXiv   pre-print
We analyze fair mixup and empirically show that it ensures a better generalization for both accuracy and fairness measurement in tabular, vision, and language benchmarks.  ...  To improve the generalizability of fair classifiers, we propose fair mixup, a new data augmentation strategy for imposing the fairness constraint.  ...  In spite of the analytical solutions and theoretical guarantees, game-theoretic approaches could be hard to scale for complex model classes.  ... 
arXiv:2103.06503v1 fatcat:upihwyscqna6dkamy2yy7atssq

Robustness in Cyber-Physical Systems (Dagstuhl Seminar 16362)

Martin Fränzle, James Kapinski, Pavithra Prabhakhar, Marc Herbstritt
2017 Dagstuhl Reports  
This seminar brought together researchers from both academia and industry working in hybrid control systems, mechatronics, formal methods, and real-time embedded systems.  ...  Electronically controlled systems have become pervasive in modern society and are increasingly being used to control safety-critical applications, such as medical devices and transportation systems.  ...  To satisfy these design objectives, we require notions of robustness that go well beyond the classical impurities of embedded systems, like sampling, measurement noise, jitter, and machine tolerances,  ... 
doi:10.4230/dagrep.6.9.29 dblp:journals/dagstuhl-reports/FranzleKP16 fatcat:uiivaekedzdqdpmn2shsecrpve

Fairness Amidst Non-IID Graph Data: A Literature Review [article]

Wenbin Zhang, Jeremy C. Weiss, Shuigeng Zhou, Toby Walsh
2022 arXiv   pre-print
In this survey, we review such recent advance in fairness amidst non-IID graph data and identify datasets and evaluation metrics available for future research.  ...  It is therefore of great importance to bridge the traditional fairness literature designed on IID data and ubiquitous non-IID graph representations to tackle bias in ML systems.  ...  The authors also theoretically prove the proposed framework obtains optimal solutions in comparison to sub-optimal solutions of previous work.  ... 
arXiv:2202.07170v2 fatcat:b4ri7at2b5blncdgbpzbwhe6ea

Generalized Spectral Clustering via Gromov-Wasserstein Learning [article]

Samir Chowdhury, Tom Needham
2021 arXiv   pre-print
We establish a bridge between spectral clustering and Gromov-Wasserstein Learning (GWL), a recent optimal transport-based approach to graph partitioning.  ...  This in turn yields a new insight into the k-cut graph partitioning problem through the lens of optimal transport.  ...  Acknowledgement We would like to thank Facundo Mémoli for introducing us to the Gromov-Wasserstein problem and for many conversations on the topic.  ... 
arXiv:2006.04163v2 fatcat:4nczdfbn7faabjzkaw6o7g3s4u

Adaptive and Momentum Methods on Manifolds Through Trivializations [article]

Mario Lezcano-Casado
2020 arXiv   pre-print
We introduce a framework to generalize adaptive and momentum methods to arbitrary manifolds by noting that for every differentiable manifold, there exists a radially convex open set that covers almost  ...  For its implementation, we bring an approximation to the exponential of matrices that needs just of 5 matrix multiplications, making it particularly efficient on GPUs.  ...  point Convergence guarantees In the case when the optimizer is gradient descent, we can give exact guarantees for the algorithm by using first and second order bounds on the Riemannian exponential.  ... 
arXiv:2010.04617v1 fatcat:vcadnpmrznbtpjk3g7lya3zndq

Maintenance intervention predictions using entity-embedding neural networks

Zaharah Allah Bukhsh, Irina Stipanovic, Aaqib Saeed, Andre G. Doree
2020 Automation in Construction  
bridges.  ...  The analysis of results shows that a unified multi-task learning model performed best for the considered problems followed by task-specific neural networks with entity embedding and class weights.  ...  Acknowledgement This study has been performed under funding from the European Union's Horizon 2020 -Research and Innovation Framework Programme with grant agreement No 636285 DESTination Rail.  ... 
doi:10.1016/j.autcon.2020.103202 fatcat:jhxa5ir2a5dw5ncerjbxio2om4

Stability of Entropic Optimal Transport and Schrödinger Bridges [article]

Promit Ghosal, Marcel Nutz, Espen Bernton
2021 arXiv   pre-print
More generally, our results apply to a class of static Schrödinger bridge problems including entropic optimal transport.  ...  We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function.  ...  Skorokhod embeddings [5, 8] and weak transport [4] .  ... 
arXiv:2106.03670v1 fatcat:kf5zxfiq2zegzca5n2k5tvyukm
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