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PERMUTATION INVARIANT REPRESENTATIONS with APPLICATIONS to GRAPH DEEP LEARNING

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arXiv 2022年

作者： Balan, Radu Haghani, Naveed Singh, Maneesh Department of Mathematics University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States Verisk Analytics Jersey CityNJ07310 United States

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is invariant to node relabeling. Two embedding schemes are introduced, one based on sorting and the other based on algebras of multivariate polynomials. While both embeddings exhibit a computational complexity exponential in problem size, the sorting based embedding is globally bi-Lipschitz and admits a low dimensional target space. Additionally, an almost everywhere injective scheme can be implemented with minimal redundancy and low computational cost. In turn, this proves that almost any classifier can be implemented with an arbitrary small loss of performance. Numerical experiments are carried out on two data sets, a chemical compound data set (QM9) and a proteins data set (PROTEINS FULL).MSC Codes 05C62, 20C32, 68R12 © 2022, CC BY.

关键词： Embeddings

Fractional Integrable Nonlinear Soliton Equations

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arXiv 2022年

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional nonlinear evolution equations describing dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process utilizing completeness relations, dispersion relations, and inverse scattering transform techniques. As examples, this general method is used to characterize fractional extensions to two physically relevant, pervasive integrable nonlinear equations: the Korteweg–deVries and nonlinear Schrödinger equations. These equations are shown to predict super-dispersive transport of non-dissipative solitons in fractional media. © 2022, CC BY.

关键词： Nonlinear equations

A new method for multiancestry polygenic prediction improves performance across diverse populations

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Nature Genetics 2023年第10期55卷 1757-1768页

作者： Zhang, Haoyu Zhan, Jianan Jin, Jin Zhang, Jingning Lu, Wenxuan Zhao, Ruzhang Ahearn, Thomas U. Yu, Zhi O’Connell, Jared Jiang, Yunxuan Chen, Tony Okuhara, Dayne Aslibekyan, Stella Auton, Adam Babalola, Elizabeth Bell, Robert K. Bielenberg, Jessica Bryc, Katarzyna Bullis, Emily Coker, Daniella Partida, Gabriel Cuellar Dhamija, Devika Das, Sayantan Elson, Sarah L. Eriksson, Nicholas Filshtein, Teresa Fitch, Alison Fletez-Brant, Kipper Fontanillas, Pierre Freyman, Will Granka, Julie M. Heilbron, Karl Hernandez, Alejandro Hicks, Barry Hinds, David A. Jewett, Ethan M. Kukar, Katelyn Kwong, Alan Lin, Keng-Han Llamas, Bianca A. Lowe, Maya McCreight, Jey C. McIntyre, Matthew H. Micheletti, Steven J. Moreno, Meghan E. Nandakumar, Priyanka Nguyen, Dominique T. Noblin, Elizabeth S. Petrakovitz, Aaron A. Poznik, G. David Reynoso, Alexandra Schumacher, Morgan Shastri, Anjali J. Shelton, Janie F. Shi, Jingchunzi Shringarpure, Suyash Su, Qiaojuan Jane Tat, Susana A. Tchakouté, Christophe Toukam Tran, Vinh Tung, Joyce Y. Wang, Xin Wang, Wei Weldon, Catherine H. Wilton, Peter Wong, Corinna D. Garcia-Closas, Montserrat Lin, Xihong Koelsch, Bertram L. Chatterjee, Nilanjan Division of Cancer Epidemiology and Genetics National Cancer Institute Bethesda MD United States Department of Biostatistics Harvard T.H. Chan School of Public Health Boston MA United States 23andMe Inc. Sunnyvale CA United States Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Baltimore MD United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania Philadelphia PA United States Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD United States Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA United States Booz Allen Hamilton Inc. McLean VA United States Division of Genetics and Epidemiology Institute of Cancer Research London United Kingdom Department of Statistics Harvard University Cambridge MA United States Department of Oncology School of Medicine Johns Hopkins University Baltimore MD United States

Polygenic risk scores (PRSs) increasingly predict complex traits;however, suboptimal performance in non-European populations raise concerns about clinical applications and health inequities. We developed CT-SLEB, a powerful and scalable method to calculate PRSs, using ancestry-specific genome-wide association study summary statistics from multiancestry training samples, integrating clumping and thresholding, empirical Bayes and superlearning. We evaluated CT-SLEB and nine alternative methods with large-scale simulated genome-wide association studies (~19 million common variants) and datasets from 23andMe, Inc., the Global Lipids Genetics Consortium, All of Us and UK Biobank, involving 5.1 million individuals of diverse ancestry, with 1.18 million individuals from four non-European populations across 13 complex traits. Results demonstrated that CT-SLEB significantly improves PRS performance in non-European populations compared with simple alternatives, with comparable or superior performance to a recent, computationally intensive method. Moreover, our simulation studies offered insights into sample size requirements and SNP density effects on multiancestry risk prediction. © 2023, The Author(s), under exclusive licence to Springer Nature America, Inc.

关键词： Genome-wide association studies Preventive medicine

Sensitivity Analysis of Wind Energy Resources with Bayesian non-Gaussian and nonstationary Functional ANOVA

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arXiv 2021年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia’s planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade. © 2021, CC BY-NC-ND.

关键词： Sensitivity analysis

Nonstationary spatial modeling of massive global satellite data

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arXiv 2021年

作者： Huang, Huang Blake, Lewis R. Katzfuss, Matthias Hammerling, Dorit M. Statistics Program King Abdullah University of Science and Technology Thuwal 23955-6900 Saudi Arabia Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Department of Statistics Texas A&M University College StationTX77843 United States

Earth-observing satellite instruments obtain a massive number of observations every day. For example, tens of millions of sea surface temperature (SST) observations on a global scale are collected daily by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. Despite their size, such datasets are incomplete and noisy, necessitating spatial statistical inference to obtain complete, high-resolution fields with quantified uncertainties. Such inference is challenging due to the high computational cost, the nonstationary behavior of environmental processes on a global scale, and land barriers affecting the dependence of SST. In this work, we develop a multi-resolution approximation (M-RA) of a Gaussian process (GP) whose nonstationary, global covariance function is obtained using local fits. The M-RA requires domain partitioning, which can be set up application-specifically. In the SST case, we partition the domain purposefully to account for and weaken dependence across land barriers. Our M-RA implementation is tailored to distributed-memory computation in high-performance-computing environments. We analyze a MODIS SST dataset consisting of more than 43 million observations, to our knowledge the largest dataset ever analyzed using a probabilistic GP model. We show that our nonstationary model based on local fits provides substantially improved predictive performance relative to a stationary approach. © 2021, CC BY.

关键词： Atmospheric temperature

Feature selection using stochastic gates 37

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Feature selection using stochastic gates

37th International Conference on Machine Learning, ICML 2020

作者： Yamada, Yutaro Lindenbaum, Ofir Negahban, Sahand Kluger, Yuval Department of Statistics and Data Science Yale University CT United States Program in Applied Mathematics Yale University CT United States School of Medicine Yale University CT United States

ISBN: (纸本)9781713821120

Feature selection problems have been extensively studied in the setting of linear estimation (e.g. LASSO), but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in neural network estimation problems. The new procedure is based on probabilistic relaxation of the `0 norm of features, or the count of the number of selected features. Our `0-based regularization relies on a continuous relaxation of the Bernoulli distribution;such relaxation allows our model to learn the parameters of the approximate Bernoulli distributions via gradient descent. The proposed framework simultaneously learns either a nonlinear regression or classification function while selecting a small subset of features. We provide an information-theoretic justification for incorporating Bernoulli distribution into feature selection. Furthermore, we evaluate our method using synthetic and real-life data to demonstrate that our approach outperforms other commonly used methods in both predictive performance and feature selection. Copyright 2020 by the author(s).

关键词： Feature Selection

Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

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arXiv 2025年

作者： Wei, Lu Jia, Zhian Wang, Yufeng Kaszlikowski, Dagomir Ling, Haibin Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY11794 United States Program of Data Science Stony Brook University Stony BrookNY11794 United States Centre for Quantum Technologies National University of Singapore SG 117543 Singapore Department of Physics National University of Singapore SG 117543 Singapore Department of Computer Science Stony Brook University Stony BrookNY11794 United States

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the transformer density operator ansatz for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state’s coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting steady states. © 2025, CC BY.

关键词： Hilbert spaces

On Time Uniform Wong-Zakai Approximation Theorems

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arXiv 2023年

作者： Del Moral, Pierre Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux Bordeaux33405 France School of Statistics and Mathematics Zhongnan University of Economics and Law China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Wenlan School of Business Zhongnan University of Economics and Law China

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations;e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion *** Codes 60H35(Primary), 65C30(Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Brownian movement

An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

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Computers, Materials & Continua 2022年第7期72卷 1373-1389页

作者： Chandrashekhar Meshram Agbotiname Lucky Imoize Sajjad Shaukat Jamal Parkash Tambare Adel R.Alharbi Iqtadar Hussain Department of Post Graduate Studies and Research in Mathematics Jayawanti Haksar Government Post-Graduation CollegeCollege of Chhindwara UniversityBetul460001M.P.India Department of Electrical and Electronics Engineering Faculty of EngineeringUniversity of LagosAkokaLagos100213Nigeria Department of Electrical Engineering and Information Technology Institute of Digital CommunicationRuhr University44801BochumGermany Department of Mathematics College of ScienceKing Khalid UniversityAbhaSaudi Arabia Water Resources&Applied Mathematics Research Lab Nagpur440027India College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy *** users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key *** of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and *** order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic *** new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password *** projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT *** results show that our new technique is resistant to password guessing attacks since it does not use a ***,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no ***,our new technique offers better security features than the techniques currently available in the literature.

关键词： Three-party authenticated key agreement anonymity fractional chaotic maps Chebyshev polynomial password table human-centered internet of things(HC-IoT)