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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando 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 Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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Analysis of UN Voting Patterns via Diffusion Geometry and Thematic Clustering

Analysis of UN Voting Patterns via Diffusion Geometry and Th...

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IEEE International Conference on Data Mining Workshops (ICDM Workshops)

作者： Minh-Tam Le Mathew Lawlor Bruce M. Russett John Sweeney Steven W. Zucker Dept. of Computer Science Yale University New Haven CT Program in Applied Mathematics Yale University New Haven CT Dept. of Political Science Yale University New Haven CT

We apply a range of data mining techniques to analyze voting patterns in the United Nations. We begin with non-linear dimensionality reduction, showing that diffusion geometry reveals an historically relevant organization of countries based on their UN voting patterns. Key historical events can be ``read out'' from these embeddings, such as de Gaulle's influence on France and the breakup of the Soviet Union. These events are not apparent in other (e.g., PCA) embeddings. We then switch to an organization of resolutions, revealing dominant themes during different political epochs. Formally themes are introduced as summaries (eigenfunctions) within a modified hierarchical clustering algorithm.

关键词： Vectors Organizations Eigenvalues and eigenfunctions Kernel Geometry Educational institutions Assembly

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Instantaneous Radar Polarimetry with Multiple Dually-polarized Antennas

Instantaneous Radar Polarimetry with Multiple Dually-polariz...

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Asilomar Conference on Signals, Systems & computers

作者： A. R. Calderbank S. D. Howard W. Moran A. Pezeshki M. Zoltowski Program Applied and Computational Mathematics Princeton University Princeton NJ USA Defence Science and Technology Organization Edinburgh Australia Electrical Engineering and Computer Science University of Melbourne Melbourne Australia Electrical and Computer Engineering Purdue University West Lafayette IN USA

Fully polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes . In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi- antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.

关键词： Radar polarimetry Radar antennas Polarization Radar detection Radar signal processing Transmitters Receiving antennas Transmitting antennas Computational efficiency Matched filters

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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

arXiv

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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Learning shared neural manifolds from multi-subject FMRI data

arXiv

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arXiv 2021年

作者： Huang, Jessie Busch, Erica L. Wallenstein, Tom Gerasimiuk, Michal Benz, Andrew Lajoie, Guillaume Wolf, Guy Turk-Browne, Nicholas B. Krishnaswamy, Smita Department Of Computer Science Department Of Psychology Department Of Mathematics Department Of Genetics Program In Applied Mathematics Wu Tsai Institute Yale University United States Department Of Mathematics And Statistics Université De Montréal Canada Mila Quebec AI Institute Canada

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal averaging required by the measurement resolution. In addition, the data is extremely high dimensional, with the space of the activity typically having much lower intrinsic dimension. In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure. Specifically, we assume that while noise varies significantly between individuals, true responses to stimuli will share common, low-dimensional features between subjects which are jointly discoverable. Similar approaches have been exploited previously but they have mainly used linear methods such as PCA and shared response modeling (SRM). In contrast, we propose a neural network called MRMD-AE (manifold-regularized multiple decoder, autoencoder), that learns a common embedding from multiple subjects in an experiment while retaining the ability to decode to individual raw fMRI signals. We show that our learned common space represents an extensible manifold (where new points not seen during training can be mapped), improves the classification accuracy of stimulus features of unseen timepoints, as well as improves cross-subject translation of fMRI signals. We believe this framework can be used for many downstream applications such as guided brain-computer interface (BCI) training in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

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Autonomous Electron Tomography Reconstruction Using Bayesian Optimization

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1915-1916页

作者： Millsaps, William Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Hovden, Robert Department of Nuclear Engineering Radiological Sciences University of Michigan Ann Arbor MI United States Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Advanced Photon Source Facility Argonne National Laboratory Lemont IL United States Applied Physics Program University of Michigan Ann Arbor MI United States

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Developing a medical artificial intelligence course for high school students

Developing a medical artificial intelligence course for high...

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International Forum on Medical Imaging in Asia 2021, IFMIA 2021

作者： Huang, Chao-Jung Wu, Tinghui Lu, Jui-Ting Lin, Beatrice Chang, Dawei Wang, Pochuan Wang, Mei-Chi Lee, Peijung Wang, Weichung National Taiwan University-Stanford Joint Program Office of AI in Biotechnology Ministry of Science and Technology Joint Research Center for Artificial Intelligence Technology and All Vista Healthcare Taipei Taiwan Institute of Applied Mathematical Sciences National Taiwan University Taipei Taiwan Department of Mathematics Ecole Normale Supérieure de Lyon Lyon France Department of Computer Science and Information Engineering National Taiwan University Taipei Taiwan Department of Electronic and Computer Engineering National Taiwan University of Science and Technology Taipei Taiwan Department of Mathematics National Taiwan University Taipei Taiwan

ISBN: (数字)9781510644212

ISBN: (纸本)9781510644205

Artificial intelligence (AI) training courses often require prerequisites such as calculus or statistics. It is hence challenging to design and develop an introductory AI course for students of secondary education. This research intends to develop a medical AI course, provide high school students with an overview of deep learning applications in medical image analysis, and inspire them to pursue careers in the field of medical AI. We designed a 20-hour course, including lectures and two hands-on projects based on medical image classification. The proposed courses provided medical AI disciplines and built up their knowledge from basic to advanced levels. During the ten-day online courses, all the students were fully engaged and gave us positive feedback. The students endeavored to complete the experimental study in training, testing, and hypothesis of medical images application in the course. Their performance exceeded all expectations, for they did further analysis by tuning different hyperparameters. We designed a course evaluation form, which suggested that the students found it essential and expected to interact with the instructors. The results indicate that combining lectures with hands-on sessions would lead to evidently better achievement in terms of high school students' medical AI knowledge and positive attitudes while addressing real-world problems in the projects. Through this innovative education model, high school students regained their enthusiasm and were encouraged to cultivate their medical AI skills through self-learning while finishing the project. We conclude that this course could be successfully applied to interdisciplinary education in high school. © 2021 SPIE.

关键词： Students

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Bayesian Spectral Graph Denoising with Smoothness Prior

Bayesian Spectral Graph Denoising with Smoothness Prior

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Annual Conference on Information sciences and Systems (CISS)

作者： Sam Leone Xingzhi Sun Michael Perlmutter Smita Krishnaswamy Program for Applied Mathematics Yale University Department of Computer Science Yale University Department of Mathematics Boise State University Department of Genetics Yale School of Medicine Wu Tsai Institute Yale University FAIR Meta AI Computational Biology and Bioinformatics Program Yale University

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms’ ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data.

关键词：

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The Null Field and the Interior Field Methods For Mixed Types of Boundary Conditions of Laplace's Equations in Elliptic Domains with Elliptic Holes

The Null Field and the Interior Field Methods For Mixed Type...

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Joint International Conference on Trefftz Method Ⅶ and Method of Fundamental Solutions Ⅲ(Trefftz/MFS 2015)

作者： Liping Zhang Ming-Gong Lee Zi-Cai Li College of Science Zhejiang University of Technology Department of Leisure and Recreation Management Ph.D.Program in Engineering ScienceChung Hua University Department of Applied Mathematics Department of Computer Science and EngineeringNational Sun Yat-sen University

The particular solutions(PS) and fundamental solutions(FS) in polar coordinates can be found in many textbooks, but with much less coverage in elliptic coordinates [1]. Since the elliptic domains with elliptic holes may be found in some engineering problems, the PS and the FS expansions in elliptic coordinates are essential for numerical computations. For Dirichlet problems of Laplace's equation in elliptic domains, the null field method(NFM), the interior field method(IFM) and the collocation Trefftz method(CTM) are reported in [2]. There seems to exist very few reports for mixed problems, where the Dirichlet and Neumann conditions are assigned on the exterior and the interior boundaries, simultaneously. This paper is devoted to such mixed problems by the NFM and the IFM, and the explicit algebraic equations are derived for elliptic domains. Besides, other effective particular solutions(PS) are sought, and the collocation Trefftz method(CTM) [3] is employed. The CTM may be used for Robin problems in elliptic domains. The effective algorithms for the mixed problems of Laplace's equation on elliptic domains are the main goal of this paper.

关键词： Null field method Interior field method collocation Trefftz method circular domains elliptic domains Elliptic Holes fundamental solutions Particular Solutions Dirichlet condition Neumann condition Robin Problems

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Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

arXiv

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arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay 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 School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

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