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Bounding the sum of the largest signless Laplacian eigenvalues of a graph

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arXiv 2022年

作者： Abiad, Aida de Lima, Leonardo Kalantarzadeh, Sina Mohammadi, Mona Oliveira, Carla Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Belgium Department of Mathematics and Data Science Vrije Universiteit Brussel Belgium Graduate Program in Mathematics Federal University of Parana Curitiba Brazil Sharif University of Technology Iran Department of Mathematical National School of Statistical Sciences Rio de Janeiro Brazil

关键词： Eigenvalues and eigenfunctions

Robust PCA for anomaly detection in cyber networks

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arXiv 2018年

作者： Paffenroth, Randy Kay, Kathleen Servi, Les Department of Mathematical Sciences Department of Computer Science Data Science Program Worcester Polytechnic Institute WorcesterMA01609 United States Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Mitre Corporation BedfordMA01730 United States

This paper uses network packet capture data to demonstrate how Robust Principal Component Analysis (RPCA) can be used in a new way to detect anomalies which serve as cyber-network attack indicators. The approach requires only a few parameters to be learned using partitioned training data and shows promise of ameliorating the need for an exhaustive set of examples of different types of network attacks. For Lincoln Labs DARPA intrusion detection data set, the method achieves low false-positive rates while maintaining reasonable truepositive rates on individual packets. In addition, the method correctly detected packet streams in which an attack which was not previously encountered, or trained on, *** Codes 68M10 Copyright © 2018, The Authors. All rights reserved.

关键词： Network security

Facilitating team-based data science: Lessons learned from the DSC-WAV project

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arXiv 2021年

作者： Legacy, Chelsey Zieffler, Andrew Baumer, Benjamin S. Barr, Valerie Horton, Nicholas J. Department of Educational Psychology University of Minnesota MinneapolisMN55455 United States Program in Statistical & Data Sciences Smith College NorthamptonMA01063 United States Department of Computer Science Mount Holyoke College South HadleyMA01075 United States Department of Mathematics and Statistics Amherst College Amherst MA01002 United States

While coursework provides undergraduate data science students with some relevant analytic skills, many are not given the rich experiences with data and computing they need to be successful in the workplace. Additionally, students often have limited exposure to team-based data science and the principles and tools of collaboration that are encountered outside of school. In this paper, we describe the DSC-WAV program, an NSF-funded data science workforce development project in which teams of undergraduate sophomores and juniors work with a local non-profit organization on a data-focused problem. To help students develop a sense of agency and improve confidence in their technical and non-technical data science skills, the project promoted a team-based approach to data science, adopting several processes and tools intended to facilitate this collaboration. Evidence from the project evaluation, including participant survey and interview data, is presented to document the degree to which the project was successful in engaging students in team-based data science, and how the project changed the students’ perceptions of their technical and non-technical skills. We also examine opportunities for improvement and offer insight to other data science educators who may want to implement a similar team-based approach to data science projects at their own *** Codes 97K80, 97P99 Copyright © 2021, The Authors. All rights reserved.

关键词： Students

Antithetic Multilevel Methods for Elliptic and Hypo-Elliptic Diffusions with Applications

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arXiv 2024年

作者： Iguchi, Yuga Jasra, Ajay Maama, Mohamed Beskos, Alexandros Department of Statistical Science University College London LondonWC1E 6BT United Kingdom School of Data Science The Chinese University of Hong Kong Shenzhen 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

In this paper we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable Lévy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods. © 2024, CC BY.

关键词： Diffusion

Bayesian multinomial logistic normal models through marginally latent matrix-T processes

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2022年第1期23卷 255-296页

作者： Justin D. Silverman Kimberly Roche Zachary C. Holmes Lawrence A. David Sayan Mukherjee College of Information Science and Technology Department of Statistics and Institute for Computational and Data Science Penn State University University Park PA Program in Computational Biology and Bioinformatics Duke University Durham NC Department of Molecular Genetics and Microbiology Duke University Durham NC Department of Molecular Genetics and Microbiology and Center for Genomic and Computational Biology Duke University Durham NC Departments of Statistical Science Mathematics Computer Science Biostatistics & Bioinformatics Duke University Durham NC

Bayesian multinomial logistic-normal (MLN) models are popular for the analysis of sequence count data (e.g., microbiome or gene expression data) due to their ability to model multivariate count data with complex covariance structure. However, existing implementations of MLN models are limited to small datasets due to the non-conjugacy of the multinomial and logistic-normal distributions. Motivated by the need to develop efficient inference for Bayesian MLN models, we develop two key ideas. First, we develop the class of Marginally Latent Matrix-T Process (Marginally LTP) models. We demonstrate that many popular MLN models, including those with latent linear, non-linear, and dynamic linear structure are special cases of this class. Second, we develop an efficient inference scheme for Marginally LTP models with specific accelerations for the MLN subclass. Through application to MLN models, we demonstrate that our inference scheme are both highly accurate and often 4-5 orders of magnitude faster than MCMC.

关键词： Bayesian statistics multivariate analysis count data microbiome gene expression

Re-evaluation of the comparative effectiveness of bootstrapbased optimism correction methods in the development of multivariable clinical prediction models

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arXiv 2020年

作者： Iba, Katsuhiro Shinozaki, Tomohiro Maruo, Kazushi Noma, Hisashi Department of Statistical Science School of Multidisciplinary Sciences Graduate University for Advanced Studies Tokyo Japan Office of Biostatistics Department of Biometrics Headquarters of Clinical Development Otsuka Pharmaceutical Co. Ltd. Tokyo Japan Department of Information and Computer Technology Faculty of Engineering Tokyo Singapore University of Science Tokyo Japan Department of Biostatistics Faculty of Medicine University of Tsukuba Ibaraki Japan Department of Data Science Institute of Statistical Mathematics Tokyo Japan

Background: Multivariable prediction models are important statistical tools for providing synthetic diagnosis and prognostic algorithms based on patients' multiple characteristics. Their apparent measures for predictive accuracy usually have overestimation biases (known as 'optimism') relative to the actual performances for external populations. Existing statistical evidence and guidelines suggest that three bootstrap-based bias correction methods are preferable in practice, namely Harrell's bias correction and the .632 and .632+ estimators. Although Harrell's method has been widely adopted in clinical studies, simulation-based evidence indicates that the .632+ estimator may perform better than the other two methods. However, these methods' actual comparative effectiveness is still unclear due to limited numerical evidence. Methods: We conducted extensive simulation studies to compare the effectiveness of these three bootstrapping methods, particularly using various model building strategies: Conventional logistic regression, stepwise variable selections, Firth's penalized likelihood method, ridge, lasso, and elastic-net regression. We generated the simulation data based on the GUSTO-I trial dataset and considered how event per variable, event fraction, number of candidate predictors, and the regression coefficients of the predictors impacted the performances. The internal validity of C-statistics was evaluated. Results: Under relatively large sample settings (roughly, events per variable ≥ 10), the three bootstrap-based methods were comparable and performed well. However, all three methods had biases under small sample settings, and the directions and sizes of biases were inconsistent. In general, Harrell's and .632 methods had overestimation biases when event fraction become lager. Besides, .632+ method had a slight underestimation bias when event fraction was very small. Although the bias of the .632+ estimator was relatively small, its RMSE was comparable or som

关键词： statistical mechanics

Bounded Manifold Completion

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arXiv 2019年

作者： Gajamannage, Kelum Paffenroth, Randy Department of Mathematics and Statistics Texas A&M University–Corpus Christi Corpus ChristiTX78412 United States Department of Mathematical Sciences Department of Computer Science and Data Science Program Worcester Polytechnic Institute WorcesterMA01609 United States

Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to detect the existence of a low-dimensional manifold of a given dimension that lies within a set of bounds derived from a given point cloud. A matrix representing the appropriately defined distances on a low-dimensional manifold is low-rank, and our method is based on current techniques for recovering a partially observed matrix from a small set of fully observed entries that can be implemented as a low-rank Matrix Completion (MC) problem. MC methods are currently used to solve challenging real-world problems, such as image inpainting and recommender systems, and we leverage extent efficient optimization techniques that use a nuclear norm convex relaxation as a surrogate for non-convex and discontinuous rank minimization. Our proposed method provides several advantages over current nonlinear dimensionality reduction techniques, with the two most important being theoretical guarantees on the detection of low-dimensional embeddings and robustness to non-uniformity in the sampling of the manifold. We validate the performance of this approach using both a theoretical analysis as well as synthetic and real-world benchmark *** Codes 68T05 Copyright © 2019, The Authors. All rights reserved.

关键词： Relaxation processes

A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics

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arXiv 2017年

作者： Gajamannage, Kelum Paffenroth, Randy Bollt, Erik M. Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Department of Mathematical Sciences Department of Computer Science and Data Science Program Worcester Polytechnic Institute WorcesterMA01609 United States Clarkson Center for Complex Systems Science Clarkson University PotsdamNY13676 United States

Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by classic techniques over sparse and noisy data is not guaranteed. In fact, the embedding generated using such data may distort the geometry of the manifold and thereby produce an unfaithful embedding. Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise. Our method generates a network structure for given high-dimensional data using a nearest neighbors search and then produces piecewise linear shortest paths that are defined as geodesics. Then, we fit points in each geodesic by a smoothing spline to emphasize the smoothness. The robustness of this approach for sparse and noisy datasets is demonstrated by the implementation of the method on synthetic and real-world *** Codes 68T05 Copyright © 2017, The Authors. All rights reserved.

关键词： Nonlinear analysis

CellLENS enables cross-domain information fusion for enhanced cell population delineation in single-cell spatial omics data

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Nature Immunology 2025年 1-12页

作者： Bokai Zhu Alex K. Shalek Yunhao Bai Amy Y. Huang Sizun Jiang Sheng Gao Shuxiao Chen Yuchen Wang Jason Yeung Yao Yu Yeo Guanrui Liao Shulin Mao Ka-Chun Wong Zhenghui G. Jiang Scott J. Rodig Garry P. Nolan Zongming Ma Ragon Institute of MGH MIT and Harvard Cambridge MA USA Broad Institute of MIT and Harvard Cambridge MA USA Massachusetts Institute of Technology Cambridge MA USA Institute for Medical Engineering and Science Massachusetts Institute of Technology Cambridge MA USA Department of Chemistry Massachusetts Institute of Technology Cambridge MA USA Koch Institute for Integrative Cancer Research Massachusetts Institute of Technology Cambridge MA USA Dana-Farber Cancer Institute Boston MA USA Center for Virology and Vaccine Research Beth Israel Deaconess Medical Center Harvard Medical School Boston MA USA Department of Pathology Brigham and Women’s Hospital Harvard Medical School Boston MA USA Department of Statistics and Data Science The Wharton School University of Pennsylvania Philadelphia PA USA Department of Computer Science City University of Hong Kong Hong Kong People’s Republic of China Center of Hepato-Pancreato-Biliary Surgery The First Affiliated Hospital of Sun Yat-sen University Guangzhou People’s Republic of China Division of Genetics and Genomics Boston Children’s Hospital Harvard Medical School Boston MA USA Program in Biological and Biomedical Sciences Harvard Medical School Boston MA USA Division of Gastroenterology/Liver Center Beth Israel Deaconess Medical Center Harvard Medical School Boston MA USA Department of Pathology Stanford University Stanford CA USA Department of Statistics and Data Science Yale University New Haven CT USA

Delineating cell populations is crucial for understanding immune function in health and disease. Spatial omics technologies offer insights by capturing three complementary domains: single-cell molecular biomarker expression, cellular spatial relationships and tissue architecture. However, current computational methods often fail to fully integrate these multidimensional data, particularly for immune cell populations and intrinsic functional states. We introduce Cell Local Environment and Neighborhood Scan (CellLENS), a self-supervised computational method that learns cellular representations by fusing information across three spatial omics domains (expression, neighborhood and image). CellLENS markedly enhances de novo discovery of biologically relevant immune cell populations at fine granularity by integrating individual cells’ molecular profiles with their neighborhood context and tissue localization. By applying CellLENS to diverse spatial proteomic and transcriptomic datasets across multiple tissue types and disease settings, we uncover unique immune cell populations functionally stratified according to their spatial contexts. Our work demonstrates the power of multi-domain data integration in spatial omics to reveal insights into immune cell heterogeneity and tissue-specific functions.

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