检索结果-内蒙古大学图书馆

Guaranteed bounds for optimal stopping problems using kernel-based non-asymptotic uniform confidence bands

European Journal of Operational Research 2025年

作者： Martin Glanzer Sebastian Maier Georg Ch. Pflug University of Mannheim Business School Schloss 68131 Mannheim Germany Department of Statistical Science University College London Gower Street London WC1E 6BT United Kingdom Faculty of Economics and Statistics University of Vienna Oskar-Morgenstern Platz 1 1090 Vienna Austria Advancing Systems Analysis Program International Institute for Applied Systems Analysis Schlossplatz 1 2361 Laxenburg Austria

In this paper, we introduce an approach for obtaining probabilistically guaranteed upper and lower bounds on the true optimal value of stopping problems. Bounds of existing simulation-and-regression approaches, such as those based on least squares Monte Carlo and information relaxation, are stochastic in nature and therefore do not come with a finite sample guarantee. Our data-driven approach is fundamentally different as it allows replacing the sampling error with a pre-specified confidence level. The key to this approach is to use high- and low-biased estimates that are guaranteed to over- and underestimate, respectively, the conditional expected continuation value that appears in the stopping problem’s dynamic programming formulation with a pre-specified confidence level. By incorporating these guaranteed over- and underestimates into a backward recursive procedure, we obtain probabilistically guaranteed bounds on the problem’s true optimal value. As a byproduct we present novel kernel-based non-asymptotic uniform confidence bands for regression functions from a reproducing kernel Hilbert space. We derive closed-form formulas for the cases where the data-generating distribution is either known or unknown, which makes our data-driven approach readily applicable in a range of practical situations including simulation. We illustrate the applicability of the proposed bounding procedure by valuing a Bermudan put option.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Manifold learning with arbitrary norms

arXiv

引用

arXiv 2020年

作者： Kileel, Joe Moscovich, Amit Zelesko, Nathan Singer, Amit Department of Mathematics Oden Institute University of Texas at Austin United States Department of Statistics and Operations Research Tel-Aviv University Israel Department of Mathematics Brown University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex with each data point and a weighted edge with each pair. Existing theory shows that the Laplacian matrix of the graph converges to the Laplace-Beltrami operator of the data manifold, under the assumption that the pairwise affinities are based on the Euclidean norm. In this paper, we determine the limiting differential operator for graph Laplacians constructed using any norm. Our proof involves an interplay between the second fundamental form of the manifold and the convex geometry of the given norm's unit ball. To demonstrate the potential benefits of non-Euclidean norms in manifold learning, we consider the task of mapping the motion of large molecules with continuous variability. In a numerical simulation we show that a modified Laplacian eigenmaps algorithm, based on the Earthmover's distance, outperforms the classic Euclidean Laplacian eigenmaps, both in terms of computational cost and the sample size needed to recover the intrinsic geometry. Copyright © 2020, The Authors. All rights reserved.

关键词： Mathematical operators

来源：评论

学校读者我要写书评

暂无评论

Explaining heterogeneity in medial entorhinal cortex with task-driven neural networks 21

Explaining heterogeneity in medial entorhinal cortex with ta...

引用

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Aran Nayebi Alexander Attinger Malcolm G. Campbell Kiah Hardcastle Isabel I.C. Low Caitlin S. Mallory Gabriel C. Mel Ben Sorscher Alex H. Williams Surya Ganguli Lisa M. Giocomo Daniel L.K. Yamins Neurosciences Ph.D. Program Stanford University Department of Neurobiology Stanford University Neurosciences Ph.D. Program Stanford University and Department of Neurobiology Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Applied Physics Stanford University Department of Statistics Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Applied Physics Stanford University and Wu Tsai Neurosciences Institute Stanford University and Facebook AI Research Facebook Inc. Department of Neurobiology Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Computer Science Stanford University and Department of Psychology Stanford University and Wu Tsai Neurosciences Institute Stanford University

ISBN: (纸本)9781713845393

Medial entorhinal cortex (MEC) supports a wide range of navigational and memory related behaviors. Well-known experimental results have revealed specialized cell types in MEC — e.g. grid, border, and head-direction cells — whose highly stereotypical response profiles are suggestive of the role they might play in supporting MEC functionality. However, the majority of MEC neurons do not exhibit stereotypical firing patterns. How should the response profiles of these more "heterogeneous" cells be described, and how do they contribute to behavior? In this work, we took a computational approach to addressing these questions. We first performed a statistical analysis that shows that heterogeneous MEC cells are just as reliable in their response patterns as the more stereotypical cell types, suggesting that they have a coherent functional role. Next, we evaluated a spectrum of candidate models in terms of their ability to describe the response profiles of both stereotypical and heterogeneous MEC cells. We found that recently developed task-optimized neural network models are substantially better than traditional grid cell-centric models at matching most MEC neuronal response profiles — including those of grid cells themselves — despite not being explicitly trained for this purpose. Specific choices of network architecture (such as gated nonlinearities and an explicit intermediate place cell representation) have an important effect on the ability of the model to generalize to novel scenarios, with the best of these models closely approaching the noise ceiling of the data itself. We then performed in silico experiments on this model to address questions involving the relative functional relevance of various cell types, finding that heterogeneous cells are likely to be just as involved in downstream functional outcomes (such as path integration) as grid and border cells. Finally, inspired by recent data showing that, going beyond their spatial response selectivity, MEC cells

关键词：

来源：评论

学校读者我要写书评

暂无评论

CellBiAge: Improved single-cell age classification using data binarization

引用

Cell Reports 2023年第12期42卷 113500页

作者： Yu, Doudou Li, Manlin Linghu, Guanjie Hu, Yihuan Hajdarovic, Kaitlyn H. Wang, An Singh, Ritambhara Webb, Ashley E. Molecular Biology Cell Biology and Biochemistry Graduate Program Brown University Providence 02912 RI United States Data Science Institute Brown University Providence 02912 RI United States Neuroscience Graduate Program Brown University Providence 02912 RI United States Department of Applied Mathematics & Statistics Johns Hopkins University Baltimore 21218 MD United States Department of Computer Science Brown University Providence 02912 RI United States Center for Computational Molecular Biology Brown University Providence 02912 RI United States Department of Molecular Biology Cell Biology and Biochemistry Brown University Providence 02912 RI United States Center on the Biology of Aging Brown University Providence 02912 RI United States Carney Institute for Brain Science Brown University Providence 02912 RI United States Center for Translational Neuroscience Brown University Providence 02912 RI United States

Aging is a major risk factor for many diseases. Accurate methods for predicting age in specific cell types are essential to understand the heterogeneity of aging and to assess rejuvenation strategies. However, classifying organismal age at single-cell resolution using transcriptomics is challenging due to sparsity and noise. Here, we developed CellBiAge, a robust and easy-to-implement machine learning pipeline, to classify the age of single cells in the mouse brain using single-cell transcriptomics. We show that binarization of gene expression values for the top highly variable genes significantly improved test performance across different models, techniques, sexes, and brain regions, with potential age-related genes identified for model prediction. Additionally, we demonstrate CellBiAge's ability to capture exercise-induced rejuvenation in neural stem cells. This study provides a broadly applicable approach for robust classification of organismal age of single cells in the mouse brain, which may aid in understanding the aging process and evaluating rejuvenation methods. © 2023 The Authors

关键词： aging brain CP: Cell biology hypothalamus machine learning single-cell RNA-seq

来源：评论

学校读者我要写书评

暂无评论

Prediction of carbon nanostructure mechanical properties and role of defects using machine learning

arXiv

引用

arXiv 2021年

作者： Zhao, Qi Winetrout, Jordan J. Xu, Yanxun Wang, Yusu Heinz, Hendrik Halıcıoglu Data Science Institute University of California San Diego San diegoCA92093 United States Department of Chemical and Biological Engineering University of Colorado Boulder BoulderCO80309 United States Materials Science and Engineering Program University of Colorado Boulder BoulderCO80309 United States Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States

Carbon fiber and graphene-based nanostructures such as carbon nanotubes (CNTs) and defective structures have extraordinary potential as strong and lightweight materials. A longstanding bottleneck has been lack of understanding and implementation of atomic-scale engineering to harness the theoretical limits of modulus and tensile strength, of which only a fraction is routinely reached today. Here we demonstrate accurate and fast predictions of mechanical properties for CNTs and arbitrary 3D graphitic assemblies based on a training set of over 1000 stress-strain curves from cutting-edge reactive MD simulation and machine learning (ML). Several ML methods are compared and show that our newly proposed hierarchically structured graph neural networks with spatial information (HS-GNNs) achieve predictions in modulus and strength for any 3D nanostructure with only 5-10% error across a wide range of possible values. The reliability is sufficient for practical applications and a great improvement over off-the shelf ML methods with up to 50% deviation, as well as over earlier models for specific chemistry with 20% deviation. The algorithms allow more than 100 times faster mechanical property predictions than traditional molecular dynamics simulations, the identification of the role of defects and random 3D morphology, and high-throughput screening of 3D structures for enhanced mechanical properties. The algorithms can be scaled to morphologies up to 100 nm in size, expanded for chemically similar compounds, and trained to predict a broader range of properties. © 2021, CC BY.

关键词： Defects

来源：评论

学校读者我要写书评

暂无评论

Exponential acceleration of macroscopic quantum tunneling in a Floquet Ising model

arXiv

引用

arXiv 2023年

作者： Grattan, George Barton, Brandon A. Feeney, Sean Mossi, Gianni Patnaik, Pratik Sagal, Jacob C. Carr, Lincoln D. Oganesyan, Vadim Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St CO Golden80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Physics Colorado School of Mines 1523 Illinois St CO Golden80401 United States KBR Inc. 601 Jefferson St. HoustonTX77002 United States NASA Ames Research Center Moffett FieldCA94035 United States Department of Physics and Astronomy College of Staten Island CUNY Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center CUNY New YorkNY10016 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States

The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. Slow MQT is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate the possibility to accelerate MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three qualitatively distinct regimes as a function of drive strength: (i) for weak drive, the system exhibits exponentially slow MQT alongside robust magnetic order, as expected;(ii) at intermediate drive strength, we find polynomial decay of rates alongside vanishing magnetic order consistent with critical or paramagnetic state;(iii) at very strong drive strengths both the tunnelling rate and time-averaged magnetic order remain finite with increasing system size. We support these claims with extensive full wavefunction and matrix-product state numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers. © 2023, CC BY.

关键词： Ising model

来源：评论

学校读者我要写书评

暂无评论

Exploring the business aspects of digital pathology, deep learning in cancers

引用

Intelligence-Based Medicine 2024年 10卷 100172-100172页

作者： Reddy, Arjun Adrian Williams, Darnell K. Graifman, Gillian Hussain, Nowair Amiel, Maytal Priscilla, Tran Haider, Ali Kavitesh, Bali Kumar Li, Austin Alishahian, Leael Perera, Nichelle Efros, Corey Babu, Myoungmee Tharakan, Mathew Etienne, Mill Babu, Benson A. Applied Mathematics & Statistics Stony Brook University LabelMD New York United States Medical Scientist Training Program Albert Einstein College of Medicine Bronx New York United States New York Medical College Valhalla New York United States Department of Internal Medicine Overlook Medical Center NJ United States Artificial Intelligence Yeshiva University New York United States Centre for Frontier AI Research (CFAR) Agency for Science Technology and Research (A∗STAR) Singapore Artificial Intelligence and Mathematics New York City Department of Education New York United States Stonybrook Medical Center New York United States Department of Neurology New York Medical College Valhalla NY United States Department of Hospital Medicine Wyckoff Medical Center Brooklyn NY United States

Introduction: Cancer remains one of the leading causes of morbidity and mortality worldwide. Deep learning in digital pathology has the potential to improve operational efficiency, costs, and care. Methods: We searched Web of Science, Arxiv, MedRxiv, Embase, PubMed, DBLP, Google Scholar, IEEE Xplore, and Cochrane databases for whole slide imaging and deep learning articles published between 2019 and 2023. The final six articles were selected from 776 articles identified through an inclusion criterion. Conclusion: Digital pathology services that utilize deep learning have the potential to enhance clinical workflow efficiencies and can have a positive impact on business activities. We anticipate cost reductions as deep learning technology advances and more companies enter the digital pathology ecosystem. However, the limited availability of business use cases, primarily due to publication bias, poses a challenge in medicine without clear examples to learn from. © 2024

关键词： Artificial intelligence Business development Cancer Computational pathology Deep learning Digital pathology Whole slide image

来源：评论

学校读者我要写书评

暂无评论

Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles

arXiv

引用

arXiv 2019年

作者： Sharon, Nir Kileel, Joe Khoo, Yuehaw Landa, Boris Singer, Amit School of Mathematical Sciences Tel Aviv University Israel Program in Applied and Computational Mathematics Princeton University United States Department of Statistics and the College University of Chicago United States Applied Mathematics Program Yale University United States Program in Applied and Computational Mathematics Department of Mathematics Princeton University United States

Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3-D structure of a molecule from several noisy 2-D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3-D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2-D images are computed and a 3-D structure is estimated by solving a system of polynomial equations. Unfortunately, Kam’s method suffers from restrictive assumptions, most notably that viewing angles should be distributed uniformly. Often unrealistic, uniformity entails the computation of higher-order correlations, as in this case first and second moments fail to determine the 3-D structure. In the present paper, we remove this hypothesis, by permitting an unknown, non-uniform distribution of viewing angles in MoM. Perhaps surprisingly, we show that this case is statistically easier than the uniform case, as now first and second moments generically suffice to determine low-resolution expansions of the molecule. In the idealized setting of a known, non-uniform distribution, we find an efficient provable algorithm inverting first and second moments. For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution. Copyright © 2019, The Authors. All rights reserved.

关键词： Method of moments

来源：评论

学校读者我要写书评

暂无评论

Improving Bayesian local spatial models in large data sets

arXiv

引用

arXiv 2019年

作者： Lenzi, Amanda Castruccio, Stefano Rue, Håvard Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

Environmental processes resolved at a sufficiently small scale in space and time will inevitably display non-stationary behavior. Such processes are both challenging to model and computationally expensive when the data size is large. Instead of modeling the global non-stationarity explicitly, local models can be applied to disjoint regions of the domain. The choice of the size of these regions is dictated by a bias-variance trade-off;large regions will have smaller variance and larger bias, whereas small regions will have higher variance and smaller bias. From both the modeling and computational point of view, small regions are preferable to better accommodate the non-stationarity. However, in practice, large regions are necessary to control the variance. We propose a novel Bayesian three-step approach that allows for smaller regions without compromising the increase of the variance that would follow. We are able to propagate the uncertainty from one step to the next without issues caused by reusing the data. The improvement in inference also results in improved prediction, as our simulated example shows. We illustrate this new approach on a data set of simulated high-resolution wind speed data over Saudi Arabia. Copyright © 2019, The Authors. All rights reserved.

关键词： Wind

来源：评论

学校读者我要写书评

暂无评论

Correction to: A dual layer security scheme for medical images using Hessenberg and singular value decompositions

引用

Multimedia Tools and Applications 2022年第10期81卷 14023-14023页

作者： Elmoasry, Ahmed Khan, Lal Said Khan, Majid Hussain, Iqtadar Department of Mathematics College of Science Al-Zulfi Majmaah University Al-Zulfi Saudi Arabia Department of Avionics Engineering Institute of Space Technology Islamabad Pakistan Department of Applied Mathematics and Statistics Institute of Space Technology Islamabad Pakistan Mathematics Program Department of Mathematics Statistics and Physics College of Arts and Sciences Qatar University Doha Qatar Statistical Consulting Unit College of Arts and Science Qatar University Doha Qatar

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：