Foundations of data science (Springfield, Mo.)最新文献_第4页

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation 一种基于代理的非线性非高斯联合状态参数数据同化方法

Foundations of data science (Springfield, Mo.) Pub Date : 2020-12-08 DOI: 10.3934/fods.2021019

J. Maclean, E. Spiller

引用次数: 1

Estimating linear response statistics using orthogonal polynomials: An rkhs formulation 估计线性响应统计使用正交多项式:一个rkhs公式

Foundations of data science (Springfield, Mo.) Pub Date : 2020-12-08 DOI: 10.3934/fods.2020021

He Zhang, J. Harlim, Xiantao Li

{"title":"Estimating linear response statistics using orthogonal polynomials: An rkhs formulation","authors":"He Zhang, J. Harlim, Xiantao Li","doi":"10.3934/fods.2020021","DOIUrl":"https://doi.org/10.3934/fods.2020021","url":null,"abstract":"We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task of estimating a density function. We consider a nonparametric density estimator formulated by the kernel embedding of distributions with \"Mercer-type\" kernels, constructed based on the classical orthogonal polynomials defined on non-compact domains. While the resulting representation is analogous to Polynomial Chaos Expansion (PCE), the connection to the reproducing kernel Hilbert space (RKHS) theory allows one to establish the uniform convergence of the estimator and to systematically address a practical question of identifying the PCE basis for a consistent estimation. We also provide practical conditions for the well-posedness of not only the estimator but also of the underlying response statistics. Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and the biases due to a finite basis truncation. This error bound provides a means to understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernels. Numerically, we verify the effectiveness of the estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48255540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

ANAPT: Additive noise analysis for persistence thresholding 持久性阈值的加性噪声分析

Foundations of data science (Springfield, Mo.) Pub Date : 2020-12-07 DOI: 10.3934/fods.2022005

Audun D. Myers, Firas A. Khasawneh, Brittany Terese Fasy

引用次数: 1

Mean field limit of Ensemble Square Root filters - discrete and continuous time 集合平方根滤波器的平均场极限-离散和连续时间

Foundations of data science (Springfield, Mo.) Pub Date : 2020-11-20 DOI: 10.3934/FODS.2021003

Theresa Lange, W. Stannat

引用次数: 15

Feedback particle filter for collective inference 用于集体推理的反馈粒子滤波器

Foundations of data science (Springfield, Mo.) Pub Date : 2020-10-13 DOI: 10.3934/fods.2021018

Jin W. Kim, P. Mehta

{"title":"Feedback particle filter for collective inference","authors":"Jin W. Kim, P. Mehta","doi":"10.3934/fods.2021018","DOIUrl":"https://doi.org/10.3934/fods.2021018","url":null,"abstract":"<p style='text-indent:20px;'>The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number (<inline-formula><tex-math id=\"M1\">begin{document}$ M $end{document}</tex-math></inline-formula>) of non-interacting agents (targets) with a large number (<inline-formula><tex-math id=\"M2\">begin{document}$ M $end{document}</tex-math></inline-formula>) of non-agent specific observations (measurements) that originate from these agents. In its basic form, the problem is characterized by data association uncertainty whereby the association between the observations and agents must be deduced in addition to the agent state. In this paper, the large-<inline-formula><tex-math id=\"M3\">begin{document}$ M $end{document}</tex-math></inline-formula> limit is interpreted as a problem of collective inference. This viewpoint is used to derive the equation for the empirical distribution of the hidden agent states. A feedback particle filter (FPF) algorithm for this problem is presented and illustrated via numerical simulations. Results are presented for the Euclidean and the finite state-space cases, both in continuous-time settings. The classical FPF algorithm is shown to be the special case (with <inline-formula><tex-math id=\"M4\">begin{document}$ M = 1 $end{document}</tex-math></inline-formula>) of these more general results. The simulations help show that the algorithm well approximates the empirical distribution of the hidden states for large <inline-formula><tex-math id=\"M5\">begin{document}$ M $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46470057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Multiple hypothesis testing with persistent homology 具有持久同源性的多重假设检验

Foundations of data science (Springfield, Mo.) Pub Date : 2020-10-10 DOI: 10.3934/fods.2022018

Mikael Vejdemo-Johansson, Sayan Mukherjee

引用次数: 3

Wave-shape oscillatory model for nonstationary periodic time series analysis 非平稳周期时间序列分析的波形振荡模型

Foundations of data science (Springfield, Mo.) Pub Date : 2020-07-13 DOI: 10.3934/FODS.2021009

Yu-Ting Lin, John Malik, Hau‐Tieng Wu

{"title":"Wave-shape oscillatory model for nonstationary periodic time series analysis","authors":"Yu-Ting Lin, John Malik, Hau‐Tieng Wu","doi":"10.3934/FODS.2021009","DOIUrl":"https://doi.org/10.3934/FODS.2021009","url":null,"abstract":"The oscillations observed in many time series, particularly in biomedicine, exhibit morphological variations over time. These morphological variations are caused by intrinsic or extrinsic changes to the state of the generating system, henceforth referred to as dynamics. To model these time series (including and specifically pathophysiological ones) and estimate the underlying dynamics, we provide a novel wave-shape oscillatory model. In this model, time-dependent variations in cycle shape occur along a manifold called the wave-shape manifold. To estimate the wave-shape manifold associated with an oscillatory time series, study the dynamics, and visualize the time-dependent changes along the wave-shape manifold, we apply the well-established diffusion maps (DM) algorithm to the set of all observed oscillations. We provide a theoretical guarantee on the dynamical information recovered by the DM algorithm under the proposed model. Applying the proposed model and algorithm to arterial blood pressure (ABP) signals recorded during general anesthesia leads to the extraction of nociception information. Applying the wave-shape oscillatory model and the DM algorithm to cardiac cycles in the electrocardiogram (ECG) leads to ectopy detection and a new ECG-derived respiratory signal, even when the subject has atrial fibrillation.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45887443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 17

The (homological) persistence of gerrymandering 选区划分不公的（同源）持续性

Foundations of data science (Springfield, Mo.) Pub Date : 2020-07-05 DOI: 10.3934/FODS.2021007

M. Duchin, Tom Needham, Thomas Weighill

引用次数: 9

Posterior contraction rates for non-parametric state and drift estimation 非参数状态和漂移估计的后验收缩率

Foundations of data science (Springfield, Mo.) Pub Date : 2020-03-20 DOI: 10.3934/fods.2020016

S. Reich, P. Rozdeba

引用次数: 4

Probabilistic learning on manifolds 流形上的概率学习

Foundations of data science (Springfield, Mo.) Pub Date : 2020-02-28 DOI: 10.3934/fods.2020013

Christian Soize, R. Ghanem

{"title":"Probabilistic learning on manifolds","authors":"Christian Soize, R. Ghanem","doi":"10.3934/fods.2020013","DOIUrl":"https://doi.org/10.3934/fods.2020013","url":null,"abstract":"This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The PLoM considers a given initial dataset constituted of a small number of points given in an Euclidean space, which are interpreted as independent realizations of a vector-valued random variable for which its non-Gaussian probability measure is unknown but is, textit{a priori}, concentrated in an unknown subset of the Euclidean space. The objective is to construct a learned dataset constituted of additional realizations that allow the evaluation of converged statistics. A transport of the probability measure estimated with the initial dataset is done through a linear transformation constructed using a reduced-order diffusion-maps basis. In this paper, it is proven that this transported measure is a marginal distribution of the invariant measure of a reduced-order Ito stochastic differential equation that corresponds to a dissipative Hamiltonian dynamical system. This construction allows for preserving the concentration of the probability measure. This property is shown by analyzing a distance between the random matrix constructed with the PLoM and the matrix representing the initial dataset, as a function of the dimension of the basis. It is further proven that this distance has a minimum for a dimension of the reduced-order diffusion-maps basis that is strictly smaller than the number of points in the initial dataset. Finally, a brief numerical application illustrates the mathematical results.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44044177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16