This article introduces `cpp11eigen`, a new R package that integrates the powerful Eigen C++ library for linear algebra into the R programming environment. This article provides a detailed comparison between Armadillo and Eigen speed and syntax. The `cpp11eigen` package simplifies a part of the process of using C++ within R by offering additional ease of integration for those who require high-performance linear algebra operations in their R workflows. This work aims to discuss the tradeoff between computational efficiency and accessibility.
本文介绍了 "cpp11eigen"，这是一个新的 R 软件包，它将强大的线性代数 Eigen C++ 库集成到了 R 编程环境中。本文详细比较了 Armadillo 和 Eigen 的速度和语法。cpp11eigen "软件包简化了在 R 中使用 C++ 的部分过程，为那些在 R 工作流程中需要高性能线性代数运算的人提供了额外的集成便利。这项工作旨在讨论计算效率和易用性之间的权衡。
{"title":"Armadillo and Eigen: A Tale of Two Linear Algebra Libraries","authors":"Mauricio Vargas Sepulveda","doi":"arxiv-2409.00568","DOIUrl":"https://doi.org/arxiv-2409.00568","url":null,"abstract":"This article introduces `cpp11eigen`, a new R package that integrates the\u0000powerful Eigen C++ library for linear algebra into the R programming\u0000environment. This article provides a detailed comparison between Armadillo and\u0000Eigen speed and syntax. The `cpp11eigen` package simplifies a part of the\u0000process of using C++ within R by offering additional ease of integration for\u0000those who require high-performance linear algebra operations in their R\u0000workflows. This work aims to discuss the tradeoff between computational\u0000efficiency and accessibility.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224592","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}
Chao Dang, Marcos A. Valdebenito, Nataly A. Manque, Jun Xu, Matthias G. R. Faes
Estimation of the response probability distributions of computer simulators in the presence of randomness is a crucial task in many fields. However, achieving this task with guaranteed accuracy remains an open computational challenge, especially for expensive-to-evaluate computer simulators. In this work, a Bayesian active learning perspective is presented to address the challenge, which is based on the use of the Gaussian process (GP) regression. First, estimation of the response probability distributions is conceptually interpreted as a Bayesian inference problem, as opposed to frequentist inference. This interpretation provides several important benefits: (1) it quantifies and propagates discretization error probabilistically; (2) it incorporates prior knowledge of the computer simulator, and (3) it enables the effective reduction of numerical uncertainty in the solution to a prescribed level. The conceptual Bayesian idea is then realized by using the GP regression, where we derive the posterior statistics of the response probability distributions in semi-analytical form and also provide a numerical solution scheme. Based on the practical Bayesian approach, a Bayesian active learning (BAL) method is further proposed for estimating the response probability distributions. In this context, the key contribution lies in the development of two crucial components for active learning, i.e., stopping criterion and learning function, by taking advantage of posterior statistics. It is empirically demonstrated by five numerical examples that the proposed BAL method can efficiently estimate the response probability distributions with desired accuracy.
在存在随机性的情况下，估计计算机模拟器的响应概率分布是许多领域的一项重要任务。然而，如何在保证准确性的前提下完成这项任务仍然是一个有待解决的计算难题，尤其是对于评估成本高昂的计算机模拟器而言。首先，响应概率分布的估计在概念上被解释为贝叶斯推理问题，而不是频数推理问题。这种解释有几个重要的好处：(1)以概率方式量化和传播离散化误差；(2)纳入计算机模拟器的先验知识；(3)能够有效地将求解中的数值不确定性降低到规定水平。通过使用 GP 回归，我们以半分析的形式推导出了响应概率分布的后验统计量，并提供了数值求解方案，从而实现了概念性的贝叶斯思想。在实用贝叶斯方法的基础上，我们进一步提出了贝叶斯主动学习（BAL）方法，用于估计响应概率分布。在此背景下，贝叶斯主动学习方法的主要贡献在于利用后验统计量的优势，开发了主动学习的两个关键组件，即停止准则和学习函数，并通过五个数值示例实证证明了所提出的贝叶斯主动学习方法能够以期望的精度有效地估计响应概率分布。
{"title":"Response probability distribution estimation of expensive computer simulators: A Bayesian active learning perspective using Gaussian process regression","authors":"Chao Dang, Marcos A. Valdebenito, Nataly A. Manque, Jun Xu, Matthias G. R. Faes","doi":"arxiv-2409.00407","DOIUrl":"https://doi.org/arxiv-2409.00407","url":null,"abstract":"Estimation of the response probability distributions of computer simulators\u0000in the presence of randomness is a crucial task in many fields. However,\u0000achieving this task with guaranteed accuracy remains an open computational\u0000challenge, especially for expensive-to-evaluate computer simulators. In this\u0000work, a Bayesian active learning perspective is presented to address the\u0000challenge, which is based on the use of the Gaussian process (GP) regression.\u0000First, estimation of the response probability distributions is conceptually\u0000interpreted as a Bayesian inference problem, as opposed to frequentist\u0000inference. This interpretation provides several important benefits: (1) it\u0000quantifies and propagates discretization error probabilistically; (2) it\u0000incorporates prior knowledge of the computer simulator, and (3) it enables the\u0000effective reduction of numerical uncertainty in the solution to a prescribed\u0000level. The conceptual Bayesian idea is then realized by using the GP\u0000regression, where we derive the posterior statistics of the response\u0000probability distributions in semi-analytical form and also provide a numerical\u0000solution scheme. Based on the practical Bayesian approach, a Bayesian active\u0000learning (BAL) method is further proposed for estimating the response\u0000probability distributions. In this context, the key contribution lies in the\u0000development of two crucial components for active learning, i.e., stopping\u0000criterion and learning function, by taking advantage of posterior statistics.\u0000It is empirically demonstrated by five numerical examples that the proposed BAL\u0000method can efficiently estimate the response probability distributions with\u0000desired accuracy.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189460","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}
Phase retrieval refers to the problem of recovering a high-dimensional vector $boldsymbol{x} in mathbb{C}^N$ from the magnitude of its linear transform $boldsymbol{z} = A boldsymbol{x}$, observed through a noisy channel. To improve the ill-posed nature of the inverse problem, it is a common practice to observe the magnitude of linear measurements $boldsymbol{z}^{(1)} = A^{(1)} boldsymbol{x},..., boldsymbol{z}^{(L)} = A^{(L)}boldsymbol{x}$ using multiple sensing matrices $A^{(1)},..., A^{(L)}$, with ptychographic imaging being a remarkable example of such strategies. Inspired by existing algorithms for ptychographic reconstruction, we introduce stochasticity to Vector Approximate Message Passing (VAMP), a computationally efficient algorithm applicable to a wide range of Bayesian inverse problems. By testing our approach in the setup of phase retrieval, we show the superior convergence speed of the proposed algorithm.
{"title":"Stochastic Vector Approximate Message Passing with applications to phase retrieval","authors":"Hajime Ueda, Shun Katakami, Masato Okada","doi":"arxiv-2408.17102","DOIUrl":"https://doi.org/arxiv-2408.17102","url":null,"abstract":"Phase retrieval refers to the problem of recovering a high-dimensional vector\u0000$boldsymbol{x} in mathbb{C}^N$ from the magnitude of its linear transform\u0000$boldsymbol{z} = A boldsymbol{x}$, observed through a noisy channel. To\u0000improve the ill-posed nature of the inverse problem, it is a common practice to\u0000observe the magnitude of linear measurements $boldsymbol{z}^{(1)} = A^{(1)}\u0000boldsymbol{x},..., boldsymbol{z}^{(L)} = A^{(L)}boldsymbol{x}$ using\u0000multiple sensing matrices $A^{(1)},..., A^{(L)}$, with ptychographic imaging\u0000being a remarkable example of such strategies. Inspired by existing algorithms\u0000for ptychographic reconstruction, we introduce stochasticity to Vector\u0000Approximate Message Passing (VAMP), a computationally efficient algorithm\u0000applicable to a wide range of Bayesian inverse problems. By testing our\u0000approach in the setup of phase retrieval, we show the superior convergence\u0000speed of the proposed algorithm.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189494","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}
Rafael Flock, Yiqiu Dong, Felipe Uribe, Olivier Zahm
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing density over the mixing variables. Within this framework, the corresponding posterior distribution also takes the form of a Gaussian mixture, and we derive the closed-form expression for its posterior mixing density. To sample from the posterior Gaussian mixture, we propose a two-step sampling method. First, we sample the mixture variables from the posterior mixing density, and then we sample the variables of interest from Gaussian densities conditioned on the sampled mixing variables. However, the posterior mixing density is relatively difficult to sample from, especially in high dimensions. Therefore, we propose to replace the posterior mixing density by a dimension-reduced approximation, and we provide a bound in the Hellinger distance for the resulting approximate posterior. We apply the proposed approach to a posterior with Laplace prior, where we introduce two dimension-reduced approximations for the posterior mixing density. Our numerical experiments indicate that samples generated via the proposed approximations have very low correlation and are close to the exact posterior.
{"title":"Continuous Gaussian mixture solution for linear Bayesian inversion with application to Laplace priors","authors":"Rafael Flock, Yiqiu Dong, Felipe Uribe, Olivier Zahm","doi":"arxiv-2408.16594","DOIUrl":"https://doi.org/arxiv-2408.16594","url":null,"abstract":"We focus on Bayesian inverse problems with Gaussian likelihood, linear\u0000forward model, and priors that can be formulated as a Gaussian mixture. Such a\u0000mixture is expressed as an integral of Gaussian density functions weighted by a\u0000mixing density over the mixing variables. Within this framework, the\u0000corresponding posterior distribution also takes the form of a Gaussian mixture,\u0000and we derive the closed-form expression for its posterior mixing density. To\u0000sample from the posterior Gaussian mixture, we propose a two-step sampling\u0000method. First, we sample the mixture variables from the posterior mixing\u0000density, and then we sample the variables of interest from Gaussian densities\u0000conditioned on the sampled mixing variables. However, the posterior mixing\u0000density is relatively difficult to sample from, especially in high dimensions.\u0000Therefore, we propose to replace the posterior mixing density by a\u0000dimension-reduced approximation, and we provide a bound in the Hellinger\u0000distance for the resulting approximate posterior. We apply the proposed\u0000approach to a posterior with Laplace prior, where we introduce two\u0000dimension-reduced approximations for the posterior mixing density. Our\u0000numerical experiments indicate that samples generated via the proposed\u0000approximations have very low correlation and are close to the exact posterior.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189493","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}
Sequential Monte Carlo methods are a powerful framework for approximating the posterior distribution of a state variable in a sequential manner. They provide an attractive way of analyzing dynamic systems in real-time, taking into account the limitations of traditional approaches such as Markov Chain Monte Carlo methods, which are not well suited to data that arrives incrementally. This paper reviews and explores the application of Sequential Monte Carlo in dynamic disease modeling, highlighting its capacity for online inference and real-time adaptation to evolving disease dynamics. The integration of kernel density approximation techniques within the stochastic Susceptible-Exposed-Infectious-Recovered (SEIR) compartment model is examined, demonstrating the algorithm's effectiveness in monitoring time-varying parameters such as the effective reproduction number. Case studies, including simulations with synthetic data and analysis of real-world COVID-19 data from Ireland, demonstrate the practical applicability of this approach for informing timely public health interventions.
{"title":"A review of sequential Monte Carlo methods for real-time disease modeling","authors":"Dhorasso Temfack, Jason Wyse","doi":"arxiv-2408.15739","DOIUrl":"https://doi.org/arxiv-2408.15739","url":null,"abstract":"Sequential Monte Carlo methods are a powerful framework for approximating the\u0000posterior distribution of a state variable in a sequential manner. They provide\u0000an attractive way of analyzing dynamic systems in real-time, taking into\u0000account the limitations of traditional approaches such as Markov Chain Monte\u0000Carlo methods, which are not well suited to data that arrives incrementally.\u0000This paper reviews and explores the application of Sequential Monte Carlo in\u0000dynamic disease modeling, highlighting its capacity for online inference and\u0000real-time adaptation to evolving disease dynamics. The integration of kernel\u0000density approximation techniques within the stochastic\u0000Susceptible-Exposed-Infectious-Recovered (SEIR) compartment model is examined,\u0000demonstrating the algorithm's effectiveness in monitoring time-varying\u0000parameters such as the effective reproduction number. Case studies, including\u0000simulations with synthetic data and analysis of real-world COVID-19 data from\u0000Ireland, demonstrate the practical applicability of this approach for informing\u0000timely public health interventions.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224598","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}
Fitting models to data to obtain distributions of consistent parameter values is important for uncertainty quantification, model comparison, and prediction. Standard Markov Chain Monte Carlo (MCMC) approaches for fitting ordinary differential equations (ODEs) to time-series data involve proposing trial parameter sets, numerically integrating the ODEs forward in time, and accepting or rejecting the trial parameter sets. When the model dynamics depend nonlinearly on the parameters, as is generally the case, trial parameter sets are often rejected, and MCMC approaches become prohibitively computationally costly to converge. Here, we build on methods for numerical continuation and trajectory optimization to introduce an approach in which we use Langevin dynamics in the joint space of variables and parameters to sample models that satisfy constraints on the dynamics. We demonstrate the method by sampling Hopf bifurcations and limit cycles of a model of a biochemical oscillator in a Bayesian framework for parameter estimation, and we obtain more than a hundred fold speedup relative to a leading ensemble MCMC approach that requires numerically integrating the ODEs forward in time. We describe numerical experiments that provide insight into the speedup. The method is general and can be used in any framework for parameter estimation and model selection.
{"title":"Sampling parameters of ordinary differential equations with Langevin dynamics that satisfy constraints","authors":"Chris Chi, Jonathan Weare, Aaron R. Dinner","doi":"arxiv-2408.15505","DOIUrl":"https://doi.org/arxiv-2408.15505","url":null,"abstract":"Fitting models to data to obtain distributions of consistent parameter values\u0000is important for uncertainty quantification, model comparison, and prediction.\u0000Standard Markov Chain Monte Carlo (MCMC) approaches for fitting ordinary\u0000differential equations (ODEs) to time-series data involve proposing trial\u0000parameter sets, numerically integrating the ODEs forward in time, and accepting\u0000or rejecting the trial parameter sets. When the model dynamics depend\u0000nonlinearly on the parameters, as is generally the case, trial parameter sets\u0000are often rejected, and MCMC approaches become prohibitively computationally\u0000costly to converge. Here, we build on methods for numerical continuation and\u0000trajectory optimization to introduce an approach in which we use Langevin\u0000dynamics in the joint space of variables and parameters to sample models that\u0000satisfy constraints on the dynamics. We demonstrate the method by sampling Hopf\u0000bifurcations and limit cycles of a model of a biochemical oscillator in a\u0000Bayesian framework for parameter estimation, and we obtain more than a hundred\u0000fold speedup relative to a leading ensemble MCMC approach that requires\u0000numerically integrating the ODEs forward in time. We describe numerical\u0000experiments that provide insight into the speedup. The method is general and\u0000can be used in any framework for parameter estimation and model selection.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189496","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}
Andrew Iskauskas, Jamie A. Cohen, Danny Scarponi, Ian Vernon, Michael Goldstein, Daniel Klein, Richard G. White, Nicky McCreesh
The study of transmission and progression of human papillomavirus (HPV) is crucial for understanding the incidence of cervical cancers, and has been identified as a priority worldwide. The complexity of the disease necessitates a detailed model of HPV transmission and its progression to cancer; to infer properties of the above we require a careful process that can match to imperfect or incomplete observational data. In this paper, we describe the HPVsim simulator to satisfy the former requirement; to satisfy the latter we couple this stochastic simulator to a process of emulation and history matching using the R package hmer. With these tools, we are able to obtain a comprehensive collection of parameter combinations that could give rise to observed cancer data, and explore the implications of the variability of these parameter sets as it relates to future health interventions.
研究人类乳头瘤病毒（HPV）的传播和发展对了解宫颈癌的发病率至关重要，已被确定为全球的优先事项。由于该疾病的复杂性，有必要建立一个详细的 HPV 传播及其向癌症发展的模型；要推断上述模型的特性，我们需要一个能与不完善或不完整的观察数据相匹配的谨慎过程。在本文中，我们描述了 HPVsim 模拟器，以满足前一项要求；为了满足后一项要求，我们将该随机模拟器与使用 R 软件包 hmer 的仿真和历史匹配过程结合起来。有了这些工具，我们就能全面收集可能导致癌症观测数据的参数组合，并探索这些参数集的可变性对未来健康干预的影响。
{"title":"Investigating Complex HPV Dynamics Using Emulation and History Matching","authors":"Andrew Iskauskas, Jamie A. Cohen, Danny Scarponi, Ian Vernon, Michael Goldstein, Daniel Klein, Richard G. White, Nicky McCreesh","doi":"arxiv-2408.15805","DOIUrl":"https://doi.org/arxiv-2408.15805","url":null,"abstract":"The study of transmission and progression of human papillomavirus (HPV) is\u0000crucial for understanding the incidence of cervical cancers, and has been\u0000identified as a priority worldwide. The complexity of the disease necessitates\u0000a detailed model of HPV transmission and its progression to cancer; to infer\u0000properties of the above we require a careful process that can match to\u0000imperfect or incomplete observational data. In this paper, we describe the\u0000HPVsim simulator to satisfy the former requirement; to satisfy the latter we\u0000couple this stochastic simulator to a process of emulation and history matching\u0000using the R package hmer. With these tools, we are able to obtain a\u0000comprehensive collection of parameter combinations that could give rise to\u0000observed cancer data, and explore the implications of the variability of these\u0000parameter sets as it relates to future health interventions.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224596","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}
Quantifying the predictive capacity of a neural system, intended as the capability to store information and actively use it for dynamic system evolution, is a key component of neural information processing. Information storage (IS), the main measure quantifying the active utilization of memory in a dynamic system, is only defined for discrete-time processes. While recent theoretical work laid the foundations for the continuous-time analysis of the predictive capacity stored in a process, methods for the effective computation of the related measures are needed to favor widespread utilization on neural data. This work introduces a method for the model-free estimation of the so-called memory utilization rate (MUR), the continuous-time counterpart of the IS, specifically designed to quantify the predictive capacity stored in neural point processes. The method employs nearest-neighbor entropy estimation applied to the inter-spike intervals measured from point-process realizations to quantify the extent of memory used by a spike train. An empirical procedure based on surrogate data is implemented to compensate the estimation bias and detect statistically significant levels of memory. The method is validated in simulated Poisson processes and in realistic models of coupled cortical dynamics and heartbeat dynamics. It is then applied to real spike trains reflecting central and autonomic nervous system activities: in spontaneously growing cortical neuron cultures, the MUR detected increasing memory utilization across maturation stages, associated to emergent bursting synchronized activity; in the study of the neuro-autonomic modulation of human heartbeats, the MUR reflected the sympathetic activation occurring with postural but not with mental stress. The proposed approach offers a computationally reliable tool to analyze spike train data in computational neuroscience and physiology.
量化神经系统的预测能力是神经信息处理的一个关键组成部分，预测能力是指神经系统存储信息并积极利用信息进行动态系统进化的能力。信息存储（IS）是量化动态系统内存主动利用率的主要指标，但它只适用于离散时间过程。虽然最近的理论工作为连续时间分析过程中存储的预测能力奠定了基础，但仍需要有效计算相关度量的方法，以促进神经数据的广泛利用。本研究介绍了一种无模型估算所谓内存利用率（MUR）的方法，即 IS 的连续时间对应值，专门用于量化神经点过程中存储的预测能力。该方法采用最近邻熵估算法，将其应用于从点进程实现中测量的尖峰间间隔，以量化尖峰序列所使用的记忆程度。基于代用数据的经验程序可补偿估计偏差，并检测出具有统计学意义的记忆水平。该方法在模拟泊松过程以及耦合皮层动力学和心跳动力学的现实模型中得到了验证。然后，将该方法应用于反映中枢神经系统和自主神经系统活动的真实尖峰列车：在自发生长的皮层神经元培养物中，MUR 检测到记忆利用率在各个成熟阶段都在增加，这与突发的同步活动有关；在人类心跳的神经-自主神经调节研究中，MUR 反映了交感神经在体力压力下的激活，而不是在精神压力下的激活。所提出的方法为在计算神经科学和生理学中分析尖峰列车数据提供了一种计算上可靠的工具。
{"title":"A Model-Free Method to Quantify Memory Utilization in Neural Point Processes","authors":"Gorana Mijatovic, Sebastiano Stramaglia, Luca Faes","doi":"arxiv-2408.15875","DOIUrl":"https://doi.org/arxiv-2408.15875","url":null,"abstract":"Quantifying the predictive capacity of a neural system, intended as the\u0000capability to store information and actively use it for dynamic system\u0000evolution, is a key component of neural information processing. Information\u0000storage (IS), the main measure quantifying the active utilization of memory in\u0000a dynamic system, is only defined for discrete-time processes. While recent\u0000theoretical work laid the foundations for the continuous-time analysis of the\u0000predictive capacity stored in a process, methods for the effective computation\u0000of the related measures are needed to favor widespread utilization on neural\u0000data. This work introduces a method for the model-free estimation of the\u0000so-called memory utilization rate (MUR), the continuous-time counterpart of the\u0000IS, specifically designed to quantify the predictive capacity stored in neural\u0000point processes. The method employs nearest-neighbor entropy estimation applied\u0000to the inter-spike intervals measured from point-process realizations to\u0000quantify the extent of memory used by a spike train. An empirical procedure\u0000based on surrogate data is implemented to compensate the estimation bias and\u0000detect statistically significant levels of memory. The method is validated in\u0000simulated Poisson processes and in realistic models of coupled cortical\u0000dynamics and heartbeat dynamics. It is then applied to real spike trains\u0000reflecting central and autonomic nervous system activities: in spontaneously\u0000growing cortical neuron cultures, the MUR detected increasing memory\u0000utilization across maturation stages, associated to emergent bursting\u0000synchronized activity; in the study of the neuro-autonomic modulation of human\u0000heartbeats, the MUR reflected the sympathetic activation occurring with\u0000postural but not with mental stress. The proposed approach offers a\u0000computationally reliable tool to analyze spike train data in computational\u0000neuroscience and physiology.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224594","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}
In many population-based medical studies, the specific cause of death is unidentified, unreliable or even unavailable. Relative survival analysis addresses this scenario, outside of standard (competing risks) survival analysis, to nevertheless estimate survival with respect to a specific cause. It separates the impact of the disease itself on mortality from other factors, such as age, sex, and general population trends. Different methods were created with the aim to construct consistent and efficient estimators for this purpose. The R package relsurv is the most commonly used today in application. With Julia continuously proving itself to be an efficient and powerful programming language, we felt the need to code a pure Julia take, thus NetSurvival.jl, of the standard routines and estimators in the field. The proposed implementation is clean, future-proof, well tested, and the package is correctly documented inside the rising JuliaSurv GitHub organization, ensuring trustability of the results. Through a comprehensive comparison in terms of performance and interface to relsurv, we highlight the benefits of the Julia developing environment.
在许多基于人口的医学研究中，具体死因无法确定、不可靠甚至无法获得。相对存活率分析就是在标准（竞争风险）存活率分析之外，针对这种情况估算与特定死因相关的存活率，它将疾病本身对死亡率的影响与年龄、性别和总体人口趋势等其他因素区分开来。为实现这一目的，人们创造了不同的方法来构建一致且高效的估计器。R软件包relsurv是目前最常用的应用软件。随着 Julia 不断证明自己是一种高效、强大的编程语言，我们认为有必要对该领域的标准例程和估计器进行纯 Julia 代码转换，即 NetSurvival.jl。我们提出的实现是简洁的、面向未来的、经过良好测试的，而且该软件包在不断上升的 JuliaSurv GitHub 组织内有正确的文档记录，从而确保了结果的可信度。通过对性能和与 relsurv 接口的综合比较，我们强调了 Julia 开发环境的优势。
{"title":"NetSurvival.jl: A glimpse into relative survival analysis with Julia","authors":"Rim Alhajal, Oskar Laverny","doi":"arxiv-2408.15655","DOIUrl":"https://doi.org/arxiv-2408.15655","url":null,"abstract":"In many population-based medical studies, the specific cause of death is\u0000unidentified, unreliable or even unavailable. Relative survival analysis\u0000addresses this scenario, outside of standard (competing risks) survival\u0000analysis, to nevertheless estimate survival with respect to a specific cause.\u0000It separates the impact of the disease itself on mortality from other factors,\u0000such as age, sex, and general population trends. Different methods were created\u0000with the aim to construct consistent and efficient estimators for this purpose.\u0000The R package relsurv is the most commonly used today in application. With\u0000Julia continuously proving itself to be an efficient and powerful programming\u0000language, we felt the need to code a pure Julia take, thus NetSurvival.jl, of\u0000the standard routines and estimators in the field. The proposed implementation\u0000is clean, future-proof, well tested, and the package is correctly documented\u0000inside the rising JuliaSurv GitHub organization, ensuring trustability of the\u0000results. Through a comprehensive comparison in terms of performance and\u0000interface to relsurv, we highlight the benefits of the Julia developing\u0000environment.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189495","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}
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their validity cannot be ensured by standard Markov chains theory. Several different techniques have been suggested to analyse their theoretical properties, many of which are technically involved. The technical nature of the theory may make the methods unnecessarily unappealing. We discuss one technique -- based on a martingale decomposition -- with uniformly ergodic Markov transitions. We provide an accessible and self-contained treatment in this setting, and give detailed proofs of the results discussed in the paper, which only require basic understanding of martingale theory and general state space Markov chain concepts. We illustrate how our conditions can accomodate different types of adaptation schemes, and can give useful insight to the requirements which ensure their validity.
{"title":"An invitation to adaptive Markov chain Monte Carlo convergence theory","authors":"Pietari Laitinen, Matti Vihola","doi":"arxiv-2408.14903","DOIUrl":"https://doi.org/arxiv-2408.14903","url":null,"abstract":"Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune\u0000their parameters based on past samples, have proved extremely useful in\u0000practice. The self-tuning mechanism makes them `non-Markovian', which means\u0000that their validity cannot be ensured by standard Markov chains theory. Several\u0000different techniques have been suggested to analyse their theoretical\u0000properties, many of which are technically involved. The technical nature of the\u0000theory may make the methods unnecessarily unappealing. We discuss one technique\u0000-- based on a martingale decomposition -- with uniformly ergodic Markov\u0000transitions. We provide an accessible and self-contained treatment in this\u0000setting, and give detailed proofs of the results discussed in the paper, which\u0000only require basic understanding of martingale theory and general state space\u0000Markov chain concepts. We illustrate how our conditions can accomodate\u0000different types of adaptation schemes, and can give useful insight to the\u0000requirements which ensure their validity.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189499","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：