统计学学术速递[9.2]

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stat统计学，共计20篇

【1】 Tukey's Depth for Object Data 标题：对象数据的Tukey深度 链接：https://arxiv.org/abs/2109.00493

作者：Xiongtao Dai,Sara Lopez-Pintado 机构：Department of Statistics, Iowa State University, Ames, Iowa , USA, and, Department of Health Sciences, Northeastern University, Boston, MA , USA, for the Alzheimer’s Disease Neuroimaging Initiative‡ 摘要：我们开发了一种新的基于数据深度的非欧几里德对象数据探索工具，扩展了欧几里德数据的著名Tukey深度。建议的度量半空间深度适用于一般度量空间中的数据对象，为数据点分配深度值，这些深度值表征这些点相对于分布的中心性，并提供可解释的中心向外排序。对于度量半空间深度，建立了推广欧几里德数据假定的标准深度特性的理想理论特性。深度中值被定义为最深点，无论在理论上还是在仿真中，它作为位置描述符都具有很高的鲁棒性。我们提出了一种有效的近似度量半空间深度的算法，并说明了其适应内在数据几何的能力。公制半空间深度被应用于阿尔茨海默病研究，揭示了不同痴呆阶段受试者大脑连通性的群体差异，建模为协方差矩阵。基于7种致病性寄生虫的系统发育树，我们提出的度量半空间深度也被用于构建有意义的进化历史一致性估计，并识别潜在的异常树。 摘要：We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending the celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to data points depth values that characterize the centrality of these points with respect to the distribution and provides an interpretable center-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor both in theory and in simulation. We propose an efficient algorithm to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimer's disease study, revealing group differences in the brain connectivity, modeled as covariance matrices, for subjects in different stages of dementia. Based on phylogenetic trees of 7 pathogenic parasites, our proposed metric halfspace depth was also used to construct a meaningful consensus estimate of the evolutionary history and to identify potential outlier trees.

【2】 On Generalized Random Environment INAR Models of Higher Order: Estimation of Random Environment States 标题：关于高阶广义随机环境INAR模型：随机环境状态的估计 链接：https://arxiv.org/abs/2109.00476

作者：Bogdan A. Pirković,Petra N. Laketa,Aleksandar S. Nastić 机构：Charles University, Ke Karlovu , Praha , Czech republic, Aleksandar S. Nasti´c, University of Niˇs, Viˇsegradska , Niˇs, Serbia 摘要：具有几何边际分布{和负二项式细化算子}的高阶广义随机环境整值自回归模型的行为$RrNGINAR（\mathcal{M，A，P}）$）由称为随机环境过程的辅助马尔可夫链的实现$\{z\u n\}{n=1}^\infty$决定。元素$z_n$表示时刻$n\in\mathbb{n}$中的环境状态，并确定该时刻模型的三个不同参数。为了使用$RrNGINAR（\mathcal{M，A，P}）$模型，首先需要估计$\{z\u n\}{u{n=1}^\infty$，这是迄今为止由K-means数据聚类完成的。我们认为，这种方法忽略了一些信息，在某些情况下表现不佳。我们提出了一种估计$\{z_n\}{n=1}^\infty$的新方法，其中包括聚类前的数据转换，以减少信息损失。为了验证其有效性，我们将这种新方法与通常的方法进行了比较，并将其应用于模拟数据和实际数据，并注意到了从我们的方法中获得的所有好处。 摘要：The behavior of a generalized random environment integer-valued autoregressive model of higher order with geometric marginal distribution {and negative binomial thinning operator} (abbrev. $RrNGINAR(\mathcal{M,A,P})$) is dictated by a realization $\{z_n\}_{n=1}^\infty$ of an auxiliary Markov chain called random environment process. Element $z_n$ represents a state of the environment in moment $n\in\mathbb{N}$ and determines three different parameters of the model in that moment. In order to use $RrNGINAR(\mathcal{M,A,P})$ model, one first needs to estimate $\{z_n\}_{n=1}^\infty$, which was so far done by K-means data clustering. We argue that this approach ignores some information and performs poorly in certain situations. We propose a new method for estimating $\{z_n\}_{n=1}^\infty$, which includes the data transformation preceding the clustering, in order to reduce the information loss. To confirm its efficiency, we compare this new approach with the usual one when applied on the simulated and the real-life data, and notice all the benefits obtained from our method.

【3】 Is the mode elicitable relative to unimodal distributions? 标题：模式是否相对于单峰分布是可引出的？ 链接：https://arxiv.org/abs/2109.00464

作者：Claudio Heinrich-Mertsching,Tobias Fissler 备注：9 pages, 1 figure 摘要：如果存在一个损失函数或得分函数，且该函数是期望中的最佳预测点，则称统计函数为可导出函数。虽然平均值和分位数是可引出的，但Heinrich（2014）表明，如果真实分布可以遵循任何Lebesgue密度，则无法引出模式。我们大大加强了这一结果，表明如果真实分布是具有连续Lebesgue密度和唯一局部极大值的任何分布，则无法导出模式。 摘要：Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is the optimal point forecast in expectation. While the mean and quantiles are elicitable, it has been shown in Heinrich (2014) that the mode cannot be elicited if the true distribution can follow any Lebesgue density. We strengthen this result substantially, showing that the mode cannot be elicited if the true distribution is any distribution with continuous Lebesgue density and unique local maximum.

【4】 Bayesian data combination model with Gaussian process latent variable model for mixed observed variables under NMAR missingness 标题：NMAR缺失下混合观测变量的贝叶斯数据组合模型和高斯过程潜变量模型 链接：https://arxiv.org/abs/2109.00462

作者：Masaki Mitsuhiro,Takahiro Hoshino 摘要：在分析社会科学和商业中的观测数据时，很难获得同时观测到感兴趣变量的“（准）单源数据集”。相反，通常为不同的个人或单位获取多个源数据集。已经提出了各种方法来研究每个数据集中变量之间的关系，例如匹配和潜在变量建模。有必要将这些数据集用作缺少变量的单一源数据集。现有方法假设要集成的数据集来自同一人群，或者采样依赖于协变量。就缺失度而言，该假设称为随机缺失（MAR）。然而，如应用研究所示，这一假设在实际数据分析中可能不成立，所得结果可能有偏差。我们提出了一种数据融合方法，该方法不假设数据集是同质的。对于非MAR缺失数据，我们使用高斯过程潜变量模型。该模型假设关注变量和缺失概率取决于潜在变量。仿真研究和实际数据分析表明，该方法具有缺失数据机制和潜在的高斯过程，可以得到有效的估计，而现有方法提供了严重偏差的估计。这是第一次在数据融合问题中，在合理的假设下考虑和解决数据集的非随机分配问题。 摘要：In the analysis of observational data in social sciences and businesses, it is difficult to obtain a "(quasi) single-source dataset" in which the variables of interest are simultaneously observed. Instead, multiple-source datasets are typically acquired for different individuals or units. Various methods have been proposed to investigate the relationship between the variables in each dataset, e.g., matching and latent variable modeling. It is necessary to utilize these datasets as a single-source dataset with missing variables. Existing methods assume that the datasets to be integrated are acquired from the same population or that the sampling depends on covariates. This assumption is referred to as missing at random (MAR) in terms of missingness. However, as will been shown in application studies, it is likely that this assumption does not hold in actual data analysis and the results obtained may be biased. We propose a data fusion method that does not assume that datasets are homogenous. We use a Gaussian process latent variable model for non-MAR missing data. This model assumes that the variables of concern and the probability of being missing depend on latent variables. A simulation study and real-world data analysis show that the proposed method with a missing-data mechanism and the latent Gaussian process yields valid estimates, whereas an existing method provides severely biased estimates. This is the first study in which non-random assignment to datasets is considered and resolved under resonable assumptions in data fusion problem.

【5】 Perturbation graphs, invariant prediction and causal relations in psychology 标题：心理学中的摄动图、不变量预测与因果关系 链接：https://arxiv.org/abs/2109.00404

作者：Lourens Waldorp,Jolanda Kossakowski,Han L. J. van der Maas 机构：University of Amsterdam, Nieuwe Achtergracht ,-B, NP, the Netherlands, arXiv:,.,v, [stat.ME] , Sep 摘要：心理学中的网络（图）通常仅限于没有干预的环境。在这里，我们考虑一个框架借用生物学，涉及多个干预来自不同的环境（观察和实验）在一个单一的分析。这种方法称为扰动图。在基因调控网络中，一个基因的诱导变化在分析中对所有其他基因进行测量，从而评估可能的因果关系。对分析中的每个基因重复此操作。扰动图可得出一组正确的原因（不一定是直接原因）。随后对图中的路径进行修剪（称为传递性缩减）应能揭示直接原因。我们证明了传递约简通常不会得到正确的底层图。然而，它与另一种称为不变因果预测的方法密切相关。不变因果预测可以被认为是扰动图方法的推广，其中包括附加变量（以及对这些变量的条件作用）确实揭示了直接原因，从而取代了传递约简。我们解释了扰动图、传递约简和不变因果预测的基本思想，并研究了它们之间的联系。我们的结论是，扰动图为心理学实验设计提供了一个很有前途的新工具，并且与不变预测相结合使揭示直接原因而不是因果路径成为可能。作为一个例子，我们将扰动图和不变因果预测应用于关于肉类消费态度的数据集。 摘要：Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a single analysis. The method is called perturbation graphs. In gene regulatory networks, the induced change in one gene is measured on all other genes in the analysis, thereby assessing possible causal relations. This is repeated for each gene in the analysis. A perturbation graph leads to the correct set of causes (not necessarily direct causes). Subsequent pruning of paths in the graph (called transitive reduction) should reveal direct causes. We show that transitive reduction will not in general lead to the correct underlying graph. There is however a close relation with another method, called invariant causal prediction. Invariant causal prediction can be considered as a generalisation of the perturbation graph method where including additional variables (and so conditioning on those variables) does reveal direct causes, and thereby replacing transitive reduction. We explain the basic ideas of perturbation graphs, transitive reduction and invariant causal prediction and investigate their connections. We conclude that perturbation graphs provide a promising new tool for experimental designs in psychology, and combined with invariant prediction make it possible to reveal direct causes instead of causal paths. As an illustration we apply the perturbation graphs and invariant causal prediction to a data set about attitudes on meat consumption.

【6】 On Estimation and Cross-validation of Dynamic Treatment Regimes with Competing Risks 标题：具有竞争风险的动态治疗机制的估计与交叉验证 链接：https://arxiv.org/abs/2109.00396

作者：Pawel Morzywolek,Johan Steen,Wim Van Biesen,Johan Decruyenaere,Stijn Vansteelandt 机构：Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Centre for Justifiable Digital Healthcare, Ghent University Hospital, Department of Internal Medicine and Pediatrics, Ghent University 备注：46 pages, 4 figures 摘要：急性肾损伤（AKI）患者开始肾脏替代治疗的最佳时机仍然是重症监护肾病中一个具有挑战性的问题。多个随机对照试验试图回答这个问题，但根据定义，这些试验只能分析有限数量的治疗起始策略。有鉴于此，我们使用根特大学医院重症监护病房（ICU）常规收集的观察数据，根据血清钾的时间更新水平，研究不同的预先指定的肾脏替代治疗启动时间策略，AKI危重患者的pH值和体液平衡，旨在将30天ICU死亡率降至最低。为此，我们应用统计技术评估ICU出院时作为竞争事件的特定动态治疗方案的影响。我们讨论了两种方法，一种是使用逆概率加权Aalen-Johansen估计的非参数方法，另一种是使用动态区域边际结构模型的半参数方法。此外，我们提出了一种易于实现的交叉验证技术，可用于最佳动态处理制度的样本外性能评估。我们的工作说明了基于常规观测数据的数据驱动医疗决策支持的潜力。 摘要：The optimal moment to start renal replacement therapy in a patient with acute kidney injury (AKI) remains a challenging problem in intensive care nephrology. Multiple randomised controlled trials have tried to answer this question, but these can, by definition, only analyse a limited number of treatment initiation strategies. In view of this, we use routinely collected observational data from the Ghent University Hospital intensive care units (ICUs) to investigate different pre-specified timing strategies for renal replacement therapy initiation based on time-updated levels of serum potassium, pH and fluid balance in critically ill patients with AKI with the aim to minimize 30-day ICU mortality. For this purpose, we apply statistical techniques for evaluating the impact of specific dynamic treatment regimes in the presence of ICU discharge as a competing event. We discuss two approaches, a non-parametric one - using an inverse probability weighted Aalen-Johansen estimator - and a semiparametric one - using dynamic-regime marginal structural models. Furthermore, we suggest an easy to implement cross-validation technique that can be used for the out-of-sample performance assessment of the optimal dynamic treatment regime. Our work illustrates the potential of data-driven medical decision support based on routinely collected observational data.

【7】 A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers 标题：用于测试赛保龄球手分析的截断均值参数化Conway-Maxwell-Poisson模型 链接：https://arxiv.org/abs/2109.00378

作者：Pete Philipson 机构：PhilipsonSchool of Mathematics, Statistics & PhysicsNewcastle University 摘要：通过适当的统计模型评估职业生涯相距遥远的男女运动员的相对优点是一项复杂的任务，因为任何比较都会因体育和社会的根本变化而受到损害，并且往往因不恰当的传统指标的流行而受到阻碍。在这项工作中，我们重点关注板球和使用1877年以来第一次测试的保龄球数据对测试赛保龄球手的排名。我们开发了一个截断的平均参数化康威-麦克斯韦泊松模型，用于处理数据的过度分散和不足性质（以小计数的形式），并提取单个投球手的固有能力。通过部署马尔可夫链蒙特卡罗算法，使用贝叶斯方法进行推断，以获得参数估计和置信区间。该模型提供了一个很好的拟合，并表明常用的保龄球平均值是一个有缺陷的衡量标准。 摘要：Assessing the relative merits of sportsmen and women whose careers took place far apart in time via a suitable statistical model is a complex task as any comparison is compromised by fundamental changes to the sport and society and often handicapped by the popularity of inappropriate traditional metrics. In this work we focus on cricket and the ranking of Test match bowlers using bowling data from the first Test in 1877 onwards. A truncated, mean-parameterised Conway-Maxwell-Poisson model is developed to handle the under- and overdispersed nature of the data, which are in the form of small counts, and to extract the innate ability of individual bowlers. Inferences are made using a Bayesian approach by deploying a Markov Chain Monte Carlo algorithm to obtain parameter estimates and confidence intervals. The model offers a good fit and indicates that the commonly used bowling average is a flawed measure.

【8】 Complete natural gradients for structured variational approximations in mixtures of exponential families 标题：指数族混合中结构变分逼近的完全自然梯度 链接：https://arxiv.org/abs/2109.00375

作者：Linda S. L. Tan 机构：National University of Singapore 备注：14 pages 摘要：随机梯度方法为高维模型和大数据集的变分推理提供了可能。然而，统计模型的参数空间中最陡的上升方向不是由常用的欧几里德梯度给出的，而是由自然梯度给出的，该自然梯度通过Fisher信息矩阵的逆对欧几里德梯度进行预乘。在优化中使用自然梯度可以显著提高收敛性，但在高维情况下反转Fisher信息矩阵是令人望而生畏的。在这里，我们考虑结构变分近似与最小条件指数族表示，其中包括高度灵活的指数族分布的混合物，可以适合倾斜或多峰后验。我们推导出这类模型的完全自然梯度更新，尽管比本文之前介绍的自然梯度更新更复杂，但充分考虑了混合分布和成分分布之间的依赖性。将进行进一步的实验来评估完整自然梯度更新的性能。 摘要：Stochastic gradient methods has enabled variational inference for high-dimensional models and large data sets. However, the direction of steepest ascent in the parameter space of a statistical model is not given by the commonly used Euclidean gradient, but the natural gradient which premultiplies the Euclidean gradient by the inverse of the Fisher information matrix. Use of natural gradients in optimization can improve convergence significantly, but inverting the Fisher information matrix is daunting in high-dimensions. Here we consider structured variational approximations with a minimal conditional exponential family representation, which include highly flexible mixtures of exponential family distributions that can fit skewed or multimodal posteriors. We derive complete natural gradient updates for this class of models, which albeit more complex than the natural gradient updates presented prior to this article, account fully for the dependence between the mixing distribution and the distributions of the components. Further experiments will be carried out to evaluate the performance of the complete natural gradient updates.

【9】 Sparse principal component analysis for high-dimensional stationary time series 标题：高维平稳时间序列的稀疏主成分分析 链接：https://arxiv.org/abs/2109.00299

作者：Kou Fujimori,Yuichi Goto,Yan Liu,Masanobu Taniguchi 机构：Taniguchi¶,‡, Shinshu University§ and Waseda University¶ 备注：29 pages, 5 figures 摘要：我们考虑了高维平稳过程的稀疏主成分分析。当过程的维数较大时，标准主成分分析的性能较差。我们建立了包含重尾时间序列的过程的惩罚主成分估计的oracle不等式。即使当维数以样本量的指数增长率增长时，也可以建立估计量的一致性。我们还阐明了在惩罚估计中选择调谐参数的理论速率。通过数值模拟验证了稀疏主成分分析的性能。通过对平均温度数据的应用，说明了稀疏主成分分析对时间序列数据的实用性。 摘要：We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for penalized principal component estimators for the processes including heavy-tailed time series. The consistency of the estimators is established even when the dimension grows at the exponential rate of the sample size. We also elucidate the theoretical rate for choosing the tuning parameter in penalized estimators. The performance of the sparse principal component analysis is demonstrated by numerical simulations. The utility of the sparse principal component analysis for time series data is exemplified by the application to average temperature data.

【10】 A signed power transformation with application to white noise testing 标题：一种符号幂变换及其在白噪声测试中的应用 链接：https://arxiv.org/abs/2109.00280

作者：Georgi N. Boshnakov,Davide Ravagli 机构：Department of Mathematics, The University of Manchester, Oxford Road, Manchester, M, PL, UK 备注：11 pages 摘要：我们证明了一些ARCH型过程的符号幂变换给出了ARCH型过程。此属性适用的ARCH类型模型类包含许多常见的ARCH和GARCH模型。该结果可用于不存在四阶矩的白噪声测试和非拱型白噪声检测。 摘要：We show that signed power transforms of some ARCH-type processes give ARCH-type processes. The class of ARCH-type models for which this property holds contains many common ARCH and GARCH models. The results can be useful in testing for white noise when fourth moments don't exist and detecting white noise that is not ARCH-type.

【11】 FADE: FAir Double Ensemble Learning for Observable and Counterfactual Outcomes 标题：FADE：针对可观察和反事实结果的公平双重奏学习 链接：https://arxiv.org/abs/2109.00173

作者：Alan Mishler,Edward Kennedy 机构：Department of Statistics & Data Science, Carnegie Mellon, University, Pittsburgh, PA, USA., J. P. Morgan AI Research, New York, NY, USA. 备注：56 pages, 20 figures 摘要：建立公平预测的方法通常涉及公平性和准确性之间以及不同公平性标准之间的权衡，但这些权衡的性质各不相同。最近的工作试图在特定的问题设置中描述这些折衷，但这些方法通常不适合希望在不牺牲准确性的情况下提高现有基准模型公平性的用户，反之亦然。这些结果通常也局限于可观察的准确性和公平性标准。我们开发了一个灵活的公平集成学习框架，允许用户有效地探索公平精度空间，或改进基准模型的公平性或准确性。我们的框架可以同时针对多个可观察或反事实的公平性标准，并且使用户能够组合大量先前训练和新训练的预测因子。我们提供理论保证，我们的估计收敛速度快。我们将我们的方法应用于模拟数据和真实数据，涉及可观察和反事实的准确性和公平性标准。我们发现，令人惊讶的是，与无约束预测或现有基准模型相比，多个不公平度量有时可以同时最小化，而对准确性的影响很小。 摘要：Methods for building fair predictors often involve tradeoffs between fairness and accuracy and between different fairness criteria, but the nature of these tradeoffs varies. Recent work seeks to characterize these tradeoffs in specific problem settings, but these methods often do not accommodate users who wish to improve the fairness of an existing benchmark model without sacrificing accuracy, or vice versa. These results are also typically restricted to observable accuracy and fairness criteria. We develop a flexible framework for fair ensemble learning that allows users to efficiently explore the fairness-accuracy space or to improve the fairness or accuracy of a benchmark model. Our framework can simultaneously target multiple observable or counterfactual fairness criteria, and it enables users to combine a large number of previously trained and newly trained predictors. We provide theoretical guarantees that our estimators converge at fast rates. We apply our method on both simulated and real data, with respect to both observable and counterfactual accuracy and fairness criteria. We show that, surprisingly, multiple unfairness measures can sometimes be minimized simultaneously with little impact on accuracy, relative to unconstrained predictors or existing benchmark models.

【12】 A generalized bootstrap procedure of the standard error and confidence interval estimation for inverse probability of treatment weighting 标题：处理加权逆概率的标准误差和置信区间估计的广义Bootstrap过程 链接：https://arxiv.org/abs/2109.00171

作者：Tenglong Li,Jordan Lawson 机构：Academy of Pharmacy, Xi’an Jiaotong-Liverpool University, Suzhou, China, The Center for Computation and Visualization, Brown University, Providence RI, USA 摘要：治疗加权逆概率（IPTW）方法通常用于倾向评分分析，以推断回归模型中的因果效应。由于过大的IPTW权重和与倾向评分估计相关的误差，IPTW方法可能低估因果效应的标准误差。为了解决这一问题，建议使用bootstrap标准误差代替IPTW标准误差，但普通bootstrap（OB）程序仍可能导致标准误差估计不足，因为其采样算法效率低下，权重不稳定。在本文中，我们开发了一个广义bootstrap（GB）程序来估计IPTW方法的标准误差。与OB程序相比，GB程序低估标准误差的风险要低得多，并且对点误差和标准误差估计都更有效。GB程序的标准误差低估风险也比具有修剪权重的普通引导程序小，效率相当。我们通过模拟研究和1988年国家教育纵向研究（NELS-88）的数据集证明了GB程序的有效性。 摘要：The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient sampling algorithm and un-stabilized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error of the IPTW approach. Compared with the OB procedure, the GB procedure has much lower risk of underestimating the standard error and is more efficient for both point and standard error estimates. The GB procedure also has smaller risk of standard error underestimation than the ordinary bootstrap procedure with trimmed weights, with comparable efficiencies. We demonstrate the effectiveness of the GB procedure via a simulation study and a dataset from the National Educational Longitudinal Study-1988 (NELS-88).

【13】 Novel Bayesian method for simultaneous detection of activation signatures and background connectivity for task fMRI data 标题：同时检测任务fMRI数据激活特征和背景连通性的贝叶斯新方法 链接：https://arxiv.org/abs/2109.00160

作者：Michelle F. Miranda,Jeffrey S. Morris 机构：Department of Mathematics and Statistics, University of Victoria, Division of Biostatistics, Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania 摘要：在本文中，我们介绍了一种新的贝叶斯方法来分析任务功能磁共振成像数据，同时检测激活特征和背景连通性。我们的建模涉及一种新的混合张量时空基策略，该策略支持可伸缩计算，同时捕获附近和远处的体素间相关性和长内存时间相关性。空间基础涉及一个具有两个级别的复合混合变换：第一个级别考虑ROI内部的相关性，第二个级别考虑ROI之间的距离相关性。我们在模拟中演示了我们的基础空间回归建模策略如何提高识别激活特征的灵敏度，部分是由诱导的背景连接性驱动的，该连接性本身可以总结为揭示生物学见解。该策略导致在体素或ROI级别上进行计算可伸缩的完全贝叶斯推理，以适应多次测试。我们将该模型应用于人类连接组项目数据，以揭示与工作记忆任务相关的大脑激活模式和背景连通性。 摘要：In this paper, we introduce a new Bayesian approach for analyzing task fMRI data that simultaneously detects activation signatures and background connectivity. Our modeling involves a new hybrid tensor spatial-temporal basis strategy that enables scalable computing yet captures nearby and distant intervoxel correlation and long-memory temporal correlation. The spatial basis involves a composite hybrid transform with two levels: the first accounts for within-ROI correlation, and second between-ROI distant correlation. We demonstrate in simulations how our basis space regression modeling strategy increases sensitivity for identifying activation signatures, partly driven by the induced background connectivity that itself can be summarized to reveal biological insights. This strategy leads to computationally scalable fully Bayesian inference at the voxel or ROI level that adjusts for multiple testing. We apply this model to Human Connectome Project data to reveal insights into brain activation patterns and background connectivity related to working memory tasks.

【14】 Use of alternative data: High frequency readout of the situation -- COVID policies, mobility, and R-Number 标题：替代数据的使用：情况的高频读出--COVID政策、移动性和R号码 链接：https://arxiv.org/abs/2109.00050

作者：Ashutosh Mani Dixit,Suraj Regmi 机构：Economist, Data Scientist 摘要：替代数据有很大的作用，特别是在危机期间。数月的僵局使我们认识到它们对政策反应的重要性。在尼泊尔，政府采取了停留措施，并暂停了实物数据收集活动。2019冠状病毒疾病确诊病例稳步上升，国家处于高度戒备状态。在2019冠状病毒疾病的爆发过程中，在发病过程中产生的第二种病例的数量——生殖数有助于监测COVID-19的传播性。随着R值的迅速变化，它可能受到多种因素的影响，包括疾病的传染性，而政府对此的反应。以及人口的行为。2019冠状病毒疾病预防接种中心的建议，为世界卫生组织（WHO）建议尼泊尔政府提供若干建议，以了解尼泊尔如何应对冠状病毒大流行，我们看其他数据集，以更好地了解大流行期间的大流行政策、流动性和R值。 摘要：Alternative data have a big role, especially during a crisis. The months of stalemate have made us realize their importance for policy responses. In Nepal, the Government has exerted stay put measures, and physical data collection activities are suspended. The confirmed cases of COVID-19 have been increasing steadily and the country is on high alert. In this impasse, the number of secondary cases one would produce over the course of outbreak -- the reproduction number is useful to monitor the transmissibility of COVID-19. As the R-value is rapidly changing, it can be affected by a range of factors, including not just how infectious a disease is but how Government responds to it, and how the population behaves. The World Health Organization (WHO) has suggested to the Government of Nepal several recommendations to contain the further spread of COVID-19. To get a sense of how Nepal is coping with the coronavirus pandemic we look at the alternative data sets to get a better understanding of the pandemic policies, mobility, and R-value during COVID.

【15】 Scalable Spatiotemporally Varying Coefficient Modeling with Bayesian Kernelized Tensor Regression 标题：基于贝叶斯核张量回归的可伸缩时空变系数建模 链接：https://arxiv.org/abs/2109.00046

作者：Mengying Lei,Aurelie Labbe,Lijun Sun 机构：McGill University, Montreal, QC, Canada, HEC Montreal, Montreal, QC, Canada 摘要：时空变异系数模型（STVC）作为空间统计中的一种回归技术，是发现空间和时间上非平稳和可解释的响应协变量关联的重要工具。然而，由于计算量大，STVC难以应用于大规模时空分析。为了应对这一挑战，我们使用三阶张量结构总结了时空变化系数，并建议将时空变化系数模型重新表述为一个特殊的低阶张量回归问题。低秩分解可以有效地建模大数据的全局模式，并大大减少参数数量。为了进一步结合样本之间的局部时空依赖性，我们在时空因子矩阵上放置高斯过程（GP）先验，以便更好地编码每个因子分量上的局部时空过程。我们将总体框架称为贝叶斯核化张量回归（BKTR）。对于模型推理，我们开发了一种有效的马尔可夫链蒙特卡罗（MCMC）算法，该算法使用Gibbs采样更新因子矩阵，并使用切片采样更新核超参数。我们在合成数据集和真实数据集上进行了大量实验，我们的结果证实了BKTR在模型估计和参数推断方面的优越性能和效率。 摘要：As a regression technique in spatial statistics, spatiotemporally varying coefficient model (STVC) is an important tool to discover nonstationary and interpretable response-covariate associations over both space and time. However, it is difficult to apply STVC for large-scale spatiotemporal analysis due to the high computational cost. To address this challenge, we summarize the spatiotemporally varying coefficients using a third-order tensor structure and propose to reformulate the spatiotemporally varying coefficient model as a special low-rank tensor regression problem. The low-rank decomposition can effectively model the global patterns of the large data with substantially reduced number of parameters. To further incorporate the local spatiotemporal dependencies among the samples, we place Gaussian process (GP) priors on the spatial and temporal factor matrices to better encode local spatial and temporal processes on each factor component. We refer to the overall framework as Bayesian Kernelized Tensor Regression (BKTR). For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm, which uses Gibbs sampling to update factor matrices and slice sampling to update kernel hyperparameters. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and parameter inference.

【16】 Half-Space and Box Constraints as NUV Priors: First Results 标题：作为NUV先验的半空间约束和长方体约束：第一个结果 链接：https://arxiv.org/abs/2109.00036

作者：Raphael Keusch,Hans-Andrea Loeliger 机构：ETH Zurich, Dept. of Information Technology & Electrical Engineering 摘要：具有未知方差的法线（NUV）可以表示许多有用的先验值，并与高斯模型和消息传递算法很好地融合。稀疏先验的NUV表示早已为人所知，而二进制（和M级）先验的NUV表示最近才被提出。在本文档中，我们提出了半空间约束和框约束的NUV表示，这允许将此类约束添加到具有任何先前已知NUV先验的任何线性高斯模型中，而不影响计算的可处理性。 摘要：Normals with unknown variance (NUV) can represent many useful priors and blend well with Gaussian models and message passing algorithms. NUV representations of sparsifying priors have long been known, and NUV representations of binary (and M-level) priors have been proposed very recently. In this document, we propose NUV representations of half-space constraints and box constraints, which allows to add such constraints to any linear Gaussian model with any of the previously known NUV priors without affecting the computational tractability.

【17】 The emergence of a concept in shallow neural networks 标题：浅层神经网络中一个概念的出现 链接：https://arxiv.org/abs/2109.00454

作者：Elena Agliari,Francesco Alemanno,Adriano Barra,Giordano De Marzo 机构：Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro , Rome, Italy., Dipartimento di Matematica e Fisica, Università del Salento, Campus Ecotekne, via Monteroni, Lecce , Italy., Istituto Nazionale di Fisica Nucleare, Sezione di Lecce 摘要：我们考虑受限的Boltzmann机器（RBMS）在非结构化数据集上的训练，它由模糊但不可获得的“原型”组成，并且我们发现存在一个临界样本大小，RBM可以学习原型，即机器可以成功地作为生成模型或分类器来播放。按照操作程序。一般来说，评估临界样本量（可能与数据集的质量有关）仍然是机器学习中的一个开放问题。在这里，仅限于随机理论，在浅层网络足够且母细胞情景正确的情况下，我们利用RBMs和Hopfield网络之间的形式等价性，以获得控制参数空间中突出区域的两种神经结构的相图（即原型数，神经元的数量、训练集的大小和质量），可以完成学习。我们的研究以基于无序系统统计力学的分析方法为指导，结果通过广泛的蒙特卡罗模拟得到进一步证实。 摘要：We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable ``archetypes'' and we show that there exists a critical sample size beyond which the RBM can learn archetypes, namely the machine can successfully play as a generative model or as a classifier, according to the operational routine. In general, assessing a critical sample size (possibly in relation to the quality of the dataset) is still an open problem in machine learning. Here, restricting to the random theory, where shallow networks suffice and the grand-mother cell scenario is correct, we leverage the formal equivalence between RBMs and Hopfield networks, to obtain a phase diagram for both the neural architectures which highlights regions, in the space of the control parameters (i.e., number of archetypes, number of neurons, size and quality of the training set), where learning can be accomplished. Our investigations are led by analytical methods based on the statistical-mechanics of disordered systems and results are further corroborated by extensive Monte Carlo simulations.

【18】 Closed-form portfolio optimization under GARCH models 标题：GARCH模型下的闭式投资组合优化 链接：https://arxiv.org/abs/2109.00433

作者：Marcos Escobar-Anel,Maximilian Gollart,Rudi Zagst 机构：Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada, N,A,B, Department of Mathematics, Technical University of Munich, Munich, Germany 摘要：本文针对方差服从GARCH（1,1）过程的现货资产，给出了第一个封闭形式的最优投资组合配置公式。我们考虑一个投资者具有恒定相对风险厌恶（CRRA）效用谁想要最大化预期效用的终端财富下的赫斯顿和楠迪（2000）GARCH（HN-GARCH）模型。我们得到了最优投资策略、价值函数和最优终端财富的封闭公式。我们发现，最优策略独立于风险资产的发展，并且解收敛于连续时间Heston随机波动率模型的解，尽管是在附加条件下。对于日常交易场景，最优解对参数变化非常稳健，而数值财富等价损失（WEL）分析显示赫斯顿解的性能良好，而默顿解的性能较差。 摘要：This paper develops the first closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. We obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model, albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.

【19】 Approximation Properties of Deep ReLU CNNs 标题：深度RELU CNNs的逼近性质 链接：https://arxiv.org/abs/2109.00190

作者：Juncai He,Lin Li,Jinchao Xu 机构：Peking University, ‡Department of Mathematics 备注：27 pages 摘要：本文致力于在二维空间上建立深ReLU卷积神经网络的$L^2$逼近性质。该分析基于大空间尺寸和多通道卷积核的分解定理。在给定ReLU激活函数的分解和性质的情况下，通过显示其与具有一个隐层的ReLU深度神经网络（DNN）的联系，得到了具有经典结构的深度ReLU CNN的一个普遍逼近定理。此外，基于这些网络之间的连接，还获得了具有ResNet、pre-act ResNet和MgNet结构的神经网络的近似性质。 摘要：This paper is devoted to establishing $L^2$ approximation properties for deep ReLU convolutional neural networks (CNNs) on two-dimensional space. The analysis is based on a decomposition theorem for convolutional kernels with large spatial size and multi-channel. Given that decomposition and the property of the ReLU activation function, a universal approximation theorem of deep ReLU CNNs with classic structure is obtained by showing its connection with ReLU deep neural networks (DNNs) with one hidden layer. Furthermore, approximation properties are also obtained for neural networks with ResNet, pre-act ResNet, and MgNet architecture based on connections between these networks.

【20】 Multi Anchor Point Shrinkage for the Sample Covariance Matrix (Extended Version) 标题：样本协方差矩阵的多锚点收缩(扩展版) 链接：https://arxiv.org/abs/2109.00148

作者：Hubeyb Gurdogan,Alec Kercheval 备注：60 pages, 6 figures 摘要：面对有限样本量的投资组合经理必须使用因子模型来估计高维回报向量的协方差矩阵。对于最简单的单因素市场模型，成功取决于估计的领先特征向量“β”的质量。当只观察到收益本身时，实践者可以得到与样本协方差矩阵的前导特征向量相等的“PCA”估计。该估计器在各种方面表现不佳。为了在高维、有限样本量渐近制度下解决这一问题，并在估计最小方差投资组合的背景下，Goldberg、Papanicolau和Shkolnik开发了一种收缩方法（“GPS估计器”），该方法通过将β的PCA估计器收缩到一个恒定的目标单位向量来改进β的PCA估计器。在本文中，我们继续他们的工作，以开发一个更通用的收缩目标框架，使从业者能够利用进一步的信息来改进估计量。例子包括股票beta的部门分离，以及来自先前估计的最新信息。我们证明了一些精确的陈述，并通过一些数值实验说明了与GPS估计器相比所得到的改进。 摘要：Portfolio managers faced with limited sample sizes must use factor models to estimate the covariance matrix of a high-dimensional returns vector. For the simplest one-factor market model, success rests on the quality of the estimated leading eigenvector "beta". When only the returns themselves are observed, the practitioner has available the "PCA" estimate equal to the leading eigenvector of the sample covariance matrix. This estimator performs poorly in various ways. To address this problem in the high-dimension, limited sample size asymptotic regime and in the context of estimating the minimum variance portfolio, Goldberg, Papanicolau, and Shkolnik developed a shrinkage method (the "GPS estimator") that improves the PCA estimator of beta by shrinking it toward a constant target unit vector. In this paper we continue their work to develop a more general framework of shrinkage targets that allows the practitioner to make use of further information to improve the estimator. Examples include sector separation of stock betas, and recent information from prior estimates. We prove some precise statements and illustrate the resulting improvements over the GPS estimator with some numerical experiments.

机器翻译，仅供参考