Biometrika最新文献

英文中文

Online Inference with Debiased Stochastic Gradient Descent 基于去偏随机梯度下降的在线推理

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-07-27 DOI: 10.1093/biomet/asad046

Ruijian Han, Lan Luo, Yuanyuan Lin, Jian Huang

We propose a debiased stochastic gradient descent algorithm for online statistical inference with high-dimensional data. Our approach combines the debiasing technique developed in high-dimensional statistics with the stochastic gradient descent algorithm. It can be used for efficiently constructing confidence intervals in an online fashion. Our proposed algorithm has several appealing aspects: first, as a one-pass algorithm, it reduces the time complexity; in addition, each update step requires only the current data together with the previous estimate, which reduces the space complexity. We establish the asymptotic normality of the proposed estimator under mild conditions on the sparsity level of the parameter and the data distribution. We conduct numerical experiments to demonstrate the proposed debiased stochastic gradient descent algorithm reaches nominal coverage probability. Furthermore, we illustrate our method with a high-dimensional text dataset.

提出了一种用于高维数据在线统计推断的去偏随机梯度下降算法。我们的方法结合了高维统计中的去偏技术和随机梯度下降算法。它可以用于以在线方式有效地构建置信区间。我们提出的算法有几个吸引人的方面:首先，作为一种单遍算法，它降低了时间复杂度;此外，每个更新步骤只需要当前数据和之前的估计数据，从而降低了空间复杂度。在参数稀疏性水平和数据分布的温和条件下，我们建立了所提估计量的渐近正态性。我们通过数值实验证明了所提出的去偏随机梯度下降算法达到了标称覆盖概率。此外，我们用一个高维文本数据集来说明我们的方法。

引用次数: 3

An anomaly arising in the analysis of processes with more than one source of variability 在分析具有一个以上变率源的过程时出现的异常

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-07-18 DOI: 10.1093/biomet/asad044

H. Battey, P. McCullagh

It is frequently observed in practice that the Wald statistic gives a poor assessment of the statistical significance of a variance component. This paper provides detailed analytic insight into the phenomenon by way of two simple models, which point to an atypical geometry as the source of the aberration. The latter can in principle be checked numerically to cover situations of arbitrary complexity, such as those arising from elaborate forms of blocking in an experimental context, or models for longitudinal or clustered data. The salient point, echoing Dickey (2020), is that a suitable likelihood-ratio test should always be used for the assessment of variance components.

在实践中经常观察到Wald统计量对方差成分的统计显著性给出了很差的评估。本文通过两个简单的模型对这一现象提供了详细的分析见解，这两个模型指出非典型几何形状是像差的来源。后者原则上可以通过数值检查来涵盖任意复杂性的情况，例如在实验环境中由复杂形式的阻塞引起的情况，或者纵向或集群数据的模型。与Dickey(2020)相呼应的重点是，应该始终使用合适的似然比检验来评估方差成分。

引用次数: 0

A cross-validation-based statistical theory for point processes 基于交叉验证的点过程统计理论

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-06-27 DOI: 10.1093/biomet/asad041

O. Cronie, M. Moradi, C. Biscio

Motivated by cross-validation’s general ability to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that non-parametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state of the art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry (Euclidean domain) and a dataset in neurology (linear network).

受交叉验证减少过拟合和均方误差的一般能力的启发，我们为一般点过程开发了一种基于交叉验证的统计理论。它基于通用点过程的两个新概念的组合：交叉验证和预测误差。我们的交叉验证方法使用细化将点过程/模式划分为成对的训练集和验证集，而我们的预测误差测量两点过程之间的差异。新的统计方法可用于对不同的分布特征进行建模，利用预测误差来衡量给定模型使用相关训练集预测验证集的效果。在指出我们的新框架概括了许多现有的统计方法后，我们为它建立了不同的理论性质，包括大样本性质。我们进一步认识到，非参数强度估计是Papangelou条件强度估计的一个例子，我们利用它将我们的新统计理论应用于核强度估计。使用基于独立稀疏的交叉验证，我们在数值上表明，新方法在带宽选择方面显著优于现有技术。最后，我们对林业数据集（欧几里得域）和神经病学数据集（线性网络）进行了强度估计。

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引用次数: 0

Correction to: Ancestor regression in linear structural equation models 修正：线性结构方程模型中的祖先回归

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-06-10 DOI: 10.1093/biomet/asad028

引用次数: 0

Interpolating discriminant functions in high-dimensional Gaussian latent mixtures 高维高斯潜混合中判别函数的插值

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-06-08 DOI: 10.1093/biomet/asad037

Xin Bing, Marten Wegkamp

Abstract This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, which requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.

摘要本文研究了具有低维潜在高斯混合结构和非消失噪声的假设模型下高维特征的二分类问题。利用广义最小二乘估计估计了最优分离超平面的方向。用估计的超平面对训练数据进行插值。虽然方向向量可以被一致地估计，正如最近线性回归的结果所期望的那样，一个幼稚的插件估计不能一致地估计截距。一个简单的校正，它需要一个独立的保留样本，在许多情况下使程序最小化。后一个过程的插值属性可以保留，但令人惊讶的是，这取决于标签编码的方式。

引用次数: 1

Bayesian learning of network structures from interventional experimental data 基于介入实验数据的网络结构贝叶斯学习

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-05-11 DOI: 10.1093/biomet/asad032

F. Castelletti, S. Peluso

Directed Acyclic Graphs (DAGs) provide an effective framework for learning causal relationships among variables given multivariate observations. Under pure observational data, DAGs encoding the same conditional independencies cannot be distinguished and are collected into Markov equivalence classes. In many contexts however, observational measurements are supplemented by interventional data that improve DAG identifiability and enhance causal effect estimation. We propose a Bayesian framework for multivariate data partially generated after stochastic interventions. To this end, we introduce an effective prior elicitation procedure leading to a closed-form expression for the DAG marginal likelihood and guaranteeing score equivalence among DAGs that are Markov equivalent post intervention. Under the Gaussian setting we show, in terms of posterior ratio consistency, that the true network will be asymptotically recovered, regardless of the specific distribution of the intervened variables and of the relative asymptotic dominance between observational and interventional measurements. We validate our theoretical results in simulation and we implement on both synthetic and biological protein expression data a Markov chain Monte Carlo sampler for posterior inference on the space of DAGs.

有向无环图(dag)提供了一个有效的框架来学习变量之间的因果关系给定的多变量观察。在纯观测数据下，无法区分编码相同条件独立性的dag，并将其收集到马尔可夫等价类中。然而，在许多情况下，通过干预数据补充观察测量，可提高DAG的可识别性并增强因果效应估计。我们提出了一个贝叶斯框架，用于随机干预后部分生成的多变量数据。为此，我们引入了一个有效的先验启发程序，导致DAG边际似然的封闭形式表达式，并保证干预后马尔可夫等效DAG之间的分数相等。在高斯设置下，根据后验比一致性，我们表明，无论干预变量的具体分布以及观察和干预测量之间的相对渐近优势如何，真实网络都将渐近恢复。我们在模拟中验证了我们的理论结果，并在合成和生物蛋白表达数据上实现了一个马尔可夫链蒙特卡罗采样器，用于对dag空间的后验推理。

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引用次数: 1

Populations of Unlabelled Networks: Graph Space Geometry and Generalized Geodesic Principal Components 未标记网络的总体:图空间几何和广义测地线主成分

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-04-04 DOI: 10.1093/biomet/asad024

Anna Calissano, Aasa Feragen, S. Vantini

Statistical analysis for populations of networks is widely applicable but challenging as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks which are weighted or unweighted, uni- or multi-layered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Within this geometrical framework we define generalized geodesic principal components, and we introduce the align all and compute algorithms, all of which allow for the computation of statistics on graph space. The statistics and algorithms are compared with existing methods and empirically validated on three real datasets, showcasing the framework potential utility. The whole framework is implemented within the geomstats Python package.

网络总体的统计分析是广泛适用的，但具有挑战性，因为网络具有强烈的非欧几里德行为。图空间是一个详尽的框架，用于研究加权或未加权、单层或多层、有向或无向的未标记网络的种群。将图空间看作欧几里得空间相对于有限群作用的商，我们证明了它不是流形，并且它的曲率从上看是无界的。在这个几何框架内，我们定义了广义测地线主分量，并引入了align all和compute算法，所有这些算法都允许在图空间上计算统计信息。将统计数据和算法与现有方法进行了比较，并在三个真实数据集上进行了实证验证，展示了框架的潜在效用。整个框架是在geomstats Python包中实现的。

引用次数: 3

Development and initial validation of the Daily Goal Realization Scale. 每日目标实现量表的开发和初步验证

IF 1 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-03-23 eCollection Date: 2023-01-01 DOI: 10.5114/cipp/155945

Mariola Łaguna, Emilia Mielniczuk, Wiktor Razmus

Background: This paper presents the results of three studies allowing the design and initial validation of the Daily Goal Realization Scale (DGRS). Goal realization refers to the engagement in goal-directed behavior that leads to progress in personal goal attainment; it is considered one of the adaptive personal characteristics.

Participants and procedure: Three studies, including an initial study to develop and select the items (Study 1), an intensive longitudinal study (Study 2), and a multiple goal evaluation study (Study 3), tested factorial structure, reliability and validity of the measure.

Results: Multilevel confirmatory factor analysis confirmed the unidimensional structure of the DGRS (obtained in Study 1) both at the individual and goal level, captured as daily goal realization (Study 2) and as multiple goal realization (Study 3). The validity of the DGRS was supported by meaningful associations with other goal evaluations (Study 3). As expected, the DGRS was positively related to evaluations of progress in goal achievement, engagement, likelihood of success, and goal importance. The DGRS also demonstrated measurement invariance allowing for meaningful comparisons of scores between men and women.

Conclusions: The findings indicate that the DGRS is a brief and reliable idiographic measure of daily goal realization. The scale has excellent internal consistency and good criterion validity.

本文介绍了三个研究的结果，允许设计和初步验证的每日目标实现量表(DGRS)。目标实现是指参与目标导向的行为，从而导致个人目标实现的进步;它被认为是适应性的个人特征之一。三项研究，包括开发和选择项目的初步研究(研究1)、深入的纵向研究(研究2)和多目标评价研究(研究3)，测试了该测量的析因结构、信度和效度。多水平验证性因子分析证实了DGRS(在研究1中获得)在个人和目标水平上的单维结构，被捕获为每日目标实现(研究2)和多个目标实现(研究3)。DGRS的灵活性得到了与其他目标评估(研究3)的有意义关联的支持。正如预期的那样，DGRS与目标实现进展、参与度、成功可能性和目标重要性的评估呈正相关。DGRS还证明了测量的不变性，允许在男性和女性之间进行有意义的分数比较。研究结果表明，DGRS是一种简单可靠的日常目标实现的具体测量方法。量表具有良好的内部一致性和标准效度。

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引用次数: 0

Scalable subsampling: computation, aggregation and inference 可伸缩子抽样:计算、聚合和推理

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-03-21 DOI: 10.1093/biomet/asad021

Dimitris N Politis

Abstract Subsampling has seen a resurgence in the big data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. This paper shows how a set of appropriately chosen, nonrandom subsamples can be used to conduct effective, and computationally feasible, subsampling distribution estimation. Furthermore, the same set of subsamples can be used to yield a procedure for subsampling aggregation, also known as subagging, that is scalable with big data. Interestingly, the scalable subagging estimator can be tuned to have the same, or better, rate of convergence than that of θ^n. Statistical inference could then be based on the scalable subagging estimator instead of the original θ^n.

在大数据时代，由于标准的、全样本大小的bootstrap可能无法计算，子抽样已经重新兴起。然而，即使选择大小为b的单个随机子样本，在b和样本量n都非常大的情况下，也可能在计算上具有挑战性。本文展示了如何使用一组适当选择的非随机子样本进行有效且计算可行的子抽样分布估计。此外，同一组子样本可用于产生子样本聚合过程，也称为subagging，该过程可与大数据一起扩展。有趣的是，可伸缩subagging估计器可以被调整为具有与θ^n相同或更好的收敛率。统计推断可以基于可扩展subagging估计器而不是原始的θ^n。

引用次数: 0

Causal inference with misspecified exposure mappings: separating definitions and assumptions 具有错误指定暴露映射的因果推断：分离定义和假设

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-03-16 DOI: 10.1093/biomet/asad019

F. Sävje

Exposure mappings facilitate investigations of complex causal effects when units interact in experiments. Current methods require experimenters to use the same exposure mappings both to define the effect of interest and to impose assumptions on the interference structure. However, the two roles rarely coincide in practice, and experimenters are forced to make the often questionable assumption that their exposures are correctly specified. This paper argues that the two roles exposure mappings currently serve can, and typically should, be separated, so that exposures are used to define effects without necessarily assuming that they are capturing the complete causal structure in the experiment. The paper shows that this approach is practically viable by providing conditions under which exposure effects can be precisely estimated when the exposures are misspecified. Some important questions remain open.

当单元在实验中相互作用时，暴露映射有助于研究复杂的因果效应。目前的方法要求实验者使用相同的暴露映射来定义感兴趣的效果，并对干扰结构进行假设。然而，在实践中，这两个角色很少重合，实验者被迫做出一个经常令人怀疑的假设，即他们的暴露是正确的。本文认为，暴露映射目前所服务的两个角色可以而且通常应该分开，这样暴露就可以用来定义效应，而不必假设它们在实验中捕捉到了完整的因果结构。该论文表明，这种方法在实际中是可行的，因为它提供了一些条件，在这些条件下，当暴露被错误指定时，可以精确估计暴露效应。一些重要问题仍然悬而未决。

引用次数: 1

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