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随机点积图潜在位置的最优贝叶斯估计AI 解读

Summary We propose and prove the optimality of a Bayesian approach for estimating the latent positions in random dot product graphs, which we call posterior spectral embedding. Unlike classical spectral-based adjacency, or Laplacian spectral embedding, posterior spectral embedding is a fully likelihood-based graph estimation method that takes advantage of the Bernoulli likelihood information of the observed adjacency matrix. We develop a minimax lower bound for estimating…

模型选择与局部几何AI 解读

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than…

Fréchet 变点检测AI 解读

We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of the data sequence changes abruptly in terms of either its Fréchet mean, Fréchet variance or both. The proposed method is based on comparisons of Fréchet variances before and after putative change-point locations and does not require a…

空间自回归参数的调整准最大似然估计AI 解读

One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter λ in a spatial autoregression. The resulting estimator for λ has better finite sample properties compared to the QMLE for λ, especially in the presence of a large…

含主导单元的生产网络计量分析AI 解读

This paper introduces the notions of strongly and weakly dominant units for networks, and shows that pervasiveness of shocks to a network is measured by the degree of dominance of its most pervasive unit; shown to be equivalent to the inverse of the shape parameter of the power law fitted to the network outdegrees. New cross-section and panel extremum estimators of the degree of dominance in networks are proposed, and their asymptotic properties investigated. The small…

社群识别中均值场变分推断的理论与计算保证AI 解读

The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been…

具有异质性外部性的处理效应AI 解读

This article proposes a new method for estimating heterogeneous externalities in policy analysis when social interactions take the linear-in-means form. We establish that the parameters of interest can be identified and consistently estimated using specific functions of the share of the eligible population. We also study the finite sample performance of the proposed estimators using Monte Carlo simulations. The method is illustrated using data on the PROGRESA program. We…

混合效应时变网络模型及其在脑连接分析中的应用AI 解读

Time-varying networks are fast emerging in a wide range of scientific and business applications. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect network model that characterizes the continuous time-varying behavior of the network at the population level, meanwhile taking into account both the individual subject variability as well as the prior module information. We develop a multistep…

空间盲源分离AI 解读

Summary Recently a blind source separation model was suggested for spatial data, along with an estimator based on the simultaneous diagonalization of two scatter matrices. The asymptotic properties of this estimator are derived here, and a new estimator based on the joint diagonalization of more than two scatter matrices is proposed. The asymptotic properties and merits of the novel estimator are verified in simulation studies. A real-data example illustrates application of…

极值图模型AI 解读

Summary Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk of rare events through asymptotically justified limit models such as max-stable and multivariate Pareto distributions. Statistical modelling in this field has been limited to moderate dimensions so far, partly owing to complicated…

具有跨期优化的空间动态模型：设定与估计AI 解读

In this paper, we introduce a dynamic spatial interaction econometric model. There are n forward-looking agents of whom each has a parametric linear-quadratic payoff, and they interact with their neighbors through a spatial network. Considering a Markov perfect equilibrium (MPE), we derive a unique Nash equilibrium equation and construct a new spatial dynamic panel data (SDPD) model. For estimation, we suggest mainly the quasi-maximum likelihood (QML) method. Asymptotic…

初创企业对地方劳动力市场的作用AI 解读

Summary There are substantial differences in startup activity across US local labor markets. We study the causes and consequences of these differences. Startup productivity shocks are found to drive much of these cross‐city differences in startup activity. Examples of such shocks include breakthroughs in biotech that spurred startup formation in San Diego and Philadelphia. Overall, these shocks explain half of the forecast error variance of startup job creation, accounting…

关于“使用 ReLU 深度神经网络进行非参数回归”的讨论AI 解读

First we would like to congratulate Professor Johannes Schmidt-Hieber for his excellent paper, which shows the surprising result that deep neural networks can achieve good rates of convergence even in case of nonsmooth activation functions.In the following we divide our discussion into three parts:1.The importance of compository assumptions.2. The necessity of the sparsity of the networks.3. The theoretical difference between ReLU and sigmoidal functions.

图及其边上的各向同性协方差函数AI 解读

We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, that is, graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a…

非齐次随机图的双样本假设检验AI 解读

The study of networks leads to a wide range of high-dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations of inhomogeneous random graphs defined on the same set of $n$ vertices. The size of each population $m$ is much smaller than $n$, and can even be a constant…

使用 ReLU 深度神经网络的非参数回归AI 解读

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility…

模板独立成分分析：利用大规模总体先验估计个体脑网络AI 解读

Large brain imaging databases contain a wealth of information on brain organization in the populations they target, and on individual variability. While such databases have been used to study group-level features of populations directly, they are currently underutilized as a resource to inform single-subject analysis. Here, we propose leveraging the information contained in large functional magnetic resonance imaging (fMRI) databases by establishing population priors to…

基于广义Berk–Jones统计量的遗传变异集合检验及乳腺癌应用AI 解读

Studying the effects of groups of single nucleotide polymorphisms (SNPs), as in a gene, genetic pathway, or network, can provide novel insight into complex diseases like breast cancer, uncovering new genetic associations and augmenting the information that can be gleaned from studying SNPs individually. Common challenges in set-based genetic association testing include weak effect sizes, correlation between SNPs in a SNP-set, and scarcity of signals, with individual SNP…

利用谷歌街景车辆移动监测器进行精细时空空气污染分析AI 解读

People are increasingly concerned with understanding their personal environment, including possible exposure to harmful air pollutants. In order to make informed decisions on their day-to-day activities, they are interested in real-time information on a localized scale. Publicly available, fine-scale, high-quality air pollution measurements acquired using mobile monitors represent a paradigm shift in measurement technologies. A methodological framework utilizing these…

复杂尾部依赖结构的局部似然估计：美国极端降水应用AI 解读

To disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous United States (U.S.), we propose a flexible local approach based on factor copula models. Our subasymptotic spatial modeling framework yields nontrivial tail dependence structures, with a weakening dependence strength as events become more extreme; a feature commonly observed with precipitation data but not accounted for in classical asymptotic extreme-value…

GAP：两样本稀疏推断的信息汇聚通用框架AI 解读

Yin Xiaa, T. Tony Caib & Wenguang Sunc*a Department of Statistics, School of Management, Fudan University, Shanghai, China; b Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA; c Department of Data Sciences and Operations, University of Southern California, Los Angeles, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available…

混合与不完整数据表中的主效应和交互作用AI 解读

A mixed data frame (MDF) is a table collecting categorical, numerical, and count observations. The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems. In many cases, an MDF exhibits simultaneously main effects, such as row, column, or group effects and interactions, for which a low-rank model has often been suggested. Although the literature on low-rank approximations is very substantial, with few…

大型有向无环图的似然比检验AI 解读

Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is biologically important. Yet, frequentist inference of directionality of connections remains largely unexplored for regulatory models. In this article, we propose constrained…

无需预检跳跃的跳跃溢出检验AI 解读

This article develops statistical tools for testing conditional independence among the jump components of the daily quadratic variation, which we estimate using intraday data. To avoid sequential bias distortion, we do not pretest for the presence of jumps. If the null is true, our test statistic based on daily integrated jumps weakly converges to a Gaussian random variable if both assets have jumps. If instead at least one asset has no jumps, then the statistic approaches…