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大规模网络空间自回归模型的分布式估计与推断AI 解读

The rapid growth of online network platforms generates large-scale network data and it poses great challenges for statistical analysis using the spatial autoregression (SAR) model. In this work, we develop a novel distributed estimation and statistical inference framework for the SAR model on a distributed system. We first propose a distributed network least squares approximation (DNLSA) method. This enables us to obtain a one-step estimator by taking a weighted average of…

通过剖面化与袋装法估计稀疏时空自回归模型AI 解读

We consider a new class of spatio-temporal models with sparse autoregressive coefficient matrices and exogenous variable. To estimate the model, we first profile the exogenous variable out of the response. This leads to a profiled model structure. Next, to overcome endogeneity issue, we propose a class of generalized methods of moment (GMM) estimators to estimate the autoregressive coefficient matrices. A novel bagging-based estimator is further developed to conquer the…

先导抽样与一步更新的分布式分位数回归札记AI 解读

Quantile regression is a method of fundamental importance. How to efficiently conduct quantile regression for a large dataset on a distributed system is of great importance. We show that the popularly used one-shot estimation is statistically inefficient if data are not randomly distributed across different workers. To fix the problem, a novel one-step estimation method is developed with the following nice properties. First, the algorithm is communication efficient. That is…

网络数据中协变量的降维AI 解读

Summary A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach, called network-supervised dimension reduction, in which covariates are projected onto low-dimensional spaces to reveal the linkage pattern without assuming a model. We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer…

大规模二模网络的网络自回归模型AI 解读

A two-mode network refers to a network where the nodes are classified into two distinct types, and edges can only exist between nodes of different types. In analysis of two-mode networks, one important objective is to explore the relationship between responses of two types of nodes. To this end, we propose a network autoregressive model for two-mode networks. Different network autocorrelation coefficients are allowed. To estimate the model, a quasi-maximum likelihood…

大规模社会网络的多元空间自回归模型AI 解读

The rapid growth of social network platforms generates a large amount of social network data, where multivariate responses are frequently collected from users. To statistically model such type of data, the multivariate spatial autoregressive (MSAR) model is studied. To estimate the model, the quasi maximum likelihood estimator (QMLE) is obtained under certain technical conditions. However, it is found that the computational cost of QMLE is expensive. To fix this problem, a…

网络分位数自回归AI 解读

The complex tail dependency structure in a dynamic network with a large number of nodes is an important object to study. We propose a network quantile autoregression model (NQAR), which characterizes the dynamic quantile behavior. Our NQAR model consists of a system of equations, of which we relate a response to its connected nodes and node specific characteristics in a quantile autoregression process. We show the estimation of the NQAR model and the asymptotic properties…

大规模社交网络中的门户节点筛选AI 解读

Network autoregression model (NAM), as a powerful tool to study user social behaviors on large scale social networks, has drawn great attention in recent years. In this paper, we are interested in identifying the influential users (i.e., portal nodes) in a social network under the framework of NAM. Especially, we consider the autoregression model that allows to have a heterogeneous and sparse network effect coefficients. Therefore, the portal nodes take influential powers…

带状时空自回归模型AI 解读

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and…

利用网络结构估计协方差矩阵AI 解读

In this article, we employ a regression formulation to estimate the high-dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly, the problem of estimating a high-dimensional covariance matrix is converted to one of estimating low dimensional coefficients of the polynomial regression function, which we can…

网络向量自回归AI 解读

We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node’s response at a given time point as a linear combination…

基于抽样网络数据的空间自相关估计AI 解读

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e.,…

社交网络标签的统计模型AI 解读

We consider a social network from which one observes not only network structure (i.e., nodes and edges) but also a set of labels (or tags, keywords) for each node (or user). These labels are self-created and closely related to the user’s career status, life style, personal interests, and many others. Thus, they are of great interest for online marketing. To model their joint behavior with network structure, a complete data model is developed. The model is based on the…

尾指数回归AI 解读

In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic function to link the tail index to the linear predictor induced by covariates, which constitutes the tail index regression model. We then propose an approximate log-likelihood function to obtain regression parameter estimators, and subsequently show the asymptotic normality of those estimators.…