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度量空间上张量积再生核希尔伯特空间的方差分析AI 解读

Many methods have been developed to analyze complex data, such as non-Euclidean shape, network, and manifold data. However, there is a lack of methods for studying interactions among complex data. In this article, we first propose a novel kernel function for a metric space and construct its associated reproducing kernel Hilbert space. The new nonstationary kernel function provides a flexible and powerful tool for learning complex structures in non-Euclidean data. We then…

通过子抽样进行海量数据分析的特征筛选AI 解读

Modern statistical analysis often encounters massive datasets with ultrahigh-dimensional features. In this work, we develop a subsampling approach for feature screening with massive datasets. The approach is implemented by repeated subsampling of massive data and can be used for analyzing tasks with memory constraints. To conduct the procedure, we first calculate an R-squared screening measure (and related sample moments) based on subsamples. Second, we consider three…

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…

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…

This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure…