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通过迭代投影估计张量因子模型AI 解读

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper, we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal…

动态张量的 CP 因子模型AI 解读

Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly…

矩阵时间序列的同步去相关AI 解读

We propose a contemporaneous bilinear transformation for a $p\times q$ matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when $p$ and/or $q$ are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence an overall parsimonious model is achieved by modelling each of those small matrix series separately without the…

高维张量时间序列的因子模型AI 解读

Large tensor (multi-dimensional array) data routinely appear nowadays in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this article we present a factor model approach to the analysis of high-dimensional dynamic tensor time series and multi-category dynamic transport networks. This article presents two estimation procedures along with their theoretical properties and…