Bayesian Dynamic Tensor Regression

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors and call for appropriate statistical tools. We propose a new linear autoregressive tensor process (ART) for tensor-valued data, that encompasses some well-known time series models as special cases. We study its properties and derive the associated impulse response function. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parameterization and develop a Bayesian inference allowing for shrinking effects. We apply the ART model to time series of multilayer networks and study the propagation of shocks across nodes, layers and time.

高维与多维数组数据的可得性正日益提升，这类数据可被自然地表示为张量（tensor），因此亟需适配的统计分析工具。我们针对张量值数据提出了一种全新的线性自回归张量过程（ART），该模型将若干经典时间序列模型作为特例涵盖在内。我们对该模型的性质展开系统性研究，并推导了与之对应的脉冲响应函数。我们借助PARAFAC低秩分解实现简约参数化，并开发了支持收缩效应的贝叶斯推断（Bayesian inference）方法。我们将ART模型应用于多层网络的时间序列数据，探究冲击在节点、层级与时间维度上的传播规律。