As a regression technique in spatial statistics, spatiotemporally varying coefficient model (STVC) is an important tool to discover nonstationary and interpretable response-covariate associations over both space and time. However, it is difficult to apply STVC for large-scale spatiotemporal analysis due to the high computational cost. To address this challenge, we summarize the spatiotemporally varying coefficients using a third-order tensor structure and propose to reformulate the spatiotemporally varying coefficient model as a special low-rank tensor regression problem. The low-rank decomposition can effectively model the global patterns of the large data with substantially reduced number of parameters. To further incorporate the local spatiotemporal dependencies among the samples, we place Gaussian process (GP) priors on the spatial and temporal factor matrices to better encode local spatial and temporal processes on each factor component. We refer to the overall framework as Bayesian Kernelized Tensor Regression (BKTR). For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm, which uses Gibbs sampling to update factor matrices and slice sampling to update kernel hyperparameters. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and parameter inference.
翻译:作为空间统计的回归技术,零位变化系数模型(STVC)是发现空间和时间上非静止和可解释的可解释反应整体变化协会的一个重要工具,然而,由于计算成本高,很难应用STVC进行大规模空间时空分析。为了应对这一挑战,我们用第三阶高温结构来总结零位变化系数,并提议重新将零位变化系数模型作为特殊低级高压回归问题。低位下降可以有效地模拟大数据的全球模式,同时大幅降低参数数量。要进一步将本地的随机依赖性纳入样本,我们把Gaussian进程(GP)放在空间和时间要素矩阵上,以更好地对每个要素的当地空间和时间进程进行编码。我们提到作为Bayesian Kenneilization Tensor Regrestition (BKTR) 的总体框架。关于模型的推论,我们开发了一个高效的Markov链的蒙特卡洛大数据模式(MCC),并有效地模拟其参数数量大大减少。为了进一步将本地的随机基质依赖,我们把测算法和合成基质测算结果更新到全球测算。