一种用于多维时间序列数据修复的贝叶斯张量分解算法

A Bayesian Tensor Decomposition Algorithm for Repairing Multi-Dimensional Time-series Data

完整的多维时间序列数据集在深度分析研究中非常重要,而现实数据采集中会由于各种因素导致缺失,因此高精度稳定的数据修复意义重大。针对当前数据修复中无法实现大规模多维时间序列建模的问题,提出了一种基于贝叶斯推断的结构向量自回归张量分解数据修复算法,应用张量分解来建模多维时间序列,采用结构向量自回归过程来建模时间因子矩阵。该算法将结构向量自回归和张量因子分解集成到单个模型中,有效地实现大规模及多维时间序列建模,进而结合贝叶斯推断及吉布斯采样的方法完成数据修复。结果表明,该模型较于其他算法在处理多维张量数据时均方根误差更小,提升了数据修复性能,且对于不同缺失模式的多维数据均具有良好的稳定性。

The indispensability of complete multi-dimensional time series datasets in in-depth analytical studies is highlighted,however,real-world data collection can be compromised by various factors,resulting in missing data.This underscores the criticality of high-precision and stable data restoration.Addressing the challenge of current data restoration methods being unable to facilitate large-scale multi-dimensional time series modeling,a data restoration algorithm based on Bayesian inference and structured vector autoregressive tensor decomposition is proposed.Tensor decomposition is utilized to model multi-dimensional time series,while a structured vector autoregressive process is adopted for time factor matrix modeling.The algorithm integrates structured vector autoregression with tensor factor decomposition into a solitary model,effectively enabling large-scale and multi-dimensional time series modeling,which is then coupled with Bayesian inference and Gibbs sampling for data restoration.The results indicate that this model manifests a lower root-mean-square error in handling multi-dimensional tensor data compared to other algorithms,thereby enhancing data restoration performance.Additionally,the model exhibits robust stability across different missing data patterns in multi-dimensional data.