基于张量学习的多维数据预测
Predicting Multidimensional Data via Tensor Learning
摘要：
多维数据的分析正成为统计和机器学习研究中越来越相关的主题。考虑到它们的复杂性，这些数据对象通常被重新塑造成矩阵或向量，然后进行分析。然而，这种方法存在几个缺点。首先，它破坏了多维空间中数据点之间的内在联系，其次，模型中要估计的参数数量呈指数级增加。我们开发了一个模型，克服了这些缺点。特别是，在本文中，我们提出了一个简约的张量回归模型，保留了数据集的内在多维结构。该算法采用Tucker结构实现简约性，并引入收缩惩罚来处理过拟合和共线性问题。为了估计模型参数，交替最小二乘算法的开发。为了验证模型的性能和鲁棒性，模拟练习。此外，我们进行了实证分析，突出了该模型的预测能力相对于基准模型。这是通过在Foursquares时空数据集和宏观经济面板数据集上实现自回归规范来实现的。总体而言，该模型能够优于基准模型中存在的预测文献。
英文摘要：
The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed. However, this methodology presents several drawbacks. First of all, it destroys the intrinsic interconnections among datapoints in the multidimensional space and, secondly, the number of parameters to be estimated in a model increases exponentially. We develop a model that overcomes such drawbacks. In particular, in this paper, we propose a parsimonious tensor regression model that retains the intrinsic multidimensional structure of the dataset. Tucker structure is employed to achieve parsimony and a shrinkage penalization is introduced to deal with over-fitting and collinearity. To estimate the model parameters, an Alternating Least Squares algorithm is developed. In order to validate the model performance and robustness, a simulation exercise is produced. Moreover, we perform an empirical analysis that highlight the forecasting power of the model with respect to benchmark models. This is achieved by implementing an autoregressive specification on the Foursquares spatio-temporal dataset together with a macroeconomic panel dataset. Overall, the proposed model is able to outperform benchmark models present in the forecasting literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
