鲁棒张量-张量回归
Casewise and Cellwise Robust Tensor-on-Tensor Regression
AI总结：
本文提出ROTOT方法，用于处理张量回归中的张量级和单元级异常值，同时应对缺失值，通过单一损失函数和鲁棒多线性主成分分析提升鲁棒性。
摘要：
张量-张量（TOT）回归是分析张量数据的重要工具，旨在从对应的预测张量集预测响应张量集。然而，标准TOT回归对异常值敏感，可能存在于响应和预测中。它可能受个别观测值异常（张量级异常值）和单元异常（张量中个别异常单元）影响。后者因张量数据通常具有大量单元而更为常见。本文提出了一种新的鲁棒TOT回归方法ROTOT，能够同时处理两种类型的异常值，并处理缺失值。该方法使用单一损失函数以减少响应中张量级和单元级异常值的影响。预测中的异常值通过鲁棒多线性主成分分析方法处理。还提出了图形诊断工具以识别检测到的不同类型的异常值。通过广泛的模拟和进一步使用Labeled Faces in the Wild数据集评估ROTOT的性能，其中ROTOT用于预测面部属性。
英文摘要：
Tensor-on-tensor regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard tensor-on-tensor regression is sensitive to outliers, which may be present in both the response and the predictor. It can be affected by casewise outliers, which are observations that deviate from the bulk of the data, as well as by cellwise outliers, which are individual anomalous cells within the tensors. The latter are particularly common due to the typically large number of cells in tensor data. This paper introduces a novel robust tensor-on-tensor regression method, named ROTOT, that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers in the response. The outliers in the predictor are handled using a robust Multilinear Principal Component Analysis method. Graphical diagnostic tools are also proposed to visualize the different types of detected outliers. The performance of ROTOT is evaluated through extensive simulations and further illustrated using the Labeled Faces in the Wild dataset, where ROTOT is applied to predict facial attributes.
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。
