arXiv subjects

Mehdi Hirari

Publications and source records attributed to Mehdi Hirari.

3 recordsLinked to original sources

arXiv2026

Robust Tensor-on-Tensor Regression

Tensor-on-tensor (TOT) 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 TOT 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 TOT 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 identify the different types of outliers detected. 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.

stat.ME↗

arXiv2025

Casewise and Cellwise Robust Multilinear Principal Component Analysis

Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as tensors typically consist of many cells. This paper introduces a novel robust MPCA method 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. The solution that minimizes this loss function is computed using an iteratively reweighted least squares algorithm with a robust initialization. Graphical diagnostic tools are also proposed to identify the different types of outliers that have been found by the new robust MPCA method. The performance of the method and associated graphical displays is assessed through simulations and illustrated on two real datasets.

stat.ME↗

arXiv2023

MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way data

Multi-way data extend two-way matrices into higher-dimensional tensors, often explored through dimensional reduction techniques. In this paper, we study the Parallel Factor Analysis (PARAFAC) model for handling multi-way data, representing it more compactly through a concise set of loading matrices and scores. We assume that the data may be incomplete and could contain both rowwise and cellwise outliers, signifying cases that deviate from the majority and outlying cells dispersed throughout the data array. To address these challenges, we present a novel algorithm designed to robustly estimate both loadings and scores. Additionally, we introduce an enhanced outlier map to distinguish various patterns of outlying behavior. Through simulations and the analysis of fluorescence Excitation-Emission Matrix (EEM) data, we demonstrate the robustness of our approach. Our results underscore the effectiveness of diagnostic tools in identifying and interpreting unusual patterns within the data.

stat.ME↗