Tensor Canonical Correlation Analysis (TCCA) is a commonly employed statistical method utilized to examine linear associations between two sets of tensor datasets. However, the existing TCCA models fail to adequately address the heterogeneity present in real-world tensor data, such as brain imaging data collected from diverse groups characterized by factors like sex and race. Consequently, these models may yield biased outcomes. In order to surmount this constraint, we propose a novel approach called Multi-Group TCCA (MG-TCCA), which enables the joint analysis of multiple subgroups. By incorporating a dual sparsity structure and a block coordinate ascent algorithm, our MG-TCCA method effectively addresses heterogeneity and leverages information across different groups to identify consistent signals. This novel approach facilitates the quantification of shared and individual structures, reduces data dimensionality, and enables visual exploration. To empirically validate our approach, we conduct a study focused on investigating correlations between two brain positron emission tomography (PET) modalities (AV-45 and FDG) within an Alzheimer's disease (AD) cohort. Our results demonstrate that MG-TCCA surpasses traditional TCCA and Sparse TCCA (STCCA) in identifying sex-specific cross-modality imaging correlations. This heightened performance of MG-TCCA provides valuable insights for the characterization of multimodal imaging biomarkers in AD.

This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data. However, standard GMs can result in biased outcomes, especially when the underlying data involves sensitive characteristics or protected groups. To address this, we introduce a comprehensive framework designed to reduce bias in the estimation of GMs related to protected attributes. Our approach involves the integration of the pairwise graph disparity error and a tailored loss function into a nonsmooth multi-objective optimization problem, striving to achieve fairness across different sensitive groups while maintaining the effectiveness of the GMs. Experimental evaluations on synthetic and real-world datasets demonstrate that our framework effectively mitigates bias without undermining GMs' performance.

This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely used statistical technique for examining the relationship between two sets of variables. We present a framework that alleviates unfairness by minimizing the correlation disparity error associated with protected attributes. Our approach enables CCA to learn global projection matrices from all data points while ensuring that these matrices yield comparable correlation levels to group-specific projection matrices. Experimental evaluation on both synthetic and real-world datasets demonstrates the efficacy of our method in reducing correlation disparity error without compromising CCA accuracy.