Quantile Tensor Factor Regression With Interaction Effects and Its Application to Multimodal Data Analysis

We propose a novel quantile regression method for multimodal data where each modality is a tensor covariate. By employing a factor model to extract latent features, our approach efficiently models their main and interaction effects via a fast algorithm with theoretical guarantees. It thus integrates the robustness of quantile regression with the complex structure of multimodal data. Simulations demonstrate the method's statistical accuracy and stability. Applications to attention deficit hyperactivity disorder (ADHD)‐200 shows that it achieves superior predictive performance and greater computational efficiency than state‐of‐the‐art alternatives.