A2097
Title: Clustered Bi-convex learning
Authors: Guanhua Fang - Fudan University (China) [presenting]
Abstract: The analysis of three-mode data (subjects * items * time) is increasingly prevalent yet challenging due to the asymmetric structural heterogeneity, subjects naturally exhibit latent clustering based on shared behaviors, whereas items typically constitute a fixed, unclustered catalog. Existing methods struggle with this one-sided clustering and the resulting non-jointly convex optimization landscape. To bridge this gap, we propose a novel Clustered Bi-convex Learning (CBL) framework. To achieve scalable and stable estimation, we develop a two-step procedure that decouples the learning process: item-level parameters are first recovered via a moment-based approach, followed by the estimation of subject-level parameters and cluster assignments through convex optimization with adaptive penalties. We establish non-asymptotic error bounds for two broad model classes, proving that the item-parameter estimator achieves a nearly optimal, faster-than-standard convergence rate. Furthermore, we extend the CBL framework to an online streaming setting, providing theoretical guarantees for its robustness and adaptivity under temporal distribution shifts. The practical efficacy and interpretability of our methodology are demonstrated through two real-world data applications.
