arXiv:2607. 02681v1 Announce Type: cross Abstract: Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging.
By Ye Tian, Mengchu Li, Marco Avella Medina
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.
By Victor L\'eger, Florent Chatelain
arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.
By Fabio Centofanti, Mia Hubert, Peter J. Rousseeuw
The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.
By Jinhang Chai, Xuyuan Liu, Elynn Chen, Yujun Yan
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.
By Benedikt Seiter, Anya Fries, Julius von K\"ugelgen, Jonas Peters
arXiv:2603. 05060v2 Announce Type: replace Abstract: Multi--task learning seeks to improve the generalization error by leveraging the common information shared by multiple related tasks.
By Ayed M. Alrashdi, Oussama Dhifallah, Houssem Sifaou