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
The paper investigates which data sources should be jointly learned when training shared feature extractors. Focusing on a linear setting where sources share a low‑dimensional subspace, it shows that carefully selecting a subset of sources—an informative subpopulation—can achieve minimax optimal subspace estimation, even when much data is discarded. The authors formalize this notion, propose algorithms and heuristics for identifying such subsets, and validate their effectiveness through theory and experiments on synthetic and real datasets.
By Leo Muxing Wang, Connor Mclaughlin, Lili Su
The paper investigates the theoretical limits of transfer learning, demonstrating that careful selection of transferable information and its dependence on target problems is crucial. It establishes that the degree of probabilistic change in a transfer-learning algorithm imposes an upper bound on achievable improvement. These findings extend the algorithmic search framework to a broad class of learning tasks involving transfer.
By Jake Williams, Abel Tadesse, Tyler Sam, Huey Sun, George D. Montanez
arXiv:2412. 18081v3 Announce Type: replace-cross Abstract: We study Heterogeneous Transfer Learning (HTL) for high-dimensional regression with differing feature sets.
By Jae Ho Chang, Massimiliano Russo, Subhadeep Paul
arXiv:2607. 03005v1 Announce Type: new Abstract: In high-dimensional Ising model estimation, target sample sizes are often limited, and effectively using auxiliary binary datasets of unknown relevance remains challenging.
By Joonho Kim, Seyoung Park
The paper compares two popular data‑integration techniques—Stack‑SVD, which concatenates datasets before performing singular value decomposition, and SVD‑Stack, which first decomposes each dataset separately and then aggregates the leading singular vectors. By deriving exact asymptotic performance expressions and phase transitions in a proportional regime, the authors show that neither method uniformly dominates the other when unweighted, but optimally weighted Stack‑SVD outperforms optimally weighted SVD‑Stack when the low‑rank signal is fully shared. They also demonstrate that SVD‑Stack can excel with partially shared components and provide practical algorithms for estimating optimal weights, supported by simulations and genomic experiments.
By Tavor Z. Baharav, Phillip B. Nicol, Rafael A. Irizarry, Rong Ma
arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.
By Yuepeng Yang, Cong Ma
arXiv:2506.04166v3 Announce Type: replace
Abstract: Nearest neighbor (NN) methods have re-emerged as competitive tools for matrix completion, offering strong empirical performance and recent theoreti...
By Caleb Chin, Aashish Khubchandani, Harshvardhan Maskara, Kyuseong Choi, Jacob Feitelberg, Albert Gong, Manit Paul, Tathagata Sadhukhan, Dwaipayan Saha, Anish Agarwal, Raaz Dwivedi
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:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
By Diego Marcondes, Cl\'audia Peixoto
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.
By Haotian Lin, Matthew Reimherr
arXiv:2607. 07735v1 Announce Type: cross Abstract: Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data.
By Aryan Eftekhari, Daniel Sergio Vega, Ernst-Jan Camiel Wit, Olaf Schenk