arXiv Machine Learning
Sep 10

Low-Rank Plus Sparse Matrix Transfer Learning under Growing Representations and Ambient Dimensions

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 Machine Learning
Aug 20

On the Power of Source Screening for Learning Shared Feature Extractors

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
arXiv AI
Sep 17

Limits of Transfer Learning

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 Machine Learning
6d ago

Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration

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