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arXiv Machine Learning

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.

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arXiv Machine Learning
1d ago

High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations

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
safety
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arXiv AI
Sep 18

Randomized SVD Approximations for Spectral Co-Clustering of Word-Document Matrices

The paper introduces two randomized approaches to accelerate spectral co‑clustering of word‑document matrices: one based on randomized SVD via random projection, and another combining partial SVD with element‑wise random sampling. Experiments on real and synthetic data show both methods cut runtime compared to full SVD, with the projection technique offering more consistent performance across varied sparsity levels, while the sampling method excels on denser matrices. The study highlights that the choice of approximation should align with the data’s structural properties.

By Fateme Mazdarani, Carlos Toxtli
efficiency
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arXiv Machine Learning
Sep 22

Transfer Learning for Matrix Completion

arXiv:2507.02248v2 Announce Type: replace-cross Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank t...

By Dali Liu, Yuying Xie, Haolei Weng
fine-tuning
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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
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