arXiv Machine Learning By Georgios I. Orfanidis, Dimitris A. Pados, George Sklivanitis, Elizabeth Serena Bentley

Hankel and Toeplitz Rank-1 Decomposition of Arbitrary Matrices with Applications to Signal Direction-of-Arrival Estimation

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arXiv:2604. 26787v2 Announce Type: replace Abstract: We consider the problems of computing the optimal rank-1 Hankel and Toeplitz-structured approximation of arbitrary matrices under L2 and L1-norm error.

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arXiv Machine Learning
Aug 14

Fast Length-Squared Sampling for Positive-Semidefinite Matrices

arXiv:2608. 12503v1 Announce Type: cross Abstract: We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm.

By Rajarshi Bhattacharjee, Ethan N. Epperly, Cameron Musco, Aaron Tian
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