Kernel Singular Value Decomposition (KSVD) learns singular vectors for an asymmetric kernel matrix derived from two data sources. The paper extends KSVD to multiple data sources, introducing eKSVD, which jointly learns nonlinear feature mappings and captures maximal information across all sources while incorporating pair‑wise couplings. The authors derive a dual optimization framework, a covariance‑based approach, and demonstrate the effectiveness of eKSVD and neural‑network‑based feature mappings through numerical experiments.
arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
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.
arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
arXiv:2510.14878v3 Announce Type: replace-cross Abstract: We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoreti...
arXiv:2605. 06938v2 Announce Type: replace-cross Abstract: Recently Brown et al.
arXiv:2505. 15284v2 Announce Type: replace Abstract: Out-of-Distribution (OoD) detection is vital for the reliability of deep neural networks, the key of which lies in effectively characterizing the disparities between OoD and In-Distribution (InD) data.
arXiv:2609.14815v1 Announce Type: cross Abstract: This paper introduces a novel framework for Regularized Multivariate Functional Principal Component Analysis (ReMFPCA) via Functional Singular Value...
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.
arXiv:2610.08565v1 Announce Type: new Abstract: This article is a geometric rediscovery of the singular value decomposition, with a further claim: the construction it builds is the machinery behind m...
arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).
The paper introduces a scalable approach to learning Determinantal Point Processes (DPPs) by modeling full‑rank interactions through a nonlinear kernel function and latent features. It proposes a surrogate function for maximum likelihood estimation and employs stochastic optimization with random features of the nonlinear kernel. Experiments on real‑world datasets show that this method improves the trade‑off between expressive power and computational scalability, achieving better generalization with fewer parameters.
arXiv:2510.02532v2 Announce Type: replace-cross Abstract: Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensio...