arXiv:2601. 10199v2 Announce Type: replace Abstract: Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2607. 20857v1 Announce Type: cross Abstract: Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data.
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
The paper introduces Spectral Connectivity-Regularized Graph Learning (SCoGL), a method for learning sparse graphs from limited data by incorporating Laplacian spectral priors that promote global connectivity. SCoGL extends the graphical lasso objective with a connectivity prior derived from Laplacian eigenvalues and uses projected gradient descent with Armijo backtracking for optimization. Experiments demonstrate that SCoGL improves graph recovery and enhances downstream tasks such as graph signal denoising when observations are scarce.
arXiv:2608.29362v1 Announce Type: cross Abstract: Sparse computations are fundamental to scientific computing, graph analytics, and machine learning, yet their performance is highly sensitive to the...
SuperPCA is a new algorithm for high‑dimensional principal component analysis that exploits an approximate eigenspace of the sample covariance matrix. The authors show that the subspace spanned by several leading eigenvectors contains useful signal information long before individual eigenvectors converge, and they derive posteriori bounds on the angle between this subspace and the true signal subspace. By using only a small number of subsampled coordinates, SuperPCA can achieve up to a ten‑fold improvement in accuracy over classical PCA while reducing data acquisition costs, especially when the signals are approximately sparse.
arXiv:2609.10490v2 Announce Type: replace Abstract: This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs)...