arXiv Statistics ML
Regularization vs. Convolution in Kernel-Based Hypothesis Testing
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arXiv Machine Learning
Oct 23
Random Projections for Spectral Algorithms: Optimal Rates in Sobolev Norms
The paper studies random projections (RP) for spectral algorithms, providing a comprehensive analysis of their generalization performance under broad conditions. By exploiting the RKHS embedding property and operator similarity, it establishes optimal learning rates in Sobolev norms that match minimax lower bounds up to logarithmic factors. For common RP implementations—randomized sketches and Nyström sub-sampling—the required projection dimension scales with the effective dimension, reducing computational cost while preserving statistical efficiency.
arXiv Machine Learning
Jul 28
Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
arXiv Machine Learning
Sep 17
Fast Learning Rates for Physics-Informed Kernel Methods
arXiv:2609. 18901v1 Announce Type: cross Abstract: In physics-informed machine learning, a target function $u^*$ is learned from noisy value observations $y_i=u^*(x_i)+ \varepsilon_i$, together with differential information, given either by noisy observations $d_j=(Du^*)(z_j)+\xi_j$ or by a known physical constraint $Du^*=v$.
arXiv Machine Learning
Oct 8
Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss
The paper introduces Shared Gaussianization (SG), a characteristic‑function test that evaluates Gaussianity of the average of two normalized views scaled by an independent χ_d radius. SG detects both misalignment and non‑uniformity in contrastive learning, vanishing exactly at aligned, uniform minimizers of population InfoNCE, and provides a sharp, dimension‑free bound on InfoNCE excess. The study also explores how SG behaves under different kernels, alignment weights, batch sizes, and latent‑variable models, revealing optimization gaps and the impact of nuisance channels.
arXiv Machine Learning
Jul 9
Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.
arXiv Machine Learning
Oct 21
Gaussian Approximation of Besov Functions for Logistic Classification on Manifolds
arXiv:2610.27022v1 Announce Type: cross Abstract: We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$...