arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
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 $Du^*=v$.
By Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti, Lorenzo Rosasco
arXiv:2609.38834v1 Announce Type: cross
Abstract: Contrastive learning is a successful paradigm for learning $d$-dimensional geometric representations from a collection of ``anchor--positive--negativ...
By Dionysis Arvanitakis, Vaggos Chatziafratis, Yiyuan Luo, Konstantin Makarychev
arXiv:2609. 38412v1 Announce Type: cross Abstract: We propose a novel local-polynomial estimator of the ratio $r=f/g$ of two $d$-dimensional densities $f$ and $g$, from which independent samples are available.
By Hajo Holzmann, Alexander Meister
arXiv:2609.15179v1 Announce Type: cross
Abstract: The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian...
By Soumik Dutta, Kunal Dutta
We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.