The paper introduces the Monte Carlo Random Walk Kernel (MCRWK), an estimator that approximates the random walk kernel (RWK) without constructing the product graph. By normalizing kernel coefficients, MCRWK samples a shared walk length and estimates its contribution via random walks on the input graphs, achieving a per-pair cost independent of graph size. Experiments on synthetic and real datasets show that MCRWK is faster than Graph Voyagers and more accurate at matched runtimes, with the lowest Gram-matrix runtime among the methods tested.
By Arslan Iamaletdinov, Elfat Sabitov, Konstantin Sorokin
arXiv:2510. 07716v2 Announce Type: replace Abstract: We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph.
By Krzysztof Choromanski, Avinava Dubey, Arijit Sehanobish, Isaac Reid
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
By Charles Dufour, Ulysse Naepels, Leonardo V. Santoro
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
By Ecem Bozkurt, Antonio Ortega
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
By Hoang-Son Tran, Pranav Gupta, Subhroshekhar Ghosh
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
By Martin Carrasco, Caio F. Deberaldini Netto, Vahan A. Martirosyan, Ehimare Okoyomon, Caterina Graziani