arXiv Machine Learning By Krzysztof Choromanski, Isaac Reid, Arijit Sehanobish, Avinava Dubey

Optimal Time Complexity Algorithms for Computing General Random Walk Graph Kernels on Sparse Graphs

Read the original on arXiv Machine Learning →

The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.

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 Machine Learning
21h ago

Monte Carlo Random Walk Kernel

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 Machine Learning
Sep 4

Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control

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