Monte Carlo Random Walk Kernel

arXiv:2610.40956v1 Announce Type: new Abstract: We introduce the Monte Carlo Random Walk Kernel (MCRWK), an estimator whose per-pair cost is independent of graph size and derived directly from the random walk kernel (RWK) expansion. By normalizing the kernel coefficients, MCRWK samples a shared walk length and estimates its contribution using random walks on the input graphs. This gives a simple way to approximate RWK without constructing the product graph. For a fixed expected walk length and efficient neighbor sampling, each pairwise estimate takes $O(m)$ time for $m$ Monte Carlo samples, allowing the sample budget to control the trade-off between runtime and accuracy. We evaluate MCRWK against Graph Voyagers and classical RWK methods on synthetic and real graph datasets.