We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic termination: a procedure to sample more diverse random walks which may be of independent interest. It has a trivial drop-in implementation. We derive strong theoretical guarantees on the properties of these quasi-Monte Carlo GRFs (q-GRFs), proving that they yield lower-variance estimators of the 2-regularised Laplacian kernel under mild conditions. Remarkably, our results hold for any graph topology. We demonstrate empirical accuracy improvements on a variety of tasks including a new practical application: time-efficient approximation of the graph diffusion process. To our knowledge, q-GRFs constitute the first rigorously studied quasi-Monte Carlo scheme for kernels defined on combinatorial objects, inviting new research on correlations between graph random walks.

翻译：我们提出了一种新颖机制，用于提升近期引入的图随机特征（GRF）类方法的精度。该方法通过引入对偶终止过程来强制算法随机游走长度之间产生负相关性：一种可独立应用的采样更多样化随机游走的程序，且实现简单、即插即用。我们为准蒙特卡洛图随机特征（q-GRF）的统计性质提供了严格的理论保证，证明在温和条件下，其能产生比2-正则化拉普拉斯核更低方差的无偏估计量。值得注意的是，该结论对任意图拓扑结构均成立。我们在包括图扩散过程的高效近似这一新型实际应用在内的多项任务中验证了其经验精度提升。据我们所知，q-GRF是首个针对组合结构上定义的核函数经过严格研究的准蒙特卡洛方案，为探索图随机游走相关性开辟了新研究方向。