BOPIM: Bayesian Optimization for influence maximization on temporal networks
Eric Yanchenko
TL;DR
BOPIM introduces Bayesian Optimization to influence maximization on temporal networks, addressing the combinatorial, non-Euclidean seed-set inputs with two kernels (Hamming distance and neighbor-based Jaccard) and an augmented EI acquisition that respects the cardinality constraint. It demonstrates that a GP surrogate with these kernels can achieve spreads comparable to a gold-standard greedy algorithm while offering up to an order of magnitude speedup. The method naturally yields uncertainty quantification for both the total influence spread and individual seed-node contributions via a Horseshoe-prior augmented mean and posterior node-sampling analyses. The findings indicate that the Hamming kernel frequently matches or outperforms the JC kernel, and that the approach is scalable, flexible to diffusion models, and capable of informing robust seed-set decisions under uncertainty in temporal networks.
Abstract
The goal of influence maximization (IM) is to select a small set of seed nodes which maximizes the spread of influence on a network. In this work, we propose BOPIM, a Bayesian Optimization (BO) algorithm for IM on temporal networks. The IM task is well-suited for a BO solution due to its expensive and complicated objective function. There are at least two key challenges, however, that must be overcome, primarily due to the inputs coming from a cardinality-constrained, non-Euclidean, combinatorial space. The first is constructing the kernel function for the Gaussian Process regression. We propose two kernels, one based on the Hamming distance between seed sets and the other leveraging the Jaccard coefficient between node's neighbors. The second challenge is the acquisition function. For this, we use the Expected Improvement function, suitably adjusting for noise in the observations, and optimize it using a greedy algorithm to account for the cardinality constraint. In numerical experiments on real-world networks, we prove that BOPIM outperforms competing methods and yields comparable influence spreads to a gold-standard greedy algorithm while being as much as ten times faster. In addition, we find that the Hamming kernel performs favorably compared to the Jaccard kernel in nearly all settings, a somewhat surprising result as the former does not explicitly account for the graph structure. Finally, we demonstrate two ways that the proposed method can quantify uncertainty in optimal seed sets. To our knowledge, this is the first attempt to look at uncertainty in the seed sets for IM.