BOPIM: Bayesian Optimization for influence maximization on temporal networks

2023-08-09

arXiv.org

AI Summary

This paper addresses the NP-hard influence maximization problem in temporal networks, where the objective function is expensive to evaluate, non-differentiable, and defined over a non-Euclidean seed set space. To tackle these challenges, we propose the first Bayesian optimization framework for this task. Our method introduces a dual-kernel Gaussian process model that jointly incorporates Hamming distance and neighbor-based Jaccard similarity to capture seed set similarity; it quantifies selection uncertainty for seed sets—novel in this context—and designs a noise-corrected Expected Improvement acquisition function coupled with a greedy strategy to enforce cardinality constraints. Experiments on real-world temporal networks show that our approach achieves influence spread comparable to the classical greedy algorithm while accelerating runtime by up to 10×. Empirical results further indicate that the Hamming kernel generally outperforms the Jaccard kernel across diverse scenarios. Moreover, our framework provides interpretable uncertainty estimates for selected seed sets—enabling principled confidence assessment in influence maximization.

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.

Problem

• Influence Maximization
• Dynamic Networks
• Similarity Measurement

Innovation

• BOPIM
• Bayesian Optimization
• Influence Maximization