[Paper Review] Deep Graph Representation Learning and Optimization for Influence Maximization

Ling Chen, Junji Jiang+6 more|arXiv (Cornell University)|May 1, 2023

Complex Network Analysis Techniques78 citations

TL;DR

DeepIM embeds seed sets in a continuous latent space and learns a graph diffusion model end-to-end, enabling scalable, adaptable influence maximization with node-centrality constraints and a distillation-based efficiency boost.

ABSTRACT

Influence maximization (IM) is formulated as selecting a set of initial users from a social network to maximize the expected number of influenced users. Researchers have made great progress in designing various traditional methods, and their theoretical design and performance gain are close to a limit. In the past few years, learning-based IM methods have emerged to achieve stronger generalization ability to unknown graphs than traditional ones. However, the development of learning-based IM methods is still limited by fundamental obstacles, including 1) the difficulty of effectively solving the objective function; 2) the difficulty of characterizing the diversified underlying diffusion patterns; and 3) the difficulty of adapting the solution under various node-centrality-constrained IM variants. To cope with the above challenges, we design a novel framework DeepIM to generatively characterize the latent representation of seed sets, and we propose to learn the diversified information diffusion pattern in a data-driven and end-to-end manner. Finally, we design a novel objective function to infer optimal seed sets under flexible node-centrality-based budget constraints. Extensive analyses are conducted over both synthetic and real-world datasets to demonstrate the overall performance of DeepIM. The code and data are available at: https://github.com/triplej0079/DeepIM.

Motivation & Objective

• Embed the discrete seed-set selection problem into a continuous latent space to ease optimization.
• Learn a data-driven diffusion model that captures real-world propagation patterns end-to-end.
• Provide a unified, adaptable objective for seed-set inference under node-centrality-based budget constraints.
• Improve efficiency via knowledge distillation to a lightweight student model without sacrificing accuracy.
• Demonstrate strong performance on real-world and synthetic networks under multiple diffusion models.

Proposed method

• Introduce a latent variable z to represent seed sets with p(x) = ∫ p(x|z)p(z) dz and learn via autoencoders (encoder f_phi and decoder f_psi).
• Develop a GNN-based diffusion model M(x,G;θ) that outputs infection probabilities and final spread, with a monotonicity guarantee under non-decreasing aggregation and combining functions and non-decreasing final readout.
• Enforce score and infection monotonicity for the diffusion model to reflect realistic diffusion; prove monotonicity for GNNs (e.g., GAT) under stated conditions.
• Incorporate knowledge distillation to train a lightweight student model Ms(z;λ) that directly predicts influence from latent z for efficiency.
• Combine the learned posterior p(z|x) and the diffusion model into an end-to-end training objective that jointly optimizes latent representation and diffusion prediction.
• Provide a unified constrained optimization objective for seed-set inference under arbitrary node-centrality budgets, including vanilla cardinality and degree-based constraints.
• Propose an inference procedure that optimizes z in the latent space using a projected gradient method with a regularizer Phi(x) to keep solutions feasible.

Experimental results

Research questions

• RQ1 Can a continuous latent representation of seed sets enable scalable and effective influence maximization across diverse diffusion patterns?
• RQ2 How can we jointly learn a diffusion model and seed-set representations in an end-to-end manner while preserving monotonicity properties?
• RQ3 Can we adaptively handle node-centrality-based budget constraints in a unified framework for various IM variants?
• RQ4 Does distilling a lightweight model from a high-capacity diffusion model preserve predictive accuracy while improving efficiency?

Key findings

• DeepIM consistently outperforms traditional and learning-based baselines across several real-world networks and diffusion settings.
• The framework maintains monotonicity guarantees for the learned diffusion model, aiding reliable influence estimation.
• A lightweight student model can approximate the teacher diffusion model, enabling efficient inference at scale.
• The latent-space inference procedure effectively identifies high-influence seed sets under various budget constraints, including degree-based and cardinality budgets.
• Empirical results show strong performance under IC, LT, and SIS diffusion, with scalable training and inference workflows.