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Dynamic Gradient Influencing for Viral Marketing Using Graph Neural Networks

Saurabh Sharma, Ambuj Singh

TL;DR

This work reframes viral marketing as a data-driven, graph-based diffusion problem, introducing Dynamic Viral Marketing (DVM) and solving it with Dynamic Gradient Influencing (DGI). DVM seeks the minimum budget of dynamic topology and attribute perturbations to reach a target adoption, and is shown to be NP-hard with connections to Influence Maximization. DGI employs gradient-guided node flipping, efficient budget computation, and a Meta Influence heuristic with Meta Attribute Flips to flip low-budget, high-influence non-adopters over discrete steps, achieving substantial budget and AUC improvements on real-world networks. The approach provides a practical data-driven alternative to static diffusion models and suggests promising future directions in reinforcement learning and competitive data-driven strategies.

Abstract

The problem of maximizing the adoption of a product through viral marketing in social networks has been studied heavily through postulated network models. We present a novel data-driven formulation of the problem. We use Graph Neural Networks (GNNs) to model the adoption of products by utilizing both topological and attribute information. The resulting Dynamic Viral Marketing (DVM) problem seeks to find the minimum budget and minimal set of dynamic topological and attribute changes in order to attain a specified adoption goal. We show that DVM is NP-Hard and is related to the existing influence maximization problem. Motivated by this connection, we develop the idea of Dynamic Gradient Influencing (DGI) that uses gradient ranking to find optimal perturbations and targets low-budget and high influence non-adopters in discrete steps. We use an efficient strategy for computing node budgets and develop the ''Meta-Influence'' heuristic for assessing a node's downstream influence. We evaluate DGI against multiple baselines and demonstrate gains on average of 24% on budget and 37% on AUC on real-world attributed networks. Our code is publicly available at https://github.com/saurabhsharma1993/dynamic_viral_marketing.

Dynamic Gradient Influencing for Viral Marketing Using Graph Neural Networks

TL;DR

This work reframes viral marketing as a data-driven, graph-based diffusion problem, introducing Dynamic Viral Marketing (DVM) and solving it with Dynamic Gradient Influencing (DGI). DVM seeks the minimum budget of dynamic topology and attribute perturbations to reach a target adoption, and is shown to be NP-hard with connections to Influence Maximization. DGI employs gradient-guided node flipping, efficient budget computation, and a Meta Influence heuristic with Meta Attribute Flips to flip low-budget, high-influence non-adopters over discrete steps, achieving substantial budget and AUC improvements on real-world networks. The approach provides a practical data-driven alternative to static diffusion models and suggests promising future directions in reinforcement learning and competitive data-driven strategies.

Abstract

The problem of maximizing the adoption of a product through viral marketing in social networks has been studied heavily through postulated network models. We present a novel data-driven formulation of the problem. We use Graph Neural Networks (GNNs) to model the adoption of products by utilizing both topological and attribute information. The resulting Dynamic Viral Marketing (DVM) problem seeks to find the minimum budget and minimal set of dynamic topological and attribute changes in order to attain a specified adoption goal. We show that DVM is NP-Hard and is related to the existing influence maximization problem. Motivated by this connection, we develop the idea of Dynamic Gradient Influencing (DGI) that uses gradient ranking to find optimal perturbations and targets low-budget and high influence non-adopters in discrete steps. We use an efficient strategy for computing node budgets and develop the ''Meta-Influence'' heuristic for assessing a node's downstream influence. We evaluate DGI against multiple baselines and demonstrate gains on average of 24% on budget and 37% on AUC on real-world attributed networks. Our code is publicly available at https://github.com/saurabhsharma1993/dynamic_viral_marketing.
Paper Structure (32 sections, 1 theorem, 25 equations, 7 figures, 9 tables, 2 algorithms)

This paper contains 32 sections, 1 theorem, 25 equations, 7 figures, 9 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dynamic Viral Marketing Problem
  4. Dynamic Viral Marketing (DVM)
  5. NP-Hardness of DVM decision problem:
  6. Relating DVM to Influence Maximization
  7. Dynamic Gradient Influencing Framework
  8. Gradient-Guided Node Flipping
  9. Node Flipping Budget Computation
  10. Meta Influence Using Meta Attribute Flips
  11. Experiments
  12. Datasets:
  13. Evaluation metric:
  14. Variants:
  15. Baselines:
  16. ...and 17 more sections

Key Result

Theorem 1

Let the vector $\varepsilon^t_j = x^t_j - x^{t-1}_j$ denote the change in the feature of node $j$ from time $t-1$ to $t$. Further, let the matrix $\xi = M^t - M^{t-1}$ denote the change in the L-step random walk matrix $M$ from time $t-1$ to $t$. Then the dynamic threshold and influence edge weights where $\alpha$ is a vector which depends on the parameters $\theta$ of the GNN.

Figures (7)

  • Figure 1: Overview of the Dynamic Gradient Influencing (DGI) framework. DGI picks candidate nodes to flip using Node Flipping Budget Compute, which involves gradient sorting along with bisection search, hashing and affected set estimation. The gradient-based Meta Influence Heuristic is used to tiebreak among least budget candidate nodes, as well as thresholding for Meta Attribute Flips that enhance node potency. Red lines and circles indicate candidate perturbations.
  • Figure 2: Budget spent as a function of increasing spread with GCN as the GNN propagation model. Dynamic requires consistently lower budgets across all spreads.
  • Figure 3: (a) Spread achieved with increasing time steps for Flixster with GCN backbone. Fixed and Dynamic spread faster than Base due to acceleration from Meta Attribute Flips. (b) Histogram of perturbations contributed by intermediary adopter nodes with increasing Meta Influence, where scaling is used for mapping Meta Influence to [0,1]. Higher Meta Influence adopter nodes contribute more perturbations.
  • Figure 4: (a): Visualization of cascading dynamics of DGI. Node sizes and colors correspond to number of perturbations and cascade hops respectively. Only edges added by DGI are depicted. (b): Number of flipped nodes at different cascade hops. DGI creates long and staggered cascades for DVM.
  • Figure 5: (a) Histogram of perturbations contributed by intermediary spreader nodes with increasing degree. (b) Histogram of perturbations contributed by intermediary spreader nodes with increasing GCN classification margin. Higher contributions are made by spreader nodes with low degrees and high margins.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Theorem 1