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Learning hidden cascades via classification

Derrick Gilchrist Edward Manoharan, Anubha Goel, Alexandros Iosifidis, Henri Hansen, Juho Kanniainen

TL;DR

This work tackles learning spreading dynamics when node statuses are unobserved by treating parameter inference as distribution classification over entity-level symptom representations. The proposed Distribution Classification framework avoids likelihood-based estimation and instead optimizes parameter settings so real and simulated symptom distributions become indistinguishable via per-entity classifiers. It demonstrates accurate parameter recovery across IC and LT diffusion models, scales to large networks, and outperforms Approximate Bayesian Computation and GNN baselines. The approach yields practical insights, notably higher information flow in insider networks during pre-announcement periods, highlighting its applicability to finance and epidemiology where direct observation of transmission is incomplete.

Abstract

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable, which is crucial for determining an individual's potential to further spread the infection. While final statuses are hidden, intermediate indicators such as symptoms of infection are observable and provide useful representations of the underlying diffusion process. We propose a partial observability-aware Machine Learning framework to learn the characteristics of the spreading model. We term the method Distribution Classification, which utilizes the power of classifiers to infer the underlying transmission dynamics. Through extensive benchmarking against Approximate Bayesian Computation and GNN-based baselines, our framework consistently outperforms these state-of-the-art methods, delivering accurate parameter estimates across diverse diffusion settings while scaling efficiently to large networks. We validate the method on synthetic networks and extend the study to a real-world insider trading network, demonstrating its effectiveness in analyzing spreading phenomena where direct observation of individual statuses is not possible.

Learning hidden cascades via classification

TL;DR

This work tackles learning spreading dynamics when node statuses are unobserved by treating parameter inference as distribution classification over entity-level symptom representations. The proposed Distribution Classification framework avoids likelihood-based estimation and instead optimizes parameter settings so real and simulated symptom distributions become indistinguishable via per-entity classifiers. It demonstrates accurate parameter recovery across IC and LT diffusion models, scales to large networks, and outperforms Approximate Bayesian Computation and GNN baselines. The approach yields practical insights, notably higher information flow in insider networks during pre-announcement periods, highlighting its applicability to finance and epidemiology where direct observation of transmission is incomplete.

Abstract

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable, which is crucial for determining an individual's potential to further spread the infection. While final statuses are hidden, intermediate indicators such as symptoms of infection are observable and provide useful representations of the underlying diffusion process. We propose a partial observability-aware Machine Learning framework to learn the characteristics of the spreading model. We term the method Distribution Classification, which utilizes the power of classifiers to infer the underlying transmission dynamics. Through extensive benchmarking against Approximate Bayesian Computation and GNN-based baselines, our framework consistently outperforms these state-of-the-art methods, delivering accurate parameter estimates across diverse diffusion settings while scaling efficiently to large networks. We validate the method on synthetic networks and extend the study to a real-world insider trading network, demonstrating its effectiveness in analyzing spreading phenomena where direct observation of individual statuses is not possible.
Paper Structure (26 sections, 2 equations, 4 figures, 15 tables, 3 algorithms)

This paper contains 26 sections, 2 equations, 4 figures, 15 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Method
  4. Distribution Classification
  5. Experimental Setup
  6. Modeling Hidden Cascades with the Independent Cascade Model
  7. Feature Generation from Noisy Symptom Observations
  8. Model Parameter Optimization
  9. Hyperparameter Selection for Classifier
  10. Monte Carlo experiments
  11. Evaluation on Synthetic Graphs
  12. Evaluation on Empirical Social Graph (Insiders Network)
  13. Benchmarking Against Alternative Models
  14. Robustness and Efficiency analysis
  15. Node-Specific Propagation Probabilities
  16. ...and 11 more sections

Figures (4)

  • Figure 1: Illustration of Hidden Cascades (HCs).
  • Figure 2: Network topologies used for evaluating the proposed framework. (a) A balanced tree graph with 198 edges, used to simulate a hierarchical spread process. (b) A loopy synthetic graph with 398 edges, capturing richer connectivity and feedback loops. In (a) and (b), a single seed node is marked in dark green; node size and color reflect distance from the seed (closer nodes appear larger and darker).
  • Figure 3: Empirical network derived from insider trading data, comprising 32,925 edges and 1,661 investor nodes. Multiple seed nodes are present and highlighted in red.
  • Figure 4: Distribution of positive symptoms in a loopy graph, organized by both distance from the seed node and node connectivity. Two key observations can be made. Influence of Distance from the Seed Node: Nodes closer to the seed entity (i.e., within the 1-hop neighborhood) have a higher likelihood of being infected. This is evident when moving from left to right in the figure, where nodes are arranged in increasing order of distance. The distribution becomes increasingly skewed as the distance increases, indicating a decline in the proportion of positive symptoms. Effect of Connectivity: Nodes with higher connectivity (i.e., more neighbors) have a higher chance of infection. This is observable when comparing nodes from top to bottom in the figure, where the first-row nodes have more neighbors than those in the second row. The simulated distributions, generated using the inferred parameters, closely match the actual data, confirming that the model captures key structural effects in the spreading process.