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Causality-Driven Disentangled Representation Learning in Multiplex Graphs

Saba Nasiri, Selin Aviyente, Dorina Thanou

Abstract

Learning representations from multiplex graphs, i.e., multi-layer networks where nodes interact through multiple relation types, is challenging due to the entanglement of shared (common) and layer-specific (private) information, which limits generalization and interpretability. In this work, we introduce a causal inference-based framework that disentangles common and private components in a self-supervised manner. CaDeM jointly (i) aligns shared embeddings across layers, (ii) enforces private embeddings to capture layer-specific signals, and (iii) applies backdoor adjustment to ensure that the common embeddings capture only global information while being separated from the private representations. Experiments on synthetic and real-world datasets demonstrate consistent improvements over existing baselines, highlighting the effectiveness of our approach for robust and interpretable multiplex graph representation learning.

Causality-Driven Disentangled Representation Learning in Multiplex Graphs

Abstract

Learning representations from multiplex graphs, i.e., multi-layer networks where nodes interact through multiple relation types, is challenging due to the entanglement of shared (common) and layer-specific (private) information, which limits generalization and interpretability. In this work, we introduce a causal inference-based framework that disentangles common and private components in a self-supervised manner. CaDeM jointly (i) aligns shared embeddings across layers, (ii) enforces private embeddings to capture layer-specific signals, and (iii) applies backdoor adjustment to ensure that the common embeddings capture only global information while being separated from the private representations. Experiments on synthetic and real-world datasets demonstrate consistent improvements over existing baselines, highlighting the effectiveness of our approach for robust and interpretable multiplex graph representation learning.
Paper Structure (23 sections, 9 theorems, 37 equations, 6 figures, 11 tables)

This paper contains 23 sections, 9 theorems, 37 equations, 6 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. CaDeM: Causality-Driven Disentanglement in Multiplex Graphs
  4. Problem formulation and framework overview
  5. Aligning common embeddings
  6. Causality-aware disentanglement of graph embeddings
  7. Experiments
  8. Evaluation setup
  9. Synthetic dataset
  10. Distinct graph structures with shared node features
  11. Shared features and global structure with layer-specific perturbations
  12. Layer-Specific features with spectral variations
  13. Layer-Specific Features with Dynamical Variations
  14. Real-world datasets
  15. Graph classification
  16. ...and 8 more sections

Key Result

Proposition 1

Assuming the prediction head $\phi$ is sufficiently expressive to represent the Bayes posterior $p(\mathbf{L} \mid \mathbf{P_L})$, minimizing $\mathcal{L}_{\text{self-supervised}}$ is equivalent to maximizing the mutual information $I(\mathbf{P_L}; \mathbf{L})$ between the private embeddings $\mathb

Figures (6)

  • Figure 1: CaDeM Network architecture for extracting common and private embeddings, with losses enforcing desired characteristics.
  • Figure 2: Causal diagram illustrating the roles of private and common embeddings in the layer-specific prediction task.
  • Figure 3: Clustering performance as a function of the trade-off parameter $\gamma$ on Syn2. This plot reports the ARI score obtained by applying K-means clustering to the learned embeddings.
  • Figure 4: Visualization of predicted cluster assignments for Syn3. Panel (a) shows the clusters obtained from the common embeddings. Panels (b) and (c) show the clusters obtained from the private embeddings of layer 1 and layer 2, respectively, with the corresponding ground-truth center nodes overlaid.
  • Figure 5: For each task, we display the top $10\%$ of nodes based on the mean co-activation (left) and anti-activation (right) layer embeddings across subjects. Nodes are projected onto the cortical surface and colored according to the Yeo network atlas, revealing distinct task-dependent patterns across functional brain networks.
  • ...and 1 more figures

Theorems & Definitions (15)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Theorem 1
  • proof : Proof sketch
  • Theorem 1.1
  • ...and 5 more