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Learning Invariant Graph Representations Through Redundant Information

Barproda Halder, Pasan Dissanayake, Sanghamitra Dutta

TL;DR

This work addresses the challenge of out-of-distribution generalization for graph classification by leveraging Partial Information Decomposition to focus on redundant information shared between invariant and spurious subgraphs. It introduces RIG, a multi-level, alternating-optimization framework that disentangles causal from spurious graph components by maximizing redundancy and using a contrastive objective, guided by an environment-assistant. Theoretical connections between SCMs and PID motivate the redaction of redundant information as a central objective, and extensive experiments on synthetic and real-world datasets demonstrate improved OOD robustness over strong baselines. Collectively, the approach provides a principled, information-theoretic mechanism to derive more reliable invariant graph representations for diverse distribution shifts.

Abstract

Learning invariant graph representations for out-of-distribution (OOD) generalization remains challenging because the learned representations often retain spurious components. To address this challenge, this work introduces a new tool from information theory called Partial Information Decomposition (PID) that goes beyond classical information-theoretic measures. We identify limitations in existing approaches for invariant representation learning that solely rely on classical information-theoretic measures, motivating the need to precisely focus on redundant information about the target $Y$ shared between spurious subgraphs $G_s$ and invariant subgraphs $G_c$ obtained via PID. Next, we propose a new multi-level optimization framework that we call -- Redundancy-guided Invariant Graph learning (RIG) -- that maximizes redundant information while isolating spurious and causal subgraphs, enabling OOD generalization under diverse distribution shifts. Our approach relies on alternating between estimating a lower bound of redundant information (which itself requires an optimization) and maximizing it along with additional objectives. Experiments on both synthetic and real-world graph datasets demonstrate the generalization capabilities of our proposed RIG framework.

Learning Invariant Graph Representations Through Redundant Information

TL;DR

This work addresses the challenge of out-of-distribution generalization for graph classification by leveraging Partial Information Decomposition to focus on redundant information shared between invariant and spurious subgraphs. It introduces RIG, a multi-level, alternating-optimization framework that disentangles causal from spurious graph components by maximizing redundancy and using a contrastive objective, guided by an environment-assistant. Theoretical connections between SCMs and PID motivate the redaction of redundant information as a central objective, and extensive experiments on synthetic and real-world datasets demonstrate improved OOD robustness over strong baselines. Collectively, the approach provides a principled, information-theoretic mechanism to derive more reliable invariant graph representations for diverse distribution shifts.

Abstract

Learning invariant graph representations for out-of-distribution (OOD) generalization remains challenging because the learned representations often retain spurious components. To address this challenge, this work introduces a new tool from information theory called Partial Information Decomposition (PID) that goes beyond classical information-theoretic measures. We identify limitations in existing approaches for invariant representation learning that solely rely on classical information-theoretic measures, motivating the need to precisely focus on redundant information about the target shared between spurious subgraphs and invariant subgraphs obtained via PID. Next, we propose a new multi-level optimization framework that we call -- Redundancy-guided Invariant Graph learning (RIG) -- that maximizes redundant information while isolating spurious and causal subgraphs, enabling OOD generalization under diverse distribution shifts. Our approach relies on alternating between estimating a lower bound of redundant information (which itself requires an optimization) and maximizing it along with additional objectives. Experiments on both synthetic and real-world graph datasets demonstrate the generalization capabilities of our proposed RIG framework.

Paper Structure

This paper contains 14 sections, 4 theorems, 21 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Contributions
  4. RIG: Our Proposed Framework for Invariant Graph Learning
  5. Empirical Results
  6. Limitations
  7. Appendix to Theoretical Results
  8. Appendix to Practical Implementation of the Objective
  9. Appendix to Experiments
  10. Hyperparameter Selection
  11. Ablation Study
  12. PID Estimation
  13. Runtime and Resource Usage
  14. Interpretability Visualization

Key Result

Proposition 1

The total predictive information that the invariant variable $C$ and the spurious variable $S$ contain about the target variable $Y$ decomposes into four nonnegative terms:

Figures (9)

  • Figure 1: Causally-aligned graph neural network.
  • Figure 2: Decomposition of $\mathrm{I}({Y;A,B})$.
  • Figure 3: Graph generation with distribution shifts.
  • Figure 4: Proposed redundancy-based invariant graph learning framework. Highlighted in orange are the components that are being updated in each step.
  • Figure 5: Comparison of PID values across baseline methods with Two-piece dataset {0.8,0.9}.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Definition 1: Unique information bertschinger2014quantifying
  • Proposition 1
  • Lemma 1: FIIF
  • proof
  • Lemma 2: PIIF
  • proof
  • Definition 2: $I_\cap$ measure griffith2014intersection
  • Lemma 3: Noisy Feature
  • proof