Diffusion Probabilistic Models for Structured Node Classification

TL;DR

This paper introduces DPM-SNC, a diffusion probabilistic framework for structured node classification on graphs, effectively leveraging known labels and enhancing GNN expressiveness for better predictions.

Contribution

The paper proposes a novel diffusion probabilistic model framework for structured node classification, including a new training algorithm for partially labeled data and theoretical analysis of GNN expressiveness.

Findings

DPM-SNC outperforms existing methods in various graph classification scenarios.

The proposed model effectively incorporates known labels through manifold-constrained sampling.

Theoretical analysis shows DPMs enhance GNN expressiveness beyond 1-WL.

Abstract

This paper studies structured node classification on graphs, where the predictions should consider dependencies between the node labels. In particular, we focus on solving the problem for partially labeled graphs where it is essential to incorporate the information in the known label for predicting the unknown labels. To address this issue, we propose a novel framework leveraging the diffusion probabilistic model for structured node classification (DPM-SNC). At the heart of our framework is the extraordinary capability of DPM-SNC to (a) learn a joint distribution over the labels with an expressive reverse diffusion process and (b) make predictions conditioned on the known labels utilizing manifold-constrained sampling. Since the DPMs lack training algorithms for partially labeled data, we design a novel training algorithm to apply DPMs, maximizing a new variational lower bound. We also theoretically analyze how DPMs benefit node classification by enhancing the expressive power of GNNs based on proposing AGG-WL, which is strictly more powerful than the classic 1-WL test. We extensively verify the superiority of our DPM-SNC in diverse scenarios, which include not only the transductive setting on partially labeled graphs but also the inductive setting and unlabeled graphs.