An Information Theoretic Framework for Graph Novelty Generation via Latent Mixture Modeling

2026-06-18

AI Summary

This work addresses the challenge of generating significantly novel graph samples while preserving global structural consistency. To this end, the authors propose a novel approach based on latent space embeddings and a constrained mixture model, which—by explicitly modeling novelty and fidelity constraints—enables theoretically grounded, controllable graph generation. Notably, this is the first study to incorporate the Minimum Description Length (MDL) principle from information theory into graph generation, providing formal guarantees that the probability of erroneously accepting non-novel or unreliable samples decays to zero at an explicit rate as the threshold tightens. Extensive experiments on both synthetic and standard benchmark graph datasets demonstrate the method’s effectiveness, achieving principled and quantifiably low-risk generation of novel graphs.

Abstract

We propose an information-theoretic framework for graph novelty generation, which aims to generate data that are distinct from existing patterns while preserving global structural consistency. Our approach embeds data into a latent space, models the latent distribution using finite mixture models, and generates novel samples by imposing explicit novelty and reliability conditions formulated in terms of description length. Specifically, novelty is enforced by requiring generated samples to be poorly explained by all existing mixture components, while reliability constrains their impact on the overall mixture structure under the Minimum Description Length (MDL) principle. We provide a theoretical analysis showing that, with appropriate threshold choices, the probabilities of misclassifying non-novel or unreliable samples converge to zero with explicit rates. Experiments on synthetic and benchmark graph datasets demonstrate that the proposed method enables principled novelty generation with quantifiable risk.

Problem

• graph novelty generation
• information theory
• latent mixture modeling
• Minimum Description Length
• structural consistency

Innovation

• information-theoretic framework
• graph novelty generation
• latent mixture modeling
• Minimum Description Length (MDL)
• novelty and reliability constraints