Valid Conformal Prediction for Dynamic GNNs

TL;DR

This paper introduces a conformal prediction method for dynamic GNNs using a tensor-based unfolding representation, enabling valid uncertainty quantification without modifying existing architectures.

Contribution

It presents a mathematically rigorous approach for valid prediction sets in dynamic GNNs, applicable under minimal assumptions and adaptable to various inference scenarios.

Findings

Valid prediction sets achieved in multiple dynamic graph scenarios

Improved accuracy over baseline methods in real data experiments

Identification of failure modes when assumptions are violated

Abstract

Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and inference on these systems, but getting a handle on uncertainty, especially in dynamic settings, is a challenging problem. In this work we propose to use a dynamic graph representation known in the tensor literature as the unfolding, to achieve valid prediction sets via conformal prediction. This representation, a simple graph, can be input to any standard GNN and does not require any modification to existing GNN architectures or conformal prediction routines. One of our key contributions is a careful mathematical consideration of the different inference scenarios which can arise in a dynamic graph modelling context. For a range of practically relevant cases, we obtain valid prediction sets with almost no assumptions, even dispensing with exchangeability. In a more challenging scenario, which we call the semi-inductive regime, we achieve valid prediction under stronger assumptions, akin to stationarity. We provide real data examples demonstrating validity, showing improved accuracy over baselines, and sign-posting different failure modes which can occur when those assumptions are violated.