# Extrapolating paths with graph neural networks

## TL;DR

This paper introduces Gretel, a graph neural network designed to predict the continuation of partially observed paths in various networks, demonstrating adaptability and superior performance over previous methods.

## Contribution

The paper presents Gretel, a novel GNN model for path extrapolation that effectively predicts missing path segments and evaluates path likelihoods in different graph types.

## Key findings

- Gretel accurately predicts path suffixes in GPS and Wikipedia data.
- Gretel outperforms previous solutions in diverse graph settings.
- The model efficiently samples future path distributions.

## Abstract

We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transportation network, an information seeker in Wikipedia, or a client in an online shop. Our interest is sparked by the realization that, in contrast to shortest-path problems, natural paths are usually not optimal in any graph-theoretic sense, but might still follow predictable patterns. Our main contribution is a graph neural network called Gretel. Conditioned on a path prefix, this network can efficiently extrapolate path suffixes, evaluate path likelihood, and sample from the future path distribution. Our experiments with GPS traces on a road network and user-navigation paths in Wikipedia confirm that Gretel is able to adapt to graphs with very different properties, while also comparing favorably to previous solutions.