[Paper Review] Message Passing Neural Networks for Traffic Forecasting

Arian Prabowo, Hao Xue+3 more|arXiv (Cornell University)|May 9, 2023

Traffic Prediction and Management Techniques4 citations

TL;DR

This paper proposes Message Passing Neural Networks (MPNNs) as the optimal Graph Neural Network (GNN) flavor for traffic forecasting, arguing that MPNNs uniquely capture inter-node interactions critical for accurate predictions. Experiments on real-world and synthetic data show MPNNs significantly outperform convolutional (GCN) and attentional (GAT) GNNs, achieving near-perfect performance (RMSE ≈ 0.015, R² ≈ 0.9995) on a synthetic node-interaction task where others fail.

ABSTRACT

A road network, in the context of traffic forecasting, is typically modeled as a graph where the nodes are sensors that measure traffic metrics (such as speed) at that location. Traffic forecasting is interesting because it is complex as the future speed of a road is dependent on a number of different factors. Therefore, to properly forecast traffic, we need a model that is capable of capturing all these different factors. A factor that is missing from the existing works is the node interactions factor. Existing works fail to capture the inter-node interactions because none are using the message-passing flavor of GNN, which is the one best suited to capture the node interactions This paper presents a plausible scenario in road traffic where node interactions are important and argued that the most appropriate GNN flavor to capture node interactions is message-passing. Results from real-world data show the superiority of the message-passing flavor for traffic forecasting. An additional experiment using synthetic data shows that the message-passing flavor can capture inter-node interaction better than other flavors.

Motivation & Objective

• To identify and emphasize the importance of inter-node interactions in traffic forecasting as a missing factor in existing models.
• To argue that message-passing GNNs are the most suitable GNN flavor for capturing node interactions due to their inductive bias for relational reasoning.
• To empirically validate the superiority of message-passing GNNs over convolutional and attentional GNNs in real-world traffic forecasting.
• To demonstrate through synthetic data that MPNNs can fully learn complex, non-linear node interaction patterns where other GNN flavors fail.

Proposed method

• The authors formalize traffic forecasting as a graph-based regression task using historical traffic metrics and adjacency matrices.
• They introduce a synthetic task, the Relation-Modulated Signal Generation (RMSG) task, to isolate and test the ability of GNNs to learn node interactions.
• Four models are compared: a simple average baseline, GCN (representing convolutional GNNs), GAT (representing attentional GNNs), and MPNN (representing message-passing GNNs).
• All models are adapted for regression by removing softmax layers, adding a single-layer MLP for encoding/decoding, and incorporating self-loops via identity matrix addition to the adjacency matrix.
• The models are trained and evaluated using RMSE, MAE, and R² metrics on 2^20 training, 10^5 validation, and 2^20 test samples with hyperparameters optimized via Optuna.
• The message-passing mechanism in MPNNs aggregates node features through iterative message passing, enabling explicit modeling of relational dependencies between nodes.

Experimental results

Research questions

• RQ1 Is inter-node interaction a significant factor in traffic forecasting that current models fail to capture?
• RQ2 Which GNN flavor—convolutional, attentional, or message-passing—is best suited for modeling inter-node interactions in traffic networks?
• RQ3 Can message-passing GNNs outperform other GNN flavors in real-world traffic forecasting tasks?
• RQ4 Can synthetic data experiments isolate and confirm the superior capability of message-passing GNNs in learning complex node interaction patterns?

Key findings

• On the synthetic RMSG task, MPNN achieved near-perfect performance with an RMSE of 0.01509 ± 0.002373 and an R² of 0.99952 ± 0.000147, indicating full learning of the underlying interaction pattern.
• GCN performed similarly to the average baseline (RMSE ≈ 0.6766), with an R² near zero, indicating it failed to learn the interaction pattern despite its non-linear capacity.
• GAT showed improved performance (RMSE ≈ 0.1685, R² ≈ 0.8774) but with high variance (standard deviation > 0.18), suggesting inconsistent learning of interactions.
• On real-world traffic data, MPNN demonstrated superior forecasting performance compared to GCN and GAT, confirming its effectiveness in practical scenarios.
• The results confirm that message-passing GNNs are uniquely capable of modeling complex, non-linear inter-node interactions, which other GNN flavors fail to capture.