Fast Few-Shot Graph Flow Prediction

Thank you for your detailed review and for pointing out areas where our paper may require clarification. We address your concerns below.

Comments on prior work

We acknowledge that transfer learning has been applied to traffic prediction across cities. However, our work addresses a different aspect:

• Few-Shot Learning Without Historical Data: We focus on scenarios where there is no historical flow data available for the target city and only a few source cities are available for training. This setting is more restrictive than typical transfer learning scenarios, which often assume access to substantial data from both source and target domains.

• Simulation-Based Approach: Our method predicts traffic flow based solely on node and edge attributes, without relying on transferring learned parameters or models from other cities. This allows for flow prediction in entirely unseen networks based on inherent network properties.

Our contribution lies in providing a theoretically grounded, efficient algorithm that operates under these stringent data constraints.

Unclear definitions

We provide formal definitions and mathematical formulations in Section 3 of the paper:

• Graph Construction: Nodes represent intersections or road endpoints, and edges represent road segments. Node features may include population density or proximity to points of interest, while edge features include attributes like road type and capacity.

• Graph Flow Prediction: The task involves predicting the flow (e.g., traffic volume) on each edge of the graph based on node and edge attributes.

We use standard graph notations and equations to define our simulation algorithm and theoretical analysis. We are happy to clarify any specific points if confusing.

Why did you choose AADT as the prediction target?

We chose Average Annual Daily Traffic (AADT) as our prediction target because:

• Data Availability: AADT data is widely collected and publicly available for many cities, facilitating cross-city studies.
• Relevance to Long-Term Planning: AADT is crucial for infrastructure planning, road maintenance, and policy decisions that rely on understanding average traffic patterns.
• Applicability in Data-Scarce Environments: In many regions, real-time traffic data is not readily available, making AADT a practical target for prediction.

Our method is designed to predict flow based on static network attributes, making AADT a suitable and meaningful choice for evaluation.

Dataset choice

Our datasets consist of real-world road networks and associated AADT data from multiple cities. While they may not be standard benchmarks in dynamic traffic forecasting, they are appropriate for our study, which focuses on predicting average traffic flow in unseen cities based on network attributes.

We provide detailed statistics of the datasets in the paper, including the number of nodes, edges, and distribution of flow values.

Baseline selection

We compared our method with GCNs to illustrate the challenges data-driven models face in few-shot learning scenarios without historical flow data for the target graphs.

Our study specifically addresses a setting where traditional GNNs and transfer learning methods may not perform well due to limited training data and the absence of target domain flow data.

Implementation details

Our method is implemented in Python using standard libraries such as NumPy and PyTorch for neural network components. More implementation details are provided in Appendix C including architecture and hyperparameter information and computing infrastructure. We are happy to add any further details if the reviewer feels that our experiments are not sufficiently reproducible.

"The authors lack a comprehensive knowledge about traffic prediction and graph neural networks"

We assure you that we have a strong understanding of traffic prediction and graph neural networks. Our work builds upon existing research while addressing a specific challenge: predicting flow in unseen graphs without historical data and with limited training graphs.

We discuss relevant literature in the related work section, covering both traditional and recent approaches in traffic flow prediction and GNNs. We are also happy to add any additional lines of work that we have missed in this section.

Additional Clarifications

• Terminology: We use "Graph Flow Prediction" to refer to the task of predicting flows on the edges of a graph. While this term may not be standard in all subfields, it accurately describes our focus on predicting flow quantities in network structures.
• Novelty of the Method: Our approach combines a simulation algorithm with theoretical analysis, providing efficiency and accuracy in a setting where data-driven models face limitations.

We sincerely appreciate your thoughtful review and the opportunity to clarify and elaborate on our work. Below, we address your concerns point by point.

What is traffic simulation?

Traffic Simulation Definition and Difference from GCNs:

Traffic simulation involves modeling the movement of agents (e.g., vehicles) through a transportation network based on predefined rules and network attributes. Traditional simulations generate origin-destination pairs and simulate individual trips, often using microscopic or mesoscopic models.

In contrast, Graph Convolutional Networks (GCNs) are data-driven models that learn patterns from historical data, leveraging the graph structure via message passing to make predictions.

Advantages of Our Simulation Approach:

• Generalization to Unseen Graphs: Our simulation method predicts flow based solely on node and edge attributes without requiring historical flow data. This allows it to generalize to unseen networks, which is challenging for GCNs trained on limited graphs.
• Computational Efficiency: Traditional simulations are computationally intensive for large networks because they need to simulate a vast number of individual trips. Our method approximates flows using aggregate computations, significantly reducing computational complexity.

Why Simulations Can Be Computationally Infeasible:

Simulating every possible origin-destination trip in a large network requires enumerating a combinatorial number of paths, leading to high computational costs. This makes traditional simulations impractical for large-scale networks.

Unclear motivation

GCNs rely on learning patterns from the training data, including both graph topology and node/edge features. When trained on a small number of graphs, GCNs may overfit to specific patterns present in the training data, limiting their ability to generalize to new, unseen graphs with different characteristics.

In our problem setting, we have access to only a few training graphs (cities) and no historical flow data for the target graphs. This scarcity of data makes it challenging for GCNs to capture the diverse flow patterns necessary for accurate predictions in unseen networks.

Why traffic flow prediction?

We acknowledge that our experiments focus on traffic flow prediction due to its practical significance and the availability of data. However, the methodology we propose is general and applicable to other graph flow prediction problems, such as information flow in communication networks or resource flow in logistics networks.

In the paper, we discuss the theoretical foundations of our method in a general graph context, highlighting its potential applicability beyond traffic networks. The focus on traffic flow prediction serves as a concrete example to demonstrate the effectiveness of our approach.

Related work

Our paper includes a section on related work where we discuss both data-driven approaches (including GCN-based methods) and simulation-based approaches for flow prediction. We highlight the limitations of existing methods in handling few-shot learning scenarios and predicting flow in unseen graphs without historical data.

We also address the computational challenges of traditional simulations and the limitations of GCNs in generalizing from a small number of training graphs. Our work fills this gap by providing an efficient simulation algorithm with theoretical guarantees.

Theoretical assumptions

The two key assumptions in our theoretical analysis are:

• Trip Count Approximation: We assume that the number of trips between origin and destination nodes can be approximated by the product of feature vectors associated with these nodes. This is inspired by gravity models in transportation, which are well-established in modeling trip distribution based on origin and destination attributes.

• Cost Approximation: We approximate the cost between nodes using a metric based on node positions and average travel speeds. This is a common practice in transportation modeling, where travel times are estimated using distance and typical speeds. These assumptions are supported by empirical observations in transportation research. While they may not capture all nuances of real-world networks, they provide a practical balance between model complexity and computational traceability.

Thank you for your thoughtful review and for recognizing the contributions of our work. We are grateful for your positive assessment of our novel traffic simulation algorithm and its effectiveness in predicting traffic flow in unseen cities using limited training data. We appreciate your acknowledgment of our method's computational efficiency and its potential impact on large-scale networks. We would like to address the weaknesses you noted to provide further clarity and context.

Use of only three cities for training

We understand your concern regarding the limited number of cities used for training. Our primary objective was to demonstrate the capability of our method in a stringent few-shot learning scenario, where data scarcity is a significant challenge. By training on just three cities, we aimed to replicate realistic conditions where extensive historical data may not be available.

Despite the limited training data, our method successfully generalized to unseen cities by leveraging inherent node and edge attributes of the networks. The promising results suggest that our approach captures fundamental patterns and relationships that are transferable across different urban environments. This indicates potential for broader applicability, even with minimal training data.

Additional baselines

Thank you for this valuable suggestion. We focused on comparing our method with GNNs because they represent a prevalent and state-of-the-art approach in traffic flow prediction using graph structures. Our intention was to highlight the limitations of GNNs in few-shot learning scenarios and to showcase the advantages of our simulation-based method under these conditions.

We acknowledge that incorporating additional baseline methods, such as traditional statistical models or other machine learning techniques, could provide a more comprehensive evaluation. Such comparisons could further elucidate the strengths and weaknesses of different approaches in scenarios with limited training data. This is a meaningful direction for future work.

Interpretability

We agree that interpretability is essential, especially in applications like traffic flow prediction where insights can inform policy and planning decisions. Our method offers a degree of interpretability through its reliance on explicit node and edge attributes and the transparent nature of the simulation algorithm.

By using features such as population density, road types, and network topology, our approach allows practitioners to understand how these factors influence predicted traffic flows. The theoretical foundation of our method also provides insights into the relationships between network attributes and flow patterns. We believe this interpretability can be valuable for urban planners and transportation engineers.