ST-FiT: Inductive Spatial-Temporal Forecasting with Limited Training Data

TL;DR

ST-FiT tackles inductive spatial-temporal forecasting when only a subset of nodes have temporal data during training. It integrates temporal data augmentation via manifold mix-up in a VAE latent space with a sparsity-driven spatial topology learner that leverages Gumbel-Softmax, all built to be backbone-agnostic for STGNNs. Through an iterative two-phase optimization, ST-FiT generates diverse temporal dependencies and adapts spatial relations to improve forecasting for nodes with no training data, achieving strong generalization and competitive results without fine-tuning on real datasets. This approach broadens the practical deployment of STGNNs in real-world, data-scarce scenarios by reducing data and computation requirements while preserving predictive accuracy.

Abstract

Spatial-temporal graphs are widely used in a variety of real-world applications. Spatial-Temporal Graph Neural Networks (STGNNs) have emerged as a powerful tool to extract meaningful insights from this data. However, in real-world applications, most nodes may not possess any available temporal data during training. For example, the pandemic dynamics of most cities on a geographical graph may not be available due to the asynchronous nature of outbreaks. Such a phenomenon disagrees with the training requirements of most existing spatial-temporal forecasting methods, which jeopardizes their effectiveness and thus blocks broader deployment. In this paper, we propose to formulate a novel problem of inductive forecasting with limited training data. In particular, given a spatial-temporal graph, we aim to learn a spatial-temporal forecasting model that can be easily generalized onto those nodes without any available temporal training data. To handle this problem, we propose a principled framework named ST-FiT. ST-FiT consists of two key learning components: temporal data augmentation and spatial graph topology learning. With such a design, ST-FiT can be used on top of any existing STGNNs to achieve superior performance on the nodes without training data. Extensive experiments verify the effectiveness of ST-FiT in multiple key perspectives.

Figures (8)

• Figure 1: An exemplary spatial-temporal graph where only the temporal data corresponding to a few nodes is accessible during training: on a geographical graph among different cities, only a few cities have available pandemic dynamics at the current time point (marked in red) due to the asynchronous nature of outbreaks. Here, the virus mark denotes the cities that have gone through outbreaks.
• Figure 2: An overview of ST-FiT, including a STGNN backbone, temporal data augmentation, and spatial topology learning.
• Figure 3: The performance of ST-FiT compared to baselines with different training node ratios. As training node ratio decreases, the performances of all models drops, while ST-FiT outperforms other baselines over all ratios consistently.
• Figure 4: Performance of ST-FiT with different mix-up ratios $\lambda$ and sparse thresholds $\o$. The mix-up ratio behaves slight influence, while the positive correlation between mix-up ratio $\lambda$ and the performance still exhibits. Sparsity has positive correlation with performance, while extreme sparsity brings negative influence due to loss of key connections.
• Figure 5: The performance of ST-FiT compared to baselines with different training node ratios. As training node ratio decreases, performances of all models drops, while ST-FiT outperforms other baselines over all ratios consistently.

Theorems & Definitions (1)

• Definition 1