KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy

TL;DR

KITS addresses the challenge of inductive spatio-temporal kriging under sparse sensor deployment by explicitly mitigating the graph gap between training (observed-only) and inference (observed+unobserved) graphs. It introduces an Increment training strategy that inserts virtual nodes to mimic unobserved locations, and couples this with STGC for spatio-temporal aggregation, Reference-based Feature Fusion to align virtual and observed features, and Node-aware Cycle Regulation to provide pseudo supervision. Empirical evaluations across eight real-world datasets demonstrate large performance gains over strong inductive baselines (up to 18.33% MAE and 30.54% MAPE improvements) and strong transductive results, highlighting the method’s robustness and transferability. The work advances practical kriging under sparse sensing and provides a blueprint for leveraging virtual graph augmentation in inductive graph-based interpolation tasks.

Abstract

Sensors are commonly deployed to perceive the environment. However, due to the high cost, sensors are usually sparsely deployed. Kriging is the tailored task to infer the unobserved nodes (without sensors) using the observed source nodes (with sensors). The essence of kriging task is transferability. Recently, several inductive spatio-temporal kriging methods have been proposed based on graph neural networks, being trained based on a graph built on top of observed nodes via pretext tasks such as masking nodes out and reconstructing them. However, the graph in training is inevitably much sparser than the graph in inference that includes all the observed and unobserved nodes. The learned pattern cannot be well generalized for inference, denoted as graph gap. To address this issue, we first present a novel Increment training strategy: instead of masking nodes (and reconstructing them), we add virtual nodes into the training graph so as to mitigate the graph gap issue naturally. Nevertheless, the empty-shell virtual nodes without labels could have bad-learned features and lack supervision signals. To solve these issues, we pair each virtual node with its most similar observed node and fuse their features together; to enhance the supervision signal, we construct reliable pseudo labels for virtual nodes. As a result, the learned pattern of virtual nodes could be safely transferred to real unobserved nodes for reliable kriging. We name our new Kriging model with Increment Training Strategy as KITS. Extensive experiments demonstrate that KITS consistently outperforms existing kriging methods by large margins, e.g., the improvement over MAE score could be as high as 18.33%.

Figures (9)

• Figure 1: Decrement and Increment training strategies. (a) Decrement training strategy: observe nodes 1-3 during training, and mask node-3 out to reconstruct. (b) Kriging (inference phase): observe nodes 1-3, infer the values of new nodes 4-5. (c) A scenario of training and inference data. (d) Increment training strategy: observe nodes 1-3, insert virtual nodes 4-6 to mimic the target unobserved nodes in inference, and learn to directly estimate their values.
• Figure 2: Overview of KITS. (a) Illustration of the procedure of generating multiple training graphs by inserting virtual nodes with randomness (so as to cover different possible inference graphs); (b) Illustration of the kriging model and the Node-aware Cycle Regulation (NCR) (based on Batch 1).
• Figure 3: Details of Spatio-Temporal Graph Convolution (STGC). Take the data from three time intervals, and node-1 as an example, its neighbors' information ($T_{i-1:i+1}$) would be propagated to node-1 ($T_i$) for features aggregation.
• Figure 4: Details of Reference-based Feature Fusion (RFF) for training. In the inference phase, the target unobserved nodes/features would take the role of virtual nodes/features.
• Figure 5: Comparisons between Decrement and Increment training strategies.