STDCformer: A Transformer-Based Model with a Spatial-Temporal Causal De-Confounding Strategy for Crowd Flow Prediction

Existing works typically treat spatial-temporal prediction as the task of learning a function F to transform historical observations to future observations. We further decompose this cross-time transformation into three processes: (1) Encoding (E): learning the intrinsic representation of observations, (2) Cross-Time Mapping (M): transforming past representations into future representations, and (3) Decoding (D): reconstructing future observations from the future representations. From this perspective, spatial-temporal prediction can be viewed as learning F = E · M · D, which includes learning the space transformations leftE,Dright between the observation space and the hidden representation space, as well as the spatial-temporal mapping M from future states to past states within the representation space. This leads to two key questions: Q1: What kind of representation space allows for mapping the past to the future? Q2: How to achieve map the past to the future within the representation space? To address Q1, we propose a Spatial-Temporal Backdoor Adjustment strategy, which learns a Spatial-Temporal De-Confounded (STDC) representation space and estimates the de-confounding causal effect of historical data on future data. This causal relationship we captured serves as the foundation for subsequent spatial-temporal mapping. To address Q2, we design a Spatial-Temporal Embedding (STE) that fuses the information of temporal and spatial confounders, capturing the intrinsic spatial-temporal characteristics of the representations. Additionally, we introduce a Cross-Time Attention mechanism, which queries the attention between the future and the past to guide spatial-temporal mapping.