A multi-scale patch transformer for cross-sequence forecasting: Application to EMG-respiration prediction

Accurately predicting respiratory signals from electromyography envelopes is crucial for non-invasively assessing respiratory muscle effort and fatigue. Unlike traditional forecasting, such tasks present the unique challenge of Cross-Sequence Time Series Forecasting (CSTSF), which predicts a target sequence from different source sequences. However, CSTSF is under-researched compared to traditional intra-sequence forecasting, and conventional forecasting models are often inapplicable to CSTSF tasks: they often cannot handle the differing input/output variable counts inherent to such tasks due to their architectural design. To address these limitations, we propose a novel decoupled framework that decomposes the CSTSF task into two sequential stages: intra-sequence forecasting and cross-sequence mapping, which are jointly optimized via a hybrid loss function. This design allows any conventional time series forecasting model to be readily adapted for CSTSF tasks by simply integrating a modality transition module. Within this framework, we further introduce the Multi-Scale Patch Transformer (MSPFormer), which integrates an advanced multi-scale patching backbone to capture multi-period features with our Attention-based Modality Transition (AMT) module to efficiently perform the crucial cross-sequence mapping. Extensive experiments on the private EMG-Respiration dataset and the public Traffic and Electricity dataset for CSTSF demonstrate our model's improved results over state-of-the-art forecasting methods. This work offers a robust CSTSF solution, with significant potential for applications like non-invasive physiological signal estimation.