Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignment

TL;DR

This paper introduces Spatio-Temporal Monge Alignment (STMA), an optimal transport-based method for domain adaptation in multivariate signals, enabling test-time adaptation without retraining and demonstrating significant performance improvements.

Contribution

The paper proposes a novel OT-based framework for multi-source and test-time domain adaptation on multivariate signals, with theoretical guarantees and practical effectiveness.

Findings

STMA improves cross-domain performance on biosignals and images.

Theoretical bounds show efficient bias-variance trade-off in mappings.

Numerical experiments confirm STMA's complementary role to deep learning methods.

Abstract

Machine learning applications on signals such as computer vision or biomedical data often face significant challenges due to the variability that exists across hardware devices or session recordings. This variability poses a Domain Adaptation (DA) problem, as training and testing data distributions often differ. In this work, we propose Spatio-Temporal Monge Alignment (STMA) to mitigate these variabilities. This Optimal Transport (OT) based method adapts the cross-power spectrum density (cross-PSD) of multivariate signals by mapping them to the Wasserstein barycenter of source domains (multi-source DA). Predictions for new domains can be done with a filtering without the need for retraining a model with source data (test-time DA). We also study and discuss two special cases of the method, Temporal Monge Alignment (TMA) and Spatial Monge Alignment (SMA). Non-asymptotic concentration bounds are derived for the mappings estimation, which reveals a bias-plus-variance error structure with a variance decay rate of $\mathcal{O}(n_\ell^{-1/2})$ with $n_\ell$ the signal length. This theoretical guarantee demonstrates the efficiency of the proposed computational schema. Numerical experiments on multivariate biosignals and image data show that STMA leads to significant and consistent performance gains between datasets acquired with very different settings. Notably, STMA is a pre-processing step complementary to state-of-the-art deep learning methods.