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

arXiv: https://arxiv.org/abs/2407.14303 · HTML: https://mlsanity.com/paper/2407.14303/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 74 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Generalized Source-free Domain Adaptation](https://mlsanity.com/paper/2108.01614/) (2021)
- [DeepSleepNet: a Model for Automatic Sleep Stage Scoring based on Raw Single-Channel EEG](https://mlsanity.com/paper/1703.04046/) (2017)
- [Correlation Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1612.01939/) (2016)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [XSleepNet: Multi-View Sequential Model for Automatic Sleep Staging](https://mlsanity.com/paper/2007.05492/) (2020)
- [Transfer Learning for Brain-Computer Interfaces: A Euclidean Space Data Alignment Approach](https://mlsanity.com/paper/1808.05464/) (2018)
- [Unsupervised Multi-source Domain Adaptation Without Access to Source Data](https://mlsanity.com/paper/2104.01845/) (2021)
- [Benchmarking Distribution Shift in Tabular Data with TableShift](https://mlsanity.com/paper/2312.07577/) (2023)
- [A deep learning architecture for temporal sleep stage classification using multivariate and multimodal time series](https://mlsanity.com/paper/1707.03321/) (2017)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Multi-source Domain Adaptation via Weighted Joint Distributions Optimal Transport](https://mlsanity.com/paper/2006.12938/) (2020)
- [Wasserstein Style Transfer](https://mlsanity.com/paper/1905.12828/) (2019)
- [Concentration bounds for linear Monge mapping estimation and optimal transport domain adaptation](https://mlsanity.com/paper/1905.10155/) (2019)
- [ADAST: Attentive Cross-domain EEG-based Sleep Staging Framework with Iterative Self-Training](https://mlsanity.com/paper/2107.04470/) (2021)
- [On The Effects Of Data Normalisation For Domain Adaptation On EEG Data](https://mlsanity.com/paper/2210.01081/) (2022)
- [Calibration-free online test-time adaptation for electroencephalography motor imagery decoding](https://mlsanity.com/paper/2311.18520/) (2023)
- [A Systematic Evaluation of Euclidean Alignment with Deep Learning for EEG Decoding](https://mlsanity.com/paper/2401.10746/) (2024)
- [Non-Asymptotic Pointwise and Worst-Case Bounds for Classical Spectrum Estimators](https://mlsanity.com/paper/2303.11908/) (2023)

## Built on by (most cited first, 6 of 6)

- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Leveraging Generic Time Series Foundation Models for EEG Classification](https://mlsanity.com/paper/2510.27522/) (2025)
- [PSDNorm: Test-Time Temporal Normalization for Deep Learning in Sleep Staging](https://mlsanity.com/paper/2503.04582/) (2025)
- [HEEGNet: Hyperbolic Embeddings for EEG](https://mlsanity.com/paper/2601.03322/) (2026)
- [SPDAlign: Interpretable Riemannian Alignment for EEG Forward Modeling Shifts](https://mlsanity.com/paper/2610.06315/) (2026)
- [Source-Learned Reliance for Selective Test-Time Adaptation of Multimodal Time Series](https://mlsanity.com/paper/2610.07499/) (2026)

## Abstract (arXiv)

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 O(nℓ-1/2) with nℓ 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.