Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications
This work addresses domain adaptation for neuroscience applications like MEG analysis, offering a method to handle task variations with limited labeled data, though it appears incremental as it builds on existing optimal transport and Riemannian approaches.
The paper tackles the challenge of limited labeled time series data in domain adaptation by introducing Mixing model Stiefel Adaptation (MSA), which leverages unlabeled target data and theoretical Stiefel matrix estimation to align covariances, resulting in improved performance in brain-age regression with MEG signals.
This paper introduces a novel domain adaptation technique for time series data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the challenge of limited labeled signals in the target dataset. Leveraging a domain-dependent mixing model and the optimal transport domain adaptation assumption, we exploit abundant unlabeled data in the target domain to ensure effective prediction by establishing pairwise correspondence with equivalent signal variances between domains. Theoretical foundations are laid for identifying crucial Stiefel matrices, essential for recovering underlying signal variances from a Riemannian representation of observed signal covariances. We propose an integrated cost function that simultaneously learns these matrices, pairwise domain relationships, and a predictor, classifier, or regressor, depending on the task. Applied to neuroscience problems, MSA outperforms recent methods in brain-age regression with task variations using magnetoencephalography (MEG) signals from the Cam-CAN dataset.