CPDA: Class-Conditional Path Distribution Alignment for Unsupervised Time-Series Domain Adaptation
Authors: Felix Ott, Christopher Mutschler
Organizations: Fraunhofer Institute for Integrated Circuits IIS, 90411 Nürnberg, Germany · Machine Learning and Positioning Systems Department, University of Technology Nürnberg (UTN), 90461 Nürnberg
Abstract
Unsupervised time-series domain adaptation (DA) addresses the challenge of transferring a classifier from a labeled source domain to an unlabeled target domain under distribution shifts induced by different users, sensors, devices, acquisition conditions, or temporal dynamics. Existing methods typically mitigate this shift by aligning marginal feature distributions through adversarial training, optimal transport, or moment-based discrepancies. In this paper, we propose Class-Conditional Path Distribution Alignment (CPDA), a non-adversarial discrepancy-based framework that aligns source and target class-conditional latent path distributions rather than only global feature marginals. CPDA introduces a composite signature-spectral kernel that jointly captures pooled semantic features, temporal path structure, frequency-domain information, and low-rank path-signature dynamics, while using source labels and target soft pseudo-labels to perform class-preserving alignment. We further provide a theoretical analysis showing that CPDA defines a valid kernel discrepancy, admits existing moment-matching methods as restricted cases, and yields a class-conditional target-risk bound. Extensive experiments with CNN, ResNet18, and TCN backbones on 13 different time-series DA benchmarks demonstrate the effectiveness of CPDA against 30 discrepancy, adversarial, and pseudo-labeling baselines.
The goal of source-free domain adaptation (SFDA) for time-series data is to transfer knowledge from a pre-trained source model to an unlabeled target domain without requiring access to source data, while addressing feature shift and temporal drift inherent in the signals. Although existing approaches have explored temporal dynamics in unsupervised source-free adaptation, they largely overlook spectral shifts in time-series data. Towards this end, we propose a novel approach termed temporal-Spectral Alignment with Frequency Adaptation (SAFA) for source-free time-series domain adaptation. Specifically, we first model the source domain at multiple scales by jointly capturing temporal dependencies and spectral characteristics. To adapt time-series data in the target domain, we introduce a trainable frequency adaptation module that modulates the phase and amplitude of target signals in the frequency domain to align them with the source distribution. Extensive experiments on multiple benchmark datasets demonstrate the efficacy and robustness of SAFA.
Correlation alignment and the maximum mean discrepancy are two widely used distribution-matching frameworks for unsupervised domain adaptation (UDA). However, high variance in these losses has been shown to undermine their effectiveness in minibatch optimisation settings. Furthermore, the losses lack finite-sum structure, which renders them incompatible with classical stochastic variance reduction (SVR) methods. This paper proposes Paired Sampling for Domain Adaptation (PSDA), a novel SVR technique tailored to such objectives. PSDA pairs observations both within and across domains, to form quadruplets that are always sampled together during training. The pairings are designed to minimise expected gradient variance, and reduce to solving a set of linear assignment problems. Our simulations demonstrate reduced variance compared to related methods, and experiments on three domain shift datasets show improved target domain accuracy.
We propose a unified framework for addressing three key challenges of distribution shift: (1) estimating a model's performance on an unlabeled target domain, (2) explaining the shift by identifying the features responsible, and (3) improving the target domain performance. Our method, Entropic Projection Alignment (EPA), aligns the source distribution to the target by matching carefully selected moments while simultaneously minimising the KL divergence from the source. This formulation yields a unique closed-form solution for importance weights, achieving robustness through implicit variance control. Drawing on domain adaptation theory, we establish that moment matching is sufficient for reliable estimation and adaptation, avoiding the need for full density ratio recovery. Extensive experiments, together with strong theoretical guarantees, demonstrate that EPA consistently outperforms state-of-the-art baselines while offering substantial computational efficiency.