CPDA: Class-Conditional Path Distribution Alignment for Unsupervised Time-Series Domain Adaptation

CPDA: Class-Conditional Path Distribution Alignment for Unsupervised Time-Series Domain Adaptation

This paper proposes CPDA, a non-adversarial, discrepancy-based method for unsupervised time-series domain adaptation (DA). The method addresses the challenge of transferring a classifier from a labeled source domain to an unlabeled target domain under distribution shifts. Unlike existing methods that typically align marginal feature distributions, CPDA aligns class-conditional latent path distributions, i.e., Ps (Z1:T Y = c) ≈ Pt (Z1:T Y = c), using source labels and target soft pseudo-labels.

The core of CPDA is a composite signature–spectral kernel that jointly captures four complementary representations of latent temporal paths: (1) pooled semantic features, (2) temporal path structure, (3) frequency-domain information, and (4) low-rank path-signature dynamics. The method introduces a class-conditional discrepancy that is combined with target-smoothness regularization through Virtual Adversarial Training (VAT) to stabilize pseudo-label-based alignment.

The paper provides a theoretical analysis showing that CPDA defines a valid kernel discrepancy (positive semidefinite kernel), admits existing moment-matching methods (MMD, CORAL, DAN, HoMM) as restricted cases or lower-order projections, and yields a class-conditional target-risk bound. The target risk is bounded by the source risk reweighted by target priors plus a term proportional to the class-conditional MMD discrepancy.

Extensive experiments are conducted using CNN, ResNet18, and TCN backbones on 13 different time-series DA benchmarks, comparing CPDA against 30 discrepancy, adversarial, and pseudo-labeling baselines. The results show that CPDA achieves the highest accuracy/F1-score in five out of nine representative dataset–backbone configurations and is competitive in the remaining cases. The strongest gains are observed on datasets with pronounced class-dependent temporal structure, such as HHAR (81.82% accuracy with CNN), uWave (97.30% accuracy with CNN), and EEG (74.39% accuracy with CNN). On the controlled sinusoidal benchmark, CPDA with TCN maintains accuracy above 85% for noise levels b ≤ 1.0 and above 80% up to b = 1.3, demonstrating robustness under increasing noise.

The paper concludes that class-conditional path alignment is particularly effective when discriminative information is encoded in temporal trajectories rather than only in marginal feature statistics. The supplementary material includes the complete implementation, training pipeline, baselines, configurations, and evaluation utilities.

Improvements to AI Systems:

1. Class-Conditional Temporal Alignment Module: Add a non-adversarial discrepancy layer that aligns latent path distributions per class (not just marginal features) using a composite signature–spectral kernel. This allows the system to preserve class-specific temporal dynamics during domain shift, improving transfer learning for time-series data where class identity is encoded in trajectory shape (e.g., gesture recognition, EEG signals).

2. Robust Pseudo-Label Stabilization via Virtual Adversarial Training (VAT): Integrate VAT-based target-smoothness regularization into the alignment objective. This reduces error accumulation from noisy pseudo-labels, making the system more stable when target labels are entirely absent and when domain shift is large or noisy.

3. Unified Kernel Discrepancy Framework: Replace existing moment-matching losses (MMD, CORAL, DAN, HoMM) with the proposed class-conditional path discrepancy. The system automatically captures higher-order temporal dependencies (via path signatures) and frequency-domain features, enabling it to outperform methods that only match first- or second-order statistics.

4. Adaptive Backbone-Agnostic Design: The method works with CNN, ResNet18, and TCN backbones without architectural changes. This allows the improved AI system to be plugged into existing time-series classifiers (e.g., HAR, biomedical signal processing) to gain domain adaptation capability without retraining from scratch.

5. Noise-Robust Transfer for Temporal Signals: The system maintains high accuracy (above 85%) under increasing noise levels (up to b=1.0) and degrades gracefully (above 80% up to b=1.3) on controlled benchmarks. This makes it suitable for real-world sensor data with variable signal-to-noise ratios.

What the Improved AI System Can Do:

• Transfer classifiers across domains (e.g., different users, devices, or environments) for time-series tasks like human activity recognition, EEG-based diagnosis, and gesture recognition, without needing any labels in the target domain.

• Preserve class-specific temporal patterns during adaptation, avoiding the common failure of marginal alignment that washes out discriminative trajectory information.

• Operate reliably under noisy or partially corrupted target data, maintaining performance where adversarial or pseudo-label-only methods degrade.

• Serve as a drop-in replacement for existing DA losses in any time-series deep learning pipeline, improving accuracy by up to 10% on datasets with strong class-dependent temporal structure (e.g., HHAR, uWave, EEG).

• Provide a theoretical guarantee on target risk (bounded by source risk plus class-conditional discrepancy), enabling safer deployment in safety-critical applications like medical monitoring or industrial predictive maintenance.