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.
Junhyoung Chung, Euijong Song, Won Hwa Kim +1stat.ML cs.LG math.ST stat.ME
We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure. Specifically, CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation operators. Consequently, the proposed regularization improves the robustness to local geometric variations. We further prove that the resulting CDOT discrepancy is a valid pseudometric on the space of attributed compact metric-measure spaces. In addition, we characterize the relationship between CDOT and Gromov--Wasserstein (GW) through a new notion of dispersion gap, formally elucidating the geometric source of non-convexity in GW compared to the convexity of CDOT. In the finite-sample regime, we derive a non-asymptotic risk bound decomposed into optimization and statistical errors, establishing risk consistency under a globally convergent Frank--Wolfe algorithm. Experiments on synthetic point clouds, brain connectomes, and graph classification benchmarks demonstrate better performance over existing methods, with stable and reliable behavior in practice.