Deep Joint Distribution Optimal Transport for Universal Domain Adaptation on Time Series

TL;DR

UniJDOT tackles Universal Domain Adaptation for time series by integrating unlabeled target samples into the OT alignment via a joint decision space and an auto-thresholding mechanism, while employing a Fourier Neural Operator–inspired representation for TS data. The method introduces pseudo-labelling with distance-regularized target predictions, anchors for unknown samples, and a block-structured Unbalanced OT objective that aligns common target samples to sources and isolates unknowns through anchors. Empirical results across HAR, HHAR, and Sleep-EDF demonstrate state-of-the-art performance and robustness to threshold settings, outpacing existing UniDA baselines and reducing reliance on manual hyperparameter tuning. The combination of a TS-tailored architecture, auto-thresholding, and joint distribution alignment offers a practical and scalable solution for UniDA in time series, with code available for reproducibility.

Abstract

Universal Domain Adaptation (UniDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain, even when their classes are not fully shared. Few dedicated UniDA methods exist for Time Series (TS), which remains a challenging case. In general, UniDA approaches align common class samples and detect unknown target samples from emerging classes. Such detection often results from thresholding a discriminability metric. The threshold value is typically either a fine-tuned hyperparameter or a fixed value, which limits the ability of the model to adapt to new data. Furthermore, discriminability metrics exhibit overconfidence for unknown samples, leading to misclassifications. This paper introduces UniJDOT, an optimal-transport-based method that accounts for the unknown target samples in the transport cost. Our method also proposes a joint decision space to improve the discriminability of the detection module. In addition, we use an auto-thresholding algorithm to reduce the dependence on fixed or fine-tuned thresholds. Finally, we rely on a Fourier transform-based layer inspired by the Fourier Neural Operator for better TS representation. Experiments on TS benchmarks demonstrate the discriminability, robustness, and state-of-the-art performance of UniJDOT.

Figures (4)

• Figure 1: Overview of the proposed method: The source samples $x_s$ and the target samples $x_t$ are processed by the feature extractor $g$ and the classifier $f$, resulting in a feature space representation $g(x_s)$ (resp. $g(x_t)$) and logits $f(g(x_s))$ (resp. $f(g(x_t))$). $g(x_s)$ are stored in a classwise memory, while some of the $g(x_t)$ serve as anchors in the alignment process after the pseudo-labelling step. The pseudo-labelling step relies on the target logits $f(g(x_t))$ mitigated by a classwise distance of an entire batch to automatically label the target samples as common or unknown. The network is classically trained using a cross-entropy loss on the source samples and an alignment loss between the source and target samples. This alignment loss relies on optimal transport and takes into account the pseudo-labelling step as follows: common target samples are aligned with source samples (in blue), while unknown target samples are aligned with anchors (in red).
• Figure 2: Pseudo-labelling: Each logit $h(x_t)$ is multiplied by a distance-based probability vector $\sigma(-d_t)$ computed using a classwise memory, resulting in the batch $\left\{ p'_t \right\}$. Then, a binary auto-thresholding is applied on the distribution of $\left\{\max ~ p'_t \right\}$ labelling the target samples of the batch.
• Figure 3: Illustration of the decision space on a 2D toy dataset: The color represents the confidence level, determined by either a) the maximum value of $\sigma(h(x))$ or b) the maximum value of $p'_t$. A lighter color corresponds to less confidence.
• Figure 4: Threshold sensitivity: The stars correspond for a) each dataset or b) each scenario. The dot lines show UniJDOT scores when using auto-thresholding. Each color is associated with a dataset.