Evidentially Calibrated Source-Free Time-Series Domain Adaptation with Temporal Imputation

TL;DR

This paper tackles source-free domain adaptation for time-series data by introducing MAPU, which uses a temporal imputation task to capture source temporal dynamics and enforce temporal consistency in the target through a learned imputer in feature space. An extension, E-MAPU, incorporates evidential uncertainty via a Dirichlet-based head to produce calibrated predictions and guide adaptation by minimizing evidential entropy on out-of-support target samples. Across five real-world datasets, MAPU and especially E-MAPU demonstrate substantial gains over both conventional UDA and SFDA baselines, highlighting the value of temporal imputation plus calibrated uncertainty for robust time-series adaptation. The methods are shown to be versatile, enabling integration with existing SFDA approaches, and the evidential framework provides improved calibration and reliability for practical deployment where source data cannot be accessed during adaptation.

Abstract

Source-free domain adaptation (SFDA) aims to adapt a model pre-trained on a labeled source domain to an unlabeled target domain without access to source data, preserving the source domain's privacy. While SFDA is prevalent in computer vision, it remains largely unexplored in time series analysis. Existing SFDA methods, designed for visual data, struggle to capture the inherent temporal dynamics of time series, hindering adaptation performance. This paper proposes MAsk And imPUte (MAPU), a novel and effective approach for time series SFDA. MAPU addresses the critical challenge of temporal consistency by introducing a novel temporal imputation task. This task involves randomly masking time series signals and leveraging a dedicated temporal imputer to recover the original signal within the learned embedding space, bypassing the complexities of noisy raw data. Notably, MAPU is the first method to explicitly address temporal consistency in the context of time series SFDA. Additionally, it offers seamless integration with existing SFDA methods, providing greater flexibility. We further introduce E-MAPU, which incorporates evidential uncertainty estimation to address the overconfidence issue inherent in softmax predictions. To achieve that, we leverage evidential deep learning to obtain a better-calibrated pre-trained model and adapt the target encoder to map out-of-support target samples to a new feature representation closer to the source domain's support. This fosters better alignment, ultimately enhancing adaptation performance. Extensive experiments on five real-world time series datasets demonstrate that both MAPU and E-MAPU achieve significant performance gains compared to existing methods. These results highlight the effectiveness of our proposed approaches for tackling various time series domain adaptation problems.

Figures (10)

• Figure 1: (a) How do the temporal relations matter in time series? Despite similarities in the values of the two signals, variations in the temporal position of their observations can result in different predictions. (b) Conventional entropy is not a reliable uncertainty estimator as it shows low uncertainty for both source and target domains. (c) The average calibration errors were calculated by using softmax scores and evidential learning on the UCIHAR dataset. Pre-training using evidential deep learning provides a better-calibrated model. (d) Our proposed approach with its evidential head can provide high uncertainty for the target domain and hence can detect the target samples outside the source support.
• Figure 2: Adaptation with Temporal Imputation. Left: A temporal imputer network is trained to predict the full sequence from its masked version to capture the temporal information of the source domain. Right: Once trained, the temporal imputer network guides the target model to produce temporally consistent features with the source domain. (Best in viewed in colors. Components in red color are trainable, while those in gray color are non-trainable).
• Figure 3: Adaptation with Temporal Imputation for time series data. Left: The pretraining stage of the temporal imputer network $j_\theta$ to capture the temporal dynamics of the source domain. First, we perform random masking across the time dimension of the source signal. Given the original source signal $X_S$ and its temporally masked signal $X_S^\prime$, the encoder network $f_\theta$ is used to generate the corresponding latent features $H_S$ and $H_S^\prime$ respectively. Subsequently, $j_\theta$ is updated to produce imputed features $\hat{H}_S$ from masked features $H_S^\prime$ using the mean square error loss. Right: The adaptation stage of the encoder network on the target domain data. The encoder $f_\theta$ is updated to produce source-like features that are imputable by the pre-trained $j_\theta$.
• Figure 4: The illustration of Evidential Source Free Adaptation with Temporal Masking (Best viewed in colors). Left: In the pretraining stage, the source model is trained using evidential cross-entropy loss $\mathcal{L}_{cls}^{evd}$, and the temporal imputer network is trained using $\mathcal{L}_{mapu}^S$ to impute the features of the masked signals and capture the source temporal information on the feature space. Right: In the adaptation stage, the target model is jointly trained with both an evidential adaptation loss $\mathcal{L}_{evidence}$ and our temporal imputation loss $\mathcal{L}_{mapu}^T$ to perform the adaptation while ensuring temporal consistency with the source features. The $h_S^\prime$ and $h_T^\prime$ are the feature representations of the input signals extracted by the encoder $f_\theta$ in the source and target domains, respectively.
• Figure 5: Intergrating temporal imputation with existing SFDA methods among the three datasets. (a) UCIHAR dataset. (b) MFD dataset. (c) SSC dataset. (d) HHAR dataset. (e) WISDM dataset.