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Time Series Domain Adaptation via Sparse Associative Structure Alignment

Ruichu Cai, Jiawei Chen, Zijian Li, Wei Chen, Keli Zhang, Junjian Ye, Zhuozhang Li, Xiaoyan Yang, Zhenjie Zhang

arXiv:2012.11797v2cs.LG

TL;DR

Time-series domain adaptation is difficult because time lags, offsets, and dependencies complicate domain-invariant representation extraction. SASA summarizes segments and discovers and aligns sparse associative structure across domains. It outperforms state-of-the-art time-series unsupervised domain adaptation methods on three real-world datasets.

  • Problem

    Offsets, varying time lags, and complex timestamp dependencies make domain-invariant representation extraction challenging for time series.

    Source: Introduction · p. 1

  • Method

    SASA uses adaptive segment summarization and intra- and inter-variable attention to discover sparse associative structure, then aligns that structure across domains.

    Source: Introduction · p. 2

  • Results

    SASA outperforms state-of-the-art time-series unsupervised domain adaptation methods on three real-world datasets.

    Source: Introduction · p. 2

  • Takeaways & Limitations

    The approach offers a solution for time-series domain adaptation and provides insights into what knowledge transfers across domains.

    Source: Conclusion · p. 7

    The formulation assumes source and target data are generated from a shared causal mechanism and share the same associative structure.

    Source: Problem Formulation and Overview · p. 3

Abstract

from arXiv · show

Domain adaptation on time series data is an important but challenging task. Most of the existing works in this area are based on the learning of the domain-invariant representation of the data with the help of restrictions like MMD. However, such extraction of the domain-invariant representation is a non-trivial task for time series data, due to the complex dependence among the timestamps. In detail, in the fully dependent time series, a small change of the time lags or the offsets may lead to difficulty in the domain invariant extraction. Fortunately, the stability of the causality inspired us to explore the domain invariant structure of the data. To reduce the difficulty in the discovery of causal structure, we relax it to the sparse associative structure and propose a novel sparse associative structure alignment model for domain adaptation. First, we generate the segment set to exclude the obstacle of offsets. Second, the intra-variables and inter-variables sparse attention mechanisms are devised to extract associative structure time-series data with considering time lags. Finally, the associative structure alignment is used to guide the transfer of knowledge from the source domain to the target one. Experimental studies not only verify the good performance of our methods on three real-world datasets but also provide some insightful discoveries on the transferred knowledge.

Introduction

Time-series domain adaptation uses labeled source and unlabeled target data to address domain shift, but temporal offsets, time-lag variation, and inter-variable dependencies complicate domain-invariant representation learning. SASA instead discovers and aligns sparse associative structure to transfer knowledge across domains.

  • Domain-invariant representation learning is challenging because small differences in offsets or time lags can disrupt extraction from dependent time series.Existing RNN-based approaches also assume equal conditional distributions and may ignore associations among variables, risking overfitting.Source: Introduction · p. 1
  • The method is motivated by stable causal structure shared across domains, while redundant and domain-specific associations can lead to overfitting.The paper uses sparse associative structure as a relaxed target for transfer.Source: Introduction · p. 2, Figure 2 · p. 2
  • SASA combines adaptive segment summarization, intra- and inter-variable attention, and structure alignment, outperforming state-of-the-art time-series adaptation methods on three real-world datasets.Source: Introduction · p. 2
  • Adaptive segment summarization addresses offsets, while intra- and inter-variable attention extracts associative structure in the presence of varying time lags.The paper illustrates offsets and response-time differences as distinct temporal discrepancies.Source: Figure 1 · p. 1, Introduction · p. 2

Related Works

Prior domain adaptation work includes representation alignment, adversarial approaches, and causal perspectives, while time-series methods often adapt recurrent feature extraction. This paper proposes sparse associative structure discovery and alignment for time-series adaptation.

Domain Adaptation on Non-Time Series Data

  • Non-time-series adaptation includes MMD, second-order statistics, and multi-kernel alignment, as well as adversarial domain classifiers and class-centroid alignment.Source: Related Works · p. 2

Causal domain adaptation

  • Causal perspectives classify domain adaptation settings by causal mechanism and include methods that recover disentangled semantic representations in latent space.Source: Related Works · p. 2

Domain Adaptation on Time Series data

  • The framework depicts adaptive segment summarization, sparse structure discovery through intra- and inter-variable attention, and source–target structure alignment.Source: Figure 3 · p. 3
  • Prior time-series approaches use RNN or variational RNN representations, while direct extensions of non-time-series methods may struggle to align conditional distributions across timestamps.Source: Related Works · p. 3
  • The proposed method distills sparse associative structure and filters domain-specific information to address limited alignment of time-series conditional distributions.Source: Related Works · p. 3

Sparse Associative Structure Alignment

SASA addresses unsupervised time-series domain adaptation by treating shared causal mechanisms as motivation to extract and align sparse associative structures. It uses candidate segments and intra- and inter-variable attention to form representations for target-domain prediction.

Problem Formulation and Overview

  • SASA formulates unsupervised adaptation with labeled source samples, unlabeled target samples, and a shared causal mechanism that implies shared associative structure.Its goal is to predict target labels from target time series.Source: Problem Formulation and Overview · p. 3

Adaptive Segment Summarization

  • Candidate segments address offsets that can obscure when a variable changes and when it influences other variables.The method constructs multiple segment lengths per variable and encodes segments with a variable-specific LSTM.Source: Adaptive Segment Summarization · p. 4

Sparse Associative Structure Discovery

  • Intra-variable attention selects among candidate segment representations, while MMD regularizes segment weights to make durations more similar across domains.Sparsemax produces sparse weights for the segment representations.Source: Segments Representation Selection via… · p. 4
  • Inter-variable attention reconstructs sparse associations while accounting for time lags that can make associations estimated without lag information inaccurate.Sparsemax normalizes association degrees, whose strengths are considered across segment durations.Source: Sparse Associative Structure… · pp. 4–5

Sparse Associative Structure Alignment

Model Summary

  • The model combines weighted segment and associative-structure representations as input to a label classifier, using cross-entropy for classification or RMSE for regression.The trained classifier is adapted to the target domain.Source: Task based Label Predictor · p. 5

Experiments and Result

Experiments evaluate SASA on boiler fault, air-quality forecasting, and in-hospital mortality transfer, then test its segment-length and sparse-alignment components and visualize aligned structure.

Setup

Baseline

  • For a fair comparison, baseline and SASA parameter counts are about equal, and each experiment uses three random seeds.Table 3 reports parameter totals across methods and datasets.Source: Baseline · p. 6, Table 3 · p. 6

Model Variants

  • The model variants remove either the segment-length restriction loss Lα or the sparse associative structure alignment loss Lβ.These variants are named SASA-α and SASA-β, respectively.Source: Model Variants · p. 6

Result

Ablation Study and Visualization

  • Removing Lα lowers performance because segment duration varies across domains, while the restriction excludes the influence of domain-specific durations.α represents the probability of segment length.Source: The study of the usefulness of the… · p. 7
  • Removing the sparse alignment loss makes SASA-β worse than standard SASA, though it remains better than other baselines.The paper attributes the remaining advantage to Lα aligning offsets between domains.Source: The study of the effectiveness of… · p. 7
  • The Beijing and Shenzhen associative structures are sparse and share many relationships; darker matrix colors indicate stronger associations.Figure 4 visualizes the aligned structures over the air-quality dataset.Source: Visualization of Aligned Structure · p. 7, Figure 4 · p. 7

Conclusion

The paper presents SASA for time-series unsupervised domain adaptation, combining sparse associative structure discovery with adaptive segment summarization and MMD-based structure alignment. It concludes that the approach offers an effective solution and provides insights into transferable time-series knowledge.

Conclusion

  • SASA combines sparse associative structure discovery with MMD-based alignment to transfer knowledge from source to target time-series data.Adaptive summarization of series segments supports structure extraction.Source: Conclusion · p. 7
  • The proposed approach provides an effective solution for time-series domain adaptation.Source: Conclusion · p. 7
  • The approach also offers insights into what is transferable in time-series data.Source: Conclusion · p. 7

Statement About The Potential Ethical Impact

The authors describe potential benefits of time-series domain adaptation for unlabeled test data and low-resource settings. They also note interpretability concerns and suggest incorporating causality as a possible improvement.

Statement About The Potential Ethical Impact

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