Exploiting the Prior of Generative Time Series Imputation

TL;DR

The paper tackles the challenge of imputing missing values in time series by addressing the mismatch between priors and ground truth that hampers generative imputation methods. It introduces Bridge-TS, a data-to-data framework that leverages informative priors from deterministic models and refines them via a Schrödinger Bridge to reach the target distribution efficiently. The authors formalize expert priors and compositional priors, with a tractable linear-Gaussian SB solution and a bridge-loss objective, and validate the approach on six benchmark datasets where Bridge-TS achieves state-of-the-art MSE/MAE across varying missing ratios. Ablation studies show the importance of probabilistic modeling, appropriate noise schedules, and prudent training of priors, underscoring the practical impact of integrating reliable priors into generative imputation for robust and accurate time-series reconstruction.

Abstract

Time series imputation, i.e., filling the missing values of a time recording, finds various applications in electricity, finance, and weather modelling. Previous methods have introduced generative models such as diffusion probabilistic models and Schrodinger bridge models to conditionally generate the missing values from Gaussian noise or directly from linear interpolation results. However, as their prior is not informative to the ground-truth target, their generation process inevitably suffer increased burden and limited imputation accuracy. In this work, we present Bridge-TS, building a data-to-data generation process for generative time series imputation and exploiting the design of prior with two novel designs. Firstly, we propose expert prior, leveraging a pretrained transformer-based module as an expert to fill the missing values with a deterministic estimation, and then taking the results as the prior of ground truth target. Secondly, we explore compositional priors, utilizing several pretrained models to provide different estimation results, and then combining them in the data-to-data generation process to achieve a compositional priors-to-target imputation process. Experiments conducted on several benchmark datasets such as ETT, Exchange, and Weather show that Bridge-TS reaches a new record of imputation accuracy in terms of mean square error and mean absolute error, demonstrating the superiority of improving prior for generative time series imputation.

Figures (3)

• Figure 1: Comparison of three time series imputation approaches. Deterministic methods directly map observed data to targets, ignoring missing segments' priors. Diffusion models use iterative Gaussian sampling and our proposed Bridge-TS starts with expert priors, providing a more precise starting point and efficiently reaching the target distribution via bridge models.
• Figure 2: An example of how Bridge-TS works. Prior from different experts are concatenated. The concatenated priors are fed to the Schrödinger bridge with optimization trget as concatenated truth. The final output of the bridge are averaged channel-wise to give the final result.
• Figure 3: An example of Bridge-TS-2 results. Black line corresponds to the ground truth. Red, blue and green corresponds to the outputs of Bridge-TS-2, Non-stationary Transformer and TimesNet. Non-stationary Transformer and TimesNet are used as compositional priors for the Bridge-TS-2 model. The top row gives each model's imputation results and the bottom row gives point-wise imputation errors. It is obvious that Bridge-TS-2 can generate imputed time series that has smaller errors from compositional priors with larger errors.