MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation

TL;DR

MTSCI tackles missing data in multivariate time series by enforcing imputation consistency through a conditional diffusion framework. It introduces a contrastive complementary mask to create dual views for intra-consistency and uses a context-aware mixup with an inter-consistency network to incorporate adjacent-window information during denoising. Empirical results across three real datasets show MTSCI achieving state-of-the-art performance on MAE, RMSE, and MAPE under both point and block missing patterns, with ablations confirming the necessity of both components. The approach enhances the reliability of imputed sequences and offers a principled way to leverage temporal context in diffusion-based imputation.

Abstract

Missing values are prevalent in multivariate time series, compromising the integrity of analyses and degrading the performance of downstream tasks. Consequently, research has focused on multivariate time series imputation, aiming to accurately impute the missing values based on available observations. A key research question is how to ensure imputation consistency, i.e., intra-consistency between observed and imputed values, and inter-consistency between adjacent windows after imputation. However, previous methods rely solely on the inductive bias of the imputation targets to guide the learning process, ignoring imputation consistency and ultimately resulting in poor performance. Diffusion models, known for their powerful generative abilities, prefer to generate consistent results based on available observations. Therefore, we propose a conditional diffusion model for Multivariate Time Series Consistent Imputation (MTSCI). Specifically, MTSCI employs a contrastive complementary mask to generate dual views during the forward noising process. Then, the intra contrastive loss is calculated to ensure intra-consistency between the imputed and observed values. Meanwhile, MTSCI utilizes a mixup mechanism to incorporate conditional information from adjacent windows during the denoising process, facilitating the inter-consistency between imputed samples. Extensive experiments on multiple real-world datasets demonstrate that our method achieves the state-of-the-art performance on multivariate time series imputation task under different missing scenarios. Code is available at https://github.com/JeremyChou28/MTSCI.

Figures (5)

• Figure 1: (a) Previous methods only use the observed values in a single window to impute missing values. (b) Our method uses the adjacent window to assist in imputation to maintain inter-consistency, and constraints the imputed targets reciprocally reconstruct the observed values for intra-consistency.
• Figure 2: Overview of MTSCI. The intra contrastive module is used to maintain intra-consistency between imputed and observed values. The inter-consistency condition network is utilized to facilitate the inter-consistency between adjacent windows. The model is optimized using a combination of denoising loss $\mathcal{L}_\theta$ and intra contrastive loss $\mathcal{L}_{CL}$.
• Figure 3: Ablation study of MTSCI.
• Figure 4: The visualization of the imputation results of snapshots on three datasets: MTSCI vs CSDI and MTSCI vs three variants.
• Figure 5: Hyperparameter study on four key parameters of MTSCI: the size of hidden dimension $d_h$, the number of encoder-layer $l$ in denoising network, the maximum noise level $\beta_K$ and the weighted coefficient $\lambda$ of intra-consistency loss. Both RMSE and MAPE are reported.

Theorems & Definitions (1)

• Definition 1: Multivariate Time Series.