Conditional Lagrangian Wasserstein Flow for Time Series Imputation

TL;DR

This paper introduces Conditional Lagrangian Wasserstein Flow (CLWF), a novel time series imputation method that leverages Lagrangian mechanics and denoising autoencoders to improve efficiency and accuracy over existing diffusion-based approaches.

Contribution

The paper proposes a new time series imputation method, CLWF, combining Lagrangian mechanics with gradient estimation via autoencoders, addressing diffusion model limitations.

Findings

Competitive performance against state-of-the-art methods

Faster inference due to non-diffusion approach

Effective gradient estimation with denoising autoencoder

Abstract

Time series imputation is important for numerous real-world applications. To overcome the limitations of diffusion model-based imputation methods, e.g., slow convergence in inference, we propose a novel method for time series imputation in this work, called Conditional Lagrangian Wasserstein Flow (CLWF). Following the principle of least action in Lagrangian mechanics, we learn the velocity by minimizing the corresponding kinetic energy. Moreover, to enhance the model's performance, we estimate the gradient of a task-specific potential function using a time-dependent denoising autoencoder and integrate it into the base estimator to reduce the sampling variance. Finally, the proposed method demonstrates competitive performance compared to other state-of-the-art imputation approaches.