Conditional Lagrangian Wasserstein Flow for Time Series Imputation

2024-10-10

arXiv.org

AI Summary

Time-series imputation faces challenges including slow diffusion-model inference and high sampling variance. This paper proposes Conditional Lagrangian Wasserstein Flow (CLWF), the first generative modeling framework that incorporates the principle of least action from Lagrangian mechanics. CLWF explicitly models latent-variable dynamics by jointly optimizing kinetic energy and task-oriented potential energy gradients. It couples a time-varying denoising autoencoder to estimate potential gradients, substantially reducing sampling variance; integrates Wasserstein flow with conditional diffusion priors to ensure distribution alignment and conditional consistency. Evaluated on multiple benchmark datasets, CLWF achieves state-of-the-art performance, with significantly accelerated inference—reducing required sampling steps by approximately 40%—while maintaining theoretical rigor and computational efficiency.

Technology Category

Machine Learning: Deep Generative Models & AutoencodersComputer Vision: Diffusion Models for VisionNatural Language Processing: Generation

Application Category

Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Overcoming slow convergence in diffusion-based time series imputation
• Learning velocity by minimizing kinetic energy via Lagrangian mechanics
• Enhancing performance with task-specific gradient estimation and variance reduction

Innovation

• Conditional Lagrangian Wasserstein Flow for imputation
• Minimizes kinetic energy via Lagrangian mechanics
• Integrates denoising autoencoder for variance reduction