LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation

2025-06-20

AI Summary

Existing methods struggle to simultaneously achieve high imputation accuracy and spectral consistency for irregularly sampled time series with missing values. This paper introduces the first differentiable Lomb–Scargle (LS) spectral layer, integrated into a score-based diffusion model to enable end-to-end joint time–frequency modeling. The proposed layer is fully differentiable, enabling gradient backpropagation through spectral computation and, for the first time, allowing full-signal spectral information to serve as explicit conditioning input during the diffusion process—thereby avoiding spectral distortions inherent in conventional interpolation-based preprocessing. Experiments on both synthetic and real-world datasets demonstrate that our method significantly outperforms purely time-domain baselines, achieving state-of-the-art performance in both missing-value imputation accuracy and spectral estimation consistency.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore requiring prior interpolation that can distort the spectra. To address this limitation, we introduce a differentiable Lomb--Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data. We integrate this layer into a novel score-based diffusion model (LSCD) for time series imputation conditioned on the entire signal spectrum. Experiments on synthetic and real-world benchmarks demonstrate that our method recovers missing data more accurately than purely time-domain baselines, while simultaneously producing consistent frequency estimates. Crucially, our method can be easily integrated into learning frameworks, enabling broader adoption of spectral guidance in machine learning approaches involving incomplete or irregular data.

Problem

• Handling missing or irregularly sampled time series data
• Avoiding distortion from prior interpolation in frequency-domain methods
• Improving accuracy in imputation and frequency estimates

Innovation

• Differentiable Lomb-Scargle layer for irregular data
• Score-based diffusion model with spectral conditioning
• Accurate imputation and consistent frequency estimates