用频谱引导的扩散模型，精准填补不规则采样时间序列的缺失数据。
LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation
- 引入可微分的Lomb-Scargle层，直接计算不规则采样数据的功率谱。
- 在合成与真实数据上，填补精度优于纯时域方法，且频率估计更一致。
- 模块化设计，可轻松嵌入现有学习框架，适合处理不完整或非均匀数据。
不规则采样或存在缺失值的时间序列是机器学习中的长期挑战。许多方法依赖快速傅里叶变换（FFT）在频域操作，但FFT假设均匀采样，需预先插值，可能扭曲频谱。为此，我们提出一种可微分的Lomb-Scargle层，实现对不规则采样数据的可靠功率谱计算。将该层集成到新型基于得分的扩散模型（LSCD）中，用于条件化整个信号频谱的时间序列填补。在合成与真实世界基准上的实验表明，该方法在填补缺失数据方面优于纯时域基线，同时生成更一致的频率估计。关键优势在于，该方法可轻松融入学习框架，推动频谱引导在处理不完整或非均匀数据的机器学习方法中的广泛应用。
原文摘要 · Abstract (English)
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.
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