LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation
This addresses the challenge of handling incomplete or irregular time series data in machine learning, with potential applications in domains like finance or healthcare, though it is incremental as it builds on existing diffusion models with a novel spectral conditioning approach.
The paper tackled the problem of imputing missing or irregularly sampled time series data by introducing a differentiable Lomb-Scargle layer to compute power spectra without prior interpolation, integrated into a diffusion model, resulting in more accurate data recovery and consistent frequency estimates compared to time-domain baselines.
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.