Low-pass filtering as Bayesian inference
This addresses filtering challenges in time series analysis, but it appears incremental as it builds on existing Bayesian and latent-factor approaches.
The authors tackled the problem of low-pass filtering for unevenly-sampled and noisy time series by proposing a Bayesian nonparametric method, achieving validation against standard linear filters on synthetic and real-world data.
We propose a Bayesian nonparametric method for low-pass filtering that can naturally handle unevenly-sampled and noise-corrupted observations. The proposed model is constructed as a latent-factor model for time series, where the latent factors are Gaussian processes with non-overlapping spectra. With this construction, the low-pass version of the time series can be identified as the low-frequency latent component, and therefore it can be found by means of Bayesian inference. We show that the model admits exact training and can be implemented with minimal numerical approximations. Finally, the proposed model is validated against standard linear filters on synthetic and real-world time series.