标题： 低通滤波作为贝叶斯推理 显示英文标题

标题： Low-pass filtering as Bayesian inference

摘要： 我们提出了一种贝叶斯非参数方法用于低通滤波，该方法能够自然地处理不均匀采样和噪声污染的观测数据。 所提出的模型被构建为时间序列的潜在因子模型，其中潜在因子是具有非重叠频谱的高斯过程。 通过这种构造，时间序列的低通版本可以被识别为低频潜在成分，因此可以通过贝叶斯推断找到它。 我们证明了该模型允许精确训练，并且可以以最小的数值近似实现。 最后，在合成和真实世界的时间序列上，用标准线性滤波器对该模型进行了验证。 显示英文摘要

摘要： 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.