论文标题
建模具有复杂光谱结构的非平滑信号
Modelling Non-Smooth Signals with Complex Spectral Structure
论文作者
论文摘要
高斯工艺卷积模型（GPCM； Tobar等，2015a）是具有复杂频谱结构的信号的模型。 GPCM的一个重要局限性是它假定迅速衰减的频谱：它只能对光滑信号进行建模。此外，GPCM的推断需要（1）平均田间假设，导致校准不确定性不确定性，以及（2）大量协方差矩阵的繁琐变分优化。我们重新设计了GPCM模型，以诱导对光滑度的宽松假设诱导更丰富的分布：因果高斯工艺卷积模型（CGPCM）引入了GPCM中的因果关系假设，并且可以将高斯过程卷积模型（RGPCM）解释为贝耶斯的非骨化过程。我们还提出了一种更有效的变分推理方案，超越了平均场假设：我们设计了一个直接从最佳变分溶液中取样的吉布斯采样器，完全避免了任何变分优化。在合成和现实世界数据的实验中验证了GPCM的建议变异，显示出令人鼓舞的结果。
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth signals. Moreover, inference in the GPCM currently requires (1) a mean-field assumption, resulting in poorly calibrated uncertainties, and (2) a tedious variational optimisation of large covariance matrices. We redesign the GPCM model to induce a richer distribution over the spectrum with relaxed assumptions about smoothness: the Causal Gaussian Process Convolution Model (CGPCM) introduces a causality assumption into the GPCM, and the Rough Gaussian Process Convolution Model (RGPCM) can be interpreted as a Bayesian nonparametric generalisation of the fractional Ornstein-Uhlenbeck process. We also propose a more effective variational inference scheme, going beyond the mean-field assumption: we design a Gibbs sampler which directly samples from the optimal variational solution, circumventing any variational optimisation entirely. The proposed variations of the GPCM are validated in experiments on synthetic and real-world data, showing promising results.
