A typical audio signal processing pipeline includes multiple disjoint
analysis stages, including calculation of a time-frequency representation
followed by spectrogram-based feature analysis. We show how time-frequency
analysis and nonnegative matrix factorisation can be jointly formulated as a
spectral mixture Gaussian process model with nonstationary priors over the
amplitude variance parameters. Further, we formulate this nonlinear model's
state space representation, making it amenable to infinite-horizon Gaussian
process regression with approximate inference via expectation propagation,
which scales linearly in the number of time steps and quadratically in the
state dimensionality. By doing so, we are able to process audio signals with
hundreds of thousands of data points. We demonstrate, on various tasks with
empirical data, how this inference scheme outperforms more standard techniques
that rely on extended Kalman filtering.

该研究论文介绍了如何将时间频率分析和非负矩阵分解结合为具有非静止先验的谱混合高斯过程模型，以及如何将该非线性模型的状态空间表示形式化为无限时域高斯过程回归，并演示了该推理方案在各种任务上的优越性。