Learning spectrograms with convolutional spectral kernels
This work addresses interpretability and performance in Gaussian process models for spatiotemporal data, but appears incremental as it builds on existing kernel and deep probabilistic methods.
The authors tackled the problem of modeling non-stationary patterns in Gaussian processes by introducing convolutional spectral kernels, which improved generalization on spatiotemporal datasets and enabled extraction of non-stationary periodic patterns.
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic models, using approximated Fourier transform, yielding a concise representation of input-frequency spectrogram. Observing through the lens of the spectrogram, we provide insight on the interpretability of deep models. We then infer the functional hyperparameters using scalable variational and MCMC methods. On small- and medium-sized spatiotemporal datasets, we demonstrate improved generalization of GP models when equipped with CSK, and their capability to extract non-stationary periodic patterns.