Learning spectrograms with convolutional spectral kernels

Abstract: 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.