# Learning spectrograms with convolutional spectral kernels

arXiv: https://arxiv.org/abs/1905.09917 · HTML: https://mlsanity.com/paper/1905.09917/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 2 of 2)

- [Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey](https://mlsanity.com/paper/2103.10134/) (2021)
- [Shallow and Deep Nonparametric Convolutions for Gaussian Processes](https://mlsanity.com/paper/2206.08972/) (2022)

## Abstract (arXiv)

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.