Learning spectrograms with convolutional spectral kernels

Zheyang Shen, Markus Heinonen, Samuel Kaski
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3826-3836, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-shen20a, title = {Learning spectrograms with convolutional spectral kernels}, author = {Shen, Zheyang and Heinonen, Markus and Kaski, Samuel}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3826--3836}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/shen20a/shen20a.pdf}, url = {https://proceedings.mlr.press/v108/shen20a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning spectrograms with convolutional spectral kernels %A Zheyang Shen %A Markus Heinonen %A Samuel Kaski %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-shen20a %I PMLR %P 3826--3836 %U https://proceedings.mlr.press/v108/shen20a.html %V 108 %X 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.
APA
Shen, Z., Heinonen, M. & Kaski, S.. (2020). Learning spectrograms with convolutional spectral kernels. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3826-3836 Available from https://proceedings.mlr.press/v108/shen20a.html.

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