@article{murray2010slice,
  title={Slice sampling covariance hyperparameters of latent Gaussian models},
  author={Murray, Iain and Adams, Ryan P},
  journal={Advances in neural information processing systems},
  volume={23},
  year={2010}
}

@misc{Dua2019,
  author = {Dua, Dheeru and Graff, Casey},
  year = {2017},
  title = {{UCI} Machine Learning Repository},
  url = {http://archive.ics.uci.edu/ml},
  institution = {University of California, Irvine, School of Information and Computer Sciences}
} 

@inproceedings{rahimi_random_2008,
	title = {Random {Features} for {Large}-{Scale} {Kernel} {Machines}},
	volume = {20},
	urldate = {2021-10-01},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Rahimi, Ali and Recht, Benjamin},
	year = {2008},
}

@article{lazaro-gredilla_sparse_2010,
	title = {Sparse {Spectrum} {Gaussian} {Process} {Regression}},
	volume = {11},
	number = {63},
	urldate = {2021-06-28},
	journal = {Journal of Machine Learning Research},
	author = {Lázaro-Gredilla, Miguel and Quiñnero-Candela, Joaquin and Rasmussen, Carl E. and Figueiras-Vidal, Aníbal R.},
	year = {2010},
	pages = {1865--1881},
}

@book{rudin_fourier_2011,
	address = {Hoboken},
	title = {Fourier {Analysis} on {Groups}.},
	language = {English},
	publisher = {John Wiley \& Sons},
	author = {Rudin, Walter},
	year = {2011},
}

@article{tan_variational_2016,
	title = {Variational inference for sparse spectrum {Gaussian} process regression},
	volume = {26},
	language = {en},
	number = {6},
	journal = {Statistics and Computing},
	author = {Tan, Linda S. L. and Ong, Victor M. H. and Nott, David J. and Jasra, Ajay},
	month = nov,
	year = {2016},
	pages = {1243--1261},
}

@article{alvarez2012kernels,
  title={Kernels for vector-valued functions: A review},
  author={Alvarez, Mauricio A and Rosasco, Lorenzo and Lawrence, Neil D and others},
  journal={Foundations and Trends{\textregistered} in Machine Learning},
  volume={4},
  number={3},
  pages={195--266},
  year={2012},
  publisher={Now Publishers, Inc.}
}

@article{hensman_variational_2018,
	title = {Variational {Fourier} {Features} for {Gaussian} {Processes}},
	volume = {18},
	number = {151},
	urldate = {2023-11-01},
	journal = {Journal of Machine Learning Research},
	author = {Hensman, James and Durrande, Nicolas and Solin, Arno},
	year = {2018},
	pages = {1--52},
}

@article{miller_bayesian_2022,
	title = {Bayesian spatial modeling using random {Fourier} frequencies},
	volume = {48},
	journal = {Spatial Statistics},
	author = {Miller, Matthew J. and Reich, Brian J.},
	month = apr,
	year = {2022},
	pages = {100598},
}

@inproceedings{liu_stein_2016,
	title = {Stein {Variational} {Gradient} {Descent}: {A} {General} {Purpose} {Bayesian} {Inference} {Algorithm}},
	volume = {29},
	shorttitle = {Stein {Variational} {Gradient} {Descent}},
	urldate = {2024-02-10},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Liu, Qiang and Wang, Dilin},
	year = {2016},
}

@book{rasmussen_gaussian_2006,
	address = {Cambridge, Mass},
	series = {Adaptive computation and machine learning},
	title = {Gaussian processes for machine learning},
	publisher = {MIT Press},
	author = {Rasmussen, Carl E. and Williams, Christopher},
	year = {2006},
}

@book{bishop_pattern_2006,
	series = {Information science and statistics},
	title = {Pattern recognition and machine learning},
	publisher = {Springer},
	author = {Bishop, Christopher M.},
	year = {2006},
}

@inproceedings{mallick_deep_2021,
	title = {Deep kernels with probabilistic embeddings for small-data learning},
	booktitle = {Proceedings of the {Thirty}-{Seventh} {Conference} on {Uncertainty} in {Artificial} {Intelligence}},
	publisher = {PMLR},
	author = {Mallick, Ankur and Dwivedi, Chaitanya and Kailkhura, Bhavya and Joshi, Gauri and Han, T. Yong-Jin},
	month = dec,
	year = {2021},
	pages = {918--928},
}

@inproceedings{liu_understanding_2019,
	title = {Understanding and {Accelerating} {Particle}-{Based} {Variational} {Inference}},
	language = {en},
	booktitle = {Proceedings of the 36th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Liu, Chang and Zhuo, Jingwei and Cheng, Pengyu and Zhang, Ruiyi and Zhu, Jun},
	month = may,
	year = {2019},
	pages = {4082--4092},
}

@incollection{benton_function-space_2019,
	title = {Function-space distributions over kernels},
	number = {1340},
	booktitle = {Proceedings of the 33rd {International} {Conference} on {Neural} {Information} {Processing} {Systems}},
	author = {Benton, Gregory W. and Maddox, Wesley J. and Salkey, Jayson P. and Albinati, Júlio and Wilson, Andrew Gordon},
	month = dec,
	year = {2019},
	pages = {14965--14976},
}


@inproceedings{wang_nonlinear_2019,
	title = {Nonlinear {Stein} {Variational} {Gradient} {Descent} for {Learning} {Diversified} {Mixture} {Models}},
	booktitle = {Proceedings of the 36th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Wang, Dilin and Liu, Qiang},
	month = may,
	year = {2019},
	pages = {6576--6585},
}

@inproceedings{hamid_marginalising_2022,
	title = {Marginalising over {Stationary} {Kernels} with {Bayesian} {Quadrature}},
	booktitle = {Proceedings of {The} 25th {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Hamid, Saad and Schulze, Sebastian and Osborne, Michael A. and Roberts, Stephen},
	month = may,
	year = {2022},
	pages = {9776--9792},
}

@misc{pinder_stein_2020,
      title={Stein Variational Gaussian Processes}, 
      author={Thomas Pinder and Christopher Nemeth and David Leslie},
      year={2022},
      eprint={2009.12141},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@article{ton_spatial_2018,
	series = {One world, one health},
	title = {Spatial mapping with {Gaussian} processes and nonstationary {Fourier} features},
	volume = {28},
	journal = {Spatial Statistics},
	author = {Ton, Jean-Francois and Flaxman, Seth and Sejdinovic, Dino and Bhatt, Samir},
	month = dec,
	year = {2018},
	pages = {59--78},
}


@inproceedings{wilson_gaussian_2013,
	title = {Gaussian {Process} {Kernels} for {Pattern} {Discovery} and {Extrapolation}},
	language = {en},
	booktitle = {Proceedings of the 30th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Wilson, Andrew and Adams, Ryan},
	month = may,
	year = {2013},
	pages = {1067--1075},
}

@inproceedings{yu_orthogonal_2016,
	title = {Orthogonal {Random} {Features}},
	volume = {29},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Yu, Felix Xinnan X and Suresh, Ananda Theertha and Choromanski, Krzysztof M and Holtmann-Rice, Daniel N and Kumar, Sanjiv},
	year = {2016},
}


@article{chang_data-driven_2017,
	title = {Data-driven {Random} {Fourier} {Features} using {Stein} {Effect}},
	journal = {arXiv:1705.08525 [cs, stat]},
	author = {Chang, Wei-Cheng and Li, Chun-Liang and Yang, Yiming and Poczos, Barnabas},
	month = may,
	year = {2017},
	note = {arXiv: 1705.08525},
}

@article{ohagan_bayeshermite_1991,
	title = {Bayes–{Hermite} quadrature},
	volume = {29},
	language = {en},
	number = {3},
	journal = {Journal of Statistical Planning and Inference},
	author = {O'Hagan, A.},
	month = nov,
	year = {1991},
	pages = {245--260},
}


@inproceedings{mutny_efficient_2018,
	title = {Efficient {High} {Dimensional} {Bayesian} {Optimization} with {Additivity} and {Quadrature} {Fourier} {Features}},
	volume = {31},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Mutny, Mojmir and Krause, Andreas},
	year = {2018},
}


@misc{liu_random_2021,
	title = {Random {Features} for {Kernel} {Approximation}: {A} {Survey} on {Algorithms}, {Theory}, and {Beyond}},
	shorttitle = {Random {Features} for {Kernel} {Approximation}},
	publisher = {arXiv},
	author = {Liu, Fanghui and Huang, Xiaolin and Chen, Yudong and Suykens, Johan A. K.},
	month = jul,
	year = {2021},
	note = {arXiv:2004.11154 [cs, stat]},
	keywords = {kernel learning, kernel methods, random features, random fourier features, review},
}

@misc{samo_generalized_2015,
	title = {Generalized {Spectral} {Kernels}},
	publisher = {arXiv},
	author = {Samo, Yves-Laurent Kom and Roberts, Stephen},
	month = oct,
	year = {2015},
	note = {arXiv:1506.02236 [stat]},
}

@inproceedings{remes_non-stationary_2017,
 author = {Remes, Sami and Heinonen, Markus and Kaski, Samuel},
 booktitle = {Advances in Neural Information Processing Systems},
 title = {Non-Stationary Spectral Kernels},
 volume = {30},
 year = {2017}
}

@inproceedings{shen_harmonizable_2019,
	title = {Harmonizable mixture kernels with variational {Fourier} features},
	language = {en},
	booktitle = {Proceedings of the {Twenty}-{Second} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Shen, Zheyang and Heinonen, Markus and Kaski, Samuel},
	month = apr,
	year = {2019},
	pages = {3273--3282},
}

@inproceedings{jung_efficient_2022,
	title = {Efficient {Approximate} {Inference} for {Stationary} {Kernel} on {Frequency} {Domain}},
	booktitle = {Proceedings of the 39th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Jung, Yohan and Song, Kyungwoo and Park, Jinkyoo},
	month = jun,
	year = {2022},
	pages = {10502--10538},
}

@misc{xie_deep_2019,
	title = {Deep {Kernel} {Learning} via {Random} {Fourier} {Features}},
	publisher = {arXiv},
	author = {Xie, Jiaxuan and Liu, Fanghui and Wang, Kaijie and Huang, Xiaolin},
	month = oct,
	year = {2019},
	note = {arXiv:1910.02660 [cs, stat]},
	keywords = {deep kernels, kernel learning, kernel methods, random fourier features},
}

@inproceedings{xue_deep_2019,
	address = {Macao, China},
	series = {{IJCAI}'19},
	title = {Deep spectral kernel learning},
	booktitle = {Proceedings of the 28th {International} {Joint} {Conference} on {Artificial} {Intelligence}},
	publisher = {AAAI Press},
	author = {Xue, Hui and Wu, Zheng-Fan and Sun, Wei-Xiang},
	month = aug,
	year = {2019},
	pages = {4019--4025},
}

@inproceedings{cutajar_random_2017,
	title = {Random {Feature} {Expansions} for {Deep} {Gaussian} {Processes}},
	booktitle = {Proceedings of the 34th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Cutajar, Kurt and Bonilla, Edwin V. and Michiardi, Pietro and Filippone, Maurizio},
	month = jul,
	year = {2017},
	pages = {884--893},
}


@inproceedings{zhen_learning_2020,
	title = {Learning to {Learn} {Kernels} with {Variational} {Random} {Features}},
	booktitle = {Proceedings of the 37th {International} {Conference} on {Machine} {Learning}},
	publisher = {PMLR},
	author = {Zhen, Xiantong and Sun, Haoliang and Du, Yingjun and Xu, Jun and Yin, Yilong and Shao, Ling and Snoek, Cees},
	month = nov,
	year = {2020},
	pages = {11409--11419},
}

@misc{cheema_integrated_2023,
	title = {Integrated {Variational} {Fourier} {Features} for {Fast} {Spatial} {Modelling} with {Gaussian} {Processes}},
	publisher = {arXiv},
	author = {Cheema, Talay M. and Rasmussen, Carl Edward},
	month = aug,
	year = {2023},
	note = {arXiv:2308.14142 [cs, stat]},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

%article{sun_functional_2019,
	title = {Functional {Variational} {Bayesian} {Neural} {Networks}},
	journal = {arXiv:1903.05779 [cs, stat]},
	author = {Sun, Shengyang and Zhang, Guodong and Shi, Jiaxin and Grosse, Roger},
	month = mar,
	year = {2019},
	note = {arXiv: 1903.05779},
	keywords = {machine learning},
}

@inproceedings{sun_functional_2019,
address = {New Orleans, LA, USA},
author = {Sun, Shengyang and Zhang, Guodong and Shi, Jiaxin and Grosse, Roger},
booktitle = {7th International Conference on Learning Representations (ICLR 2019)},
publisher = {OpenReview.net},
title = {Functional variational {Bayesian} neural networks},
year = {2019}
}


@inproceedings{
    sun2018functional,
    title={{FUNCTIONAL} {VARIATIONAL} {BAYESIAN} {NEURAL} {NETWORKS}},
    author={Shengyang Sun and Guodong Zhang and Jiaxin Shi and Roger Grosse},
    booktitle={International Conference on Learning Representations},
    year={2019},
}

@inproceedings{Ma2021,
    author = {Ma, Chao and {Hern{\'{a}}ndez-Lobato}, Jos{\'{e}} Miguel},
    booktitle = {35th Conference on Neural Information Processing Systems (NeurIPS 2021)},
    title = {{Functional Variational Inference based on Stochastic Process Generators}},
    year = {2021}
}

@misc{dangelo_stein_2021,
	title = {On {Stein} {Variational} {Neural} {Network} {Ensembles}},
	language = {en},
	urldate = {2024-01-08},
	author = {D'Angelo, Francesco and Fortuin, Vincent and Wenzel, Florian},
	month = jun,
	year = {2021},
}

@inproceedings{
    pielok_approximate_2022,
    title={Approximate Bayesian Inference with Stein Functional Variational Gradient Descent},
    author={Tobias Pielok and Bernd Bischl and David R{\"u}gamer},
    booktitle={The Eleventh International Conference on Learning Representations },
    year={2023},
}

@inproceedings{hensman_scalable_2015,
	title = {Scalable {Variational} {Gaussian} {Process} {Classification}},
	language = {en},
	booktitle = {Proceedings of the {Eighteenth} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Hensman, James and Matthews, Alexander and Ghahramani, Zoubin},
	month = feb,
	year = {2015},
	pages = {351--360},
}


@article{morokoff_quasi-monte_1995,
	title = {Quasi-{Monte} {Carlo} {Integration}},
	volume = {122},
	language = {en},
	number = {2},
	urldate = {2022-04-28},
	journal = {Journal of Computational Physics},
	author = {Morokoff, William J. and Caflisch, Russel E.},
	month = dec,
	year = {1995},
	pages = {218--230},
}

@inproceedings{warren_generalized_2022,
	title = {Generalized {Bayesian} {Quadrature} with {Spectral} {Kernels}},
	language = {en},
	booktitle = {Proceedings of the 38th {Conference} on {Uncertainty} in {Artificial} {Intelligence}},
	author = {Warren, Houston and Oliveira, Rafael and Ramos, Fabio},
	month = jun,
	year = {2022},
	keywords = {bayesian quadrature, physics-informed learning, random fourier features, simulation},
}

@inproceedings{wang_stein_2019,
	title = {Stein {Variational} {Gradient} {Descent} {With} {Matrix}-{Valued} {Kernels}},
	volume = {32},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Wang, Dilin and Tang, Ziyang and Bajaj, Chandrajit and Liu, Qiang},
	year = {2019},
}

@inproceedings{yang_nystrom_2012,
	title = {Nyström {Method} vs {Random} {Fourier} {Features}: {A} {Theoretical} and {Empirical} {Comparison}},
	volume = {25},
	shorttitle = {Nyström {Method} vs {Random} {Fourier} {Features}},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	author = {Yang, Tianbao and Li, Yu-feng and Mahdavi, Mehrdad and Jin, Rong and Zhou, Zhi-Hua},
	year = {2012},
}

@misc{li_implicit_2019,
	title = {Implicit {Kernel} {Learning}},
	publisher = {arXiv},
	author = {Li, Chun-Liang and Chang, Wei-Cheng and Mroueh, Youssef and Yang, Yiming and Póczos, Barnabás},
	month = feb,
	year = {2019},
	note = {arXiv:1902.10214 [cs, stat]},
}

@inproceedings{Muandet2012,
author = {Muandet, Krikamol and Fukumizu, Kenji and Dinuzzo, Francesco and Sch{\"{o}}lkopf, Bernhard},
booktitle = {Proceeding of the 26th Annual Conference on Neural Information Processing Systems (NIPS 2012)},
title = {{Learning from Distributions via Support Measure Machines}},
year = {2012}
}

@book{Gupta1999,
address = {New York, NY},
author = {Gupta, A. K. and Nagar, D. K.},
booktitle = {Monographs and Surveys in Pure and Applied Mathematics},
edition = {1},
publisher = {Chapman {\&} Hall},
title = {{Matrix Variate Distributions}},
year = {1999}
}

@book{Bauer1981,
  title={Probability theory and elements of measure theory},
  author={Bauer, Heinz},
  year={1981},
  edition={2nd},
  publisher={Academic Press},
  address={London, UK}
}


@InProceedings{Le2013Fastfood,
  title = 	 {Fastfood - Computing Hilbert Space Expansions in loglinear time},
  author = 	 {Le, Quoc and Sarlos, Tamas and Smola, Alexander},
  booktitle = {Proceedings of the 30th International Conference on Machine Learning},
  pages = 	 {244--252},
  year = 	 {2013},
  volume = 	 {28},
  number =       {3},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {17--19 Jun},
  publisher =    {PMLR},
}

@techreport{auswave,
  author       = {{Australian Bureau of Meteorology}},
  title        = {AUSWAVE},
  institution  = {Government of Australia},
  year         = {2016},
  url          = {http://www.bom.gov.au/nwp/doc/auswave/data.shtml},
}

@inproceedings{wilsonDeep2016,
  title = {Deep {{Kernel Learning}}},
  booktitle = {Proceedings of the 19th {{International Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
  author = {Wilson, Andrew Gordon and Hu, Zhiting and Salakhutdinov, Ruslan and Xing, Eric P.},
  year = {2016},
  pages = {370--378},
  publisher = {PMLR},
  issn = {1938-7228},
}