Comparison of Gaussian process software: Difference between revisions

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== Comparison table ==

{{sort-under}}

{| class="wikitable sortable sort-under" style="font-size: 90%; text-align: center; width: auto;"

|-

! rowspan="2" | Name

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! colspan="2" | Input

! colspan="2" | Output

! colspan="2" | [[Hyperparameter (Bayesian statistics)|Hyperparameters]]

! colspan="3" | [[Linear transformations]]

! rowspan="2" | Name

|-

! Exact

! {{verth|Specialized}}

! {{verth|Approxi­mate}}

! Approximate

! ND

! {{nowrap}} verth| Non-real}}

! Likelihood

! Errors

! Prior

! Posterior

! {{verth|Derivative}}

! Deriv.

! Finite

! Sum

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! [[scikit-learn]]

|-

! [http://www.cs.toronto.edu/%7Eradford/fbm.software.html fbm]<br/><ref name="vanhatalo2013" />

| {{free}}

| [[C (programming language)|C]]

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! [http://www.cs.toronto.edu/%7Eradford/fbm.software.html fbm]

|-

! [http://www.gaussianprocess.org/gpml/code/matlab/doc/index.html GPML]<br/><ref name="rasmussen2010" /><ref name="vanhatalo2013" />

| {{BSD-lic}}

| [[MATLAB]]

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! [http://www.gaussianprocess.org/gpml/code/matlab/doc/index.html GPML]

|-

! [https://research.cs.aalto.fi/pml/software/gpstuff/ GPstuff]<br/><ref name="vanhatalo2013" />

| {{GPL-lic}}

| [[MATLAB]], [[R (programming language)|R]]

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! [https://research.cs.aalto.fi/pml/software/gpstuff/ GPstuff]

|-

! [https://sheffieldml.github.io/GPy/ GPy]<br/><ref name="matthews2017" />

| {{BSD-lic}}

| [[Python (programming language)|Python]]

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! [https://sheffieldml.github.io/GPy/ GPy]

|-

! [https://www.gpflow.org GPflow]<br/><ref name="matthews2017" />

| {{free|[[Apache License|Apache]]}}

| [[Python (programming language)|Python]]

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! [https://www.gpflow.org GPflow]

|-

! [https://gpytorch.ai GPyTorch]<br/><ref name="gardner2018" />

| {{free|[[MIT License|MIT]]}}

| [[Python (programming language)|Python]]

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! [https://gpytorch.ai GPyTorch]

|-

! [https://CRAN.R-project.org/package=GPvecchia GPvecchia]<br/><ref name="zilber2021" />

| {{GPL-lic}}

| [[R (programming language)|R]]

| {{yes}}

| {{no}}

| {{yes|Sparse, HierarchicalHierarch&shy;ical}}

| {{yes|ND}}

| {{no}}

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! [https://CRAN.R-project.org/package=GPvecchia GPvecchia]

|-

! [https://github.com/marionmari/pyGPs pyGPs]<br/><ref name="neumann2015" />

| {{BSD-lic}}

| [[Python (programming language)|Python]]

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! [https://github.com/marionmari/pyGPs pyGPs]

|-

! [https://CRAN.R-project.org/package=gptk gptk]<br/><ref name="kalaitzis2011" />

| {{BSD-lic}}

| [[R (programming language)|R]]

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! [https://CRAN.R-project.org/package=gptk gptk]

|-

! [https://celerite.readthedocs.io/en/stable/ celerite]<br/><ref name="foreman2017" />

| {{free|[[MIT License|MIT]]}}

| [[Python (programming language)|Python]], [[Julia (programming language)|Julia]], [[C++]]

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! [https://celerite.readthedocs.io/en/stable/ celerite]

|-

! [http://george.readthedocs.io george]<br/><ref name="ambikasaran2016" />

| {{free|[[MIT License|MIT]]}}

| [[Python (programming language)|Python]], [[C++]]

| {{yes}}

| {{no}}

| {{yes|HierarchicalHierarch&shy;ical}}

| {{yes|ND}}

| {{no}}

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! [http://george.readthedocs.io george]

|-

! [https://github.com/google/neural-tangents neural-tangents]<br/><ref name="novak2020" />{{efn|neural-tangents is a specialized package for infinitely wide neural networks.}}

| {{free|[[Apache License|Apache]]}}

| [[Python (programming language)|Python]]

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! [https://github.com/google/neural-tangents neural-tangents]

|-

! [https://cran.r-project.org/package=DiceKriging DiceKriging]<br/><ref name="roustant2012" />

| {{GPL-lic}}

| [[R (programming language)|R]]

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! [https://cran.r-project.org/package=DiceKriging DiceKriging]

|-

! [https://openturns.github.io/www/ OpenTURNS]<br/><ref name="baudin2015" />

| {{LGPL-lic}}

| [[Python (programming language)|Python]], [[C++]]

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! [https://openturns.github.io/www/ OpenTURNS]

|-

! [http://www.uqlab.com/ UQLab]<br/><ref name="marelli2014" />

| {{proprietary}}

| [[MATLAB]]

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! [https://celerite2.readthedocs.io/en/latest/ celerite2]

|-

! [https://smt.readthedocs.io/en/latest/ SMT]<br/><ref name="saves2024" /><ref name="bouhlel2019" />

| {{free|[[BSD licenses|BSD]]}}

| [[Python (programming language)|Python]]

| {{yes}}

| {{no}}

| {{yes|POD}}{{efn|name=POD| POD (Proper Orthogonal Decomposition) is a dimensionality reduction technique used in Gaussian Process regression to approximate complex systems by projecting data onto a lower-dimensional subspace, making computations more efficient. It assumes the system is governed by a few dominant modes, making it ideal for problems with clear separability of scales, but less effective when all dimensions contribute equally to the system's behavior.<ref name="Porrello24" />}}

| {{yes|Sparse, PODI{{efn|name=PODI| PODI (Proper Orthogonal Decomposition + Interpolation) is an approximation for high-dimensional multioutput regressions. The regression function is lower-dimensional than the outcomes, and the subspace is chosen with the PCA of the (outcome, dependent variable) data. Each principal component is modeled with an a priori independent Gaussian process.<ref name="Porrello24" />}}, other}}

| {{yes|Sparse}}

| {{yes|ND}}

| {{Yesno}}

| {{no|Gaussian}}

| {{partial|i.i.d.}}

| {{yespartial|Some}}

| {{yespartial|Some}}

| {{yespartial|First}}

| {{no}}

| {{no}}

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| {{partial|Manually}}

| {{partial|Manually}}

| {{partial|ApproximateApproxi&shy;mate}}

| {{no}}

| {{yes}}

! [https://github.com/wesselb/stheno Stheno]

|-

! [https://docs.rs/egobox-gp/latest/egobox_gp/ Egobox-gp]<br/><ref name="Lafage2022" />

| {{free|[[Apache License|Apache]]}}

| [[Rust (programming language)|Rust]]

| {{yes}}

| {{no}}

| {{Yesyes|Sparse}}

| {{yes|ND}}

| {{yesno}}

| {{yesno|AnyGaussian}}

| {{partial|i.i.d.}}

| {{yesno}}

| {{yespartial|MAP}}

| {{yespartial|First}}

| {{no}}

| {{no}}

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! rowspan="2" | [[Programming language|Language]]

! Exact

! {{verth|Specialized}}

! {{verth|Approxi&shy;mate}}

! Approximate

! ND

! {{nowrap}} verth| Non-real}}

! Likelihood

! Errors

! Prior

! Posterior

! {{verth|Derivative}}

! Deriv.

! Finite

! Sum

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<ref name="foreman2017">{{cite journal |last1=Foreman-Mackey |first1=Daniel |last2=Angus |first2=Ruth |last3=Agol |first3=Eric |last4=Ambikasaran |first4=Sivaram |s2cid=88521913 |title=Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series |journal=The Astronomical Journal |date=9 November 2017 |volume=154 |issue=6 |page=220 |doi=10.3847/1538-3881/aa9332|arxiv=1703.09710 |bibcode=2017AJ....154..220F |doi-access=free }}</ref>

<ref name="gilboa2015">{{cite journal |last1=P. Cunningham |first1=John |last2=Gilboa |first2=Elad |last3=Saatçi |first3=Yunus |s2cid=6878550 |title=Scaling Multidimensional Inference for Structured Gaussian Processes |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |date=Feb 2015 |volume=37 |issue=2 |pages=424–436 |doi=10.1109/TPAMI.2013.192|pmid=26353252 |arxiv=1209.4120 |bibcode=2015ITPAM..37..424G }}</ref>

<ref name="zhang2005">{{cite book |last1=Leith |first1=D. J. |last2=Zhang |first2=Yunong |last3=Leithead |first3=W. E. |title=Proceedings of the 44th IEEE Conference on Decision and Control |chapter=Time-series Gaussian Process Regression Based on Toeplitz Computation of O(N²) Operations and O(N)-level Storage |s2cid=13627455 |date=2005 |pages=3711–3716 |doi=10.1109/CDC.2005.1582739|isbn=0-7803-9567-0 }}</ref>

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<ref name="couckuyt2014">{{cite journal |last1=Couckuyt |first1=Ivo |last2=Dhaene |first2=Tom |last3=Demeester |first3=Piet |title=ooDACE toolbox: a flexible object-oriented Kriging implementation |journal=Journal of Machine Learning Research |date=2014 |volume=15 |pages=3183–3186 |url=http://www.jmlr.org/papers/volume15/couckuyt14a/couckuyt14a.pdf |accessdate=8 July 2020}}</ref>

<ref name="zilber2021">{{cite journal |last1=Zilber |first1=Daniel |last2=Katzfuss |first2=Matthias |title=Vecchia–Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data |journal=Computational Statistics & Data Analysis |date=January 2021 |volume=153 |pagearticle-number=107081 |doi=10.1016/j.csda.2020.107081 |arxiv=1906.07828 |s2cid=195068888 |url=https://www.sciencedirect.com/science/article/pii/S0167947320301729 |access-date=1 September 2021 |issn=0167-9473}}</ref>

<ref name="kalaitzis2011">{{cite journal |last1=Kalaitzis |first1=Alfredo |last2=Lawrence |first2=Neil D. |title=A Simple Approach to Ranking Differentially Expressed Gene Expression Time Courses through Gaussian Process Regression |journal=BMC Bioinformatics |date=May 20, 2011 |volume=12 |issue=1 |pages=180 |doi=10.1186/1471-2105-12-180 |pmid=21599902 |pmc=3116489 |issn=1471-2105 |doi-access=free }}</ref>

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<ref name="baudin2015">{{cite book |first1=Michaël |last1=Baudin |first2=Anne |last2=Dutfoy |first3=Bertrand |last3=Iooss |first4=Anne-Laure |last4=Popelin |title=Handbook of Uncertainty Quantification |chapter=OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation |date=2015 |pages=1–38 |editor1= Roger Ghanem|editor2= David Higdon|editor3= Houman Owhadi|doi=10.1007/978-3-319-11259-6_64-1 |arxiv=1501.05242|isbn=978-3-319-11259-6 |s2cid=88513894 }}</ref>

<ref name="sarkka2013">{{cite journal |last1=Sarkka |first1=Simo |last2=Solin |first2=Arno |last3=Hartikainen |first3=Jouni |title=Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering |journal=IEEE Signal Processing Magazine |date=2013 |volume=30 |issue=4 |pages=51–61 |doi=10.1109/MSP.2013.2246292 |s2cid=7485363 |url=https://ieeexplore.ieee.org/document/6530736 |access-date=2 September 2021}}</ref>

<ref name="bouhlel2019">{{cite journal |last1=Saves|first1=Paul |last2=Lafage|first2=Rémi |last3=Bartoli |first3=Nathalie |last4=Diouane |first4= Youssef |last5=Bussemaker |first5= Jasper |last6=Lefebvre |first6= Thierry |last7=Hwang |first7= John T. |last8= Morlier |first8= Joseph |last9= Martins |first9= Joaquim R.R.A. |title=SMT 2.0: A Surrogate Modeling Toolbox with a focus on hierarchical and mixed variables Gaussian processes |journal=Advances in Engineering Software |date=2024 |volume=188|issue=1 |pages=103571 |doi=10.1016/j.advengsoft.2023.103571 |url=https://www.sciencedirect.com/science/article/pii/S096599782300162X|arxiv=2305.13998 }}</ref>