Comparison of Gaussian process software: Difference between revisions

Revision as of 16:13, 26 May 2022

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{{short description|Comparison of statistical analysis software that allows doing inference with Gaussian processes}}

This is a comparison of statistical analysis software that allows doing inference with [[Gaussian process|Gaussian processes]]es often using [[Gaussian process approximations|approximations]].

This article is written from the point of view of [[Bayesian statistics]], which may use a terminology different from the one commonly used in [[kriging]]. The next section should clarify the mathematical/computational meaning of the information provided in the table independently of contextual terminology.

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* '''Exact''': whether ''generic'' exact algorithms are implemented. These algorithms are usually appropriate only up to some thousands of datapoints.

* '''Specialized''': whether specialized ''exact'' algorithms for specific classes of problems are implemented. Supported specialized algorithms may be indicated as:

** ''Kronecker'': algorithms for separable kernels on grid data.<ref name="gilboa2015">< /ref>

** ''Toeplitz'': algorithms for stationary kernels on uniformly spaced data.<ref name="zhang2005">< /ref>

** ''Semisep.'': algorithms for semiseparable covariance matrices.<ref name="foreman2017">< /ref>

** ''Sparse'': algorithms optimized for [[Sparse matrix|sparse]] covariance matrices.

** ''Block'': algorithms optimized for [[Block_matrixBlock matrix#Block_diagonal_matricesBlock diagonal matrices|block diagonal]] covariance matrices.

** ''Markov'': algorithms for kernels which represent (or can be formulated as) a Markov process.<ref name="sarkka2013">< /ref>

* '''Approximate''': whether ''generic or specialized'' approximate algorithms are implemented. Supported approximate algorithms may be indicated as:

** ''Sparse'': algorithms based on choosing a set of "inducing points" in input space,<ref name="candela2005">< /ref> or more in general imposing a sparse structure on the inverse of the covariance matrix.

** ''Hierarchical'': algorithms which approximate the covariance matrix with a [[hierarchical matrix]].<ref name="ambikasaran2016">< /ref>

=== Input ===

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* '''ND''': whether multidimensional input is supported. If it is, multidimensional output is always possible by adding a dimension to the input, even without direct support.

* '''Non-real''': whether arbitrary non-[[Real numbers|real]] input is supported (for example, text or [[Complexcomplex number|complex numbers]]s).

=== Output ===

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These columns are about finding values of variables which enter somehow in the definition of the specific problem but that can not be inferred by the Gaussian process fit, for example parameters in the formula of the kernel.

* '''Prior''': whether specifying arbitrary [[Hyperprior|hyperpriorshyperprior]]s on the [[Hyperparameter|hyperparametershyperparameter]]s is supported.

* '''Posterior''': whether estimating the posterior is supported beyond [[point estimation]], possibly in conjunction with other software.

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! [[scikit-learn]]

|-

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

| {{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]<ref name="rasmussen2010">< /ref><ref name="vanhatalo2013">< /ref>

| {{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]<ref name="vanhatalo2013">< /ref>

| {{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]<ref name="matthews2017">< /ref>

| {{BSD-lic}}

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

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

|-

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

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

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

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

|-

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

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

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

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! [https://gpytorch.ai GPyTorch]

|-

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

| {{GPL-lic}}

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

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

|-

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

| {{BSD-lic}}

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

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

|-

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

| {{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]<ref name="foreman2017">< /ref>

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

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

| {{no}}

| {{yes|Semisep.}}{{efn|name=celerite|celerite implements only a specific subalgebra of kernels which can be solved in <math>O(n)</math>.<ref name="foreman2017">< /ref>}}

| {{no}}

| {{no|1D}}

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

|-

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

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

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

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

|-

! [https://github.com/google/neural-tangents neural-tangents]<ref name="novak2020">< /ref>{{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]<ref name="roustant2012">< /ref>

| {{GPL-lic}}

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

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

|-

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

| {{LGPL-lic}}

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

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

|-

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

| {{proprietary}}

| [[MATLAB]]

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! [http://www.uqlab.com/ UQLab]

|-

! [http://www.sumo.intec.ugent.be/ooDACE ooDACE]<ref name="couckuyt2014">< /ref>

| {{proprietary}}

| [[MATLAB]]