A comprehensive guide to Gaussian Process libraries

LIBRARY	LANGUAGE	LICENSE	REPOSITORY	RELEASE	INSTALLATION	DEVELOPERS & FUNDING	DOCUMENTATION	COMMUNITY SUPPORT	FRAMEWORK	GPU	SOLVERS		TREND TYPES	KERNEL \( R(x,x';\theta) \)				LIKELIHOOD			ESTIMATION METHODS	OPTIMIZATION METHODS	RESAMPLING	METRICS
LIBRARY	LANGUAGE	LICENSE	REPOSITORY	RELEASE	INSTALLATION	DEVELOPERS & FUNDING	DOCUMENTATION	COMMUNITY SUPPORT	FRAMEWORK	GPU	MODELS	COMPLEXITY	TREND TYPES	LENGTH SCALE	CORRELATION FAMILIES	MIXTURE	MIXTURE MODEL	TYPE	NUGGET	NOISE VARIANCE \( \sigma^2 \)	ESTIMATION METHODS	OPTIMIZATION METHODS	RESAMPLING	METRICS
AbstractGPs.jl JuliaGaussianProcesses (2020)	julia	MIT	JuliaGaussianProcesses/AbstractGPs.jl	v0.5.24	Pkg.jl	AbstractGPs.jl contributors	docs examples		Distributions.jl		Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) Deep Kernel Learning (DKL)		Zero Constant Custom	Isotropic Anisotropic	Squared Exponential Exponential Gamma Exponential Matern Matern12 Matern32 Matern52 Matern72 Rational Quadratic Rational Gamma Rational Linear Polynomial Piecewise Polynomial Periodic Cosine Constant White noise Exponentiated Fractional Brownian Motion Gabor Gibbs Neural Network Wiener Spectral Mixture Independent Multi-output Intrinsic Coregionalization Latent Factor Linear Mixing Model		Sum Product Scale Tensor Product	Gaussian	Custom	Inferable Custom	Maximum Likelihood Estimation (MLE) Evidence Lower Bound (ELBO) Variational Free Energy (VFE) Variational Inference (VI) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) Elliptical Slice Sampling (ESS)	Optim.jl optimizer L-BFGS Adam
albatross Swift Navigation (2018)	C++	MIT	swift-nav/albatross	master (2026-09-22)		Swift Navigation albatross contributors	docs				Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Linear Custom	Isotropic	Squared Exponential Exponential Matern32 Matern52 Constant Polynomial White noise Custom		Sum Product Scale	Gaussian	Custom	Inferable Custom	Maximum Likelihood Estimation (MLE) Leave-One-Out Cross-Validation (LOOCV) Markov Chain Monte Carlo (MCMC) Fully Independent Training Conditional (FITC) Partially Independent Training Conditional (PITC)	NLopt		Root Mean Squared Error (RMSE) Leave-One-Out Cross-Validation (LOOCV) Negative Log Predictive Density (NLPD)
ApproximateGPs.jl JuliaGaussianProcesses (2021)	julia	MIT	JuliaGaussianProcesses/ApproximateGPs.jl	v0.4.5	Pkg.jl	ApproximateGPs.jl contributors	docs user manuals API examples		Distributions.jl		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Variational Gaussian Process (SVGP)		Zero Constant Custom	Isotropic Anisotropic	Squared Exponential Exponential Gamma Exponential Matern Matern12 Matern32 Matern52 Rational Quadratic Rational Gamma Rational Linear Polynomial Piecewise Polynomial Periodic Cosine Constant White noise Exponentiated Fractional Brownian Motion Gabor Gibbs Neural Network Wiener Spectral Mixture Independent Multi-output Intrinsic Coregionalization Latent Factor Linear Mixing Model		Sum Product Scale Tensor Product	Gaussian Bernoulli	Custom	Custom	Maximum Likelihood Estimation (MLE) Evidence Lower Bound (ELBO) Variational Inference (VI) Stochastic Variational Inference (SVI) Laplace Approximation (LA)	Flux.jl optimizer Adam Optim.jl optimizer L-BFGS
AugmentedGaussianProcesses.jl Galy-Fajou et al. (2020)	julia	MIT	theogf/AugmentedGaussianProcesses.jl	v0.11.5	Pkg.jl	Technische Universität Berlin AugmentedGaussianProcesses.jl contributors	docs user manuals API examples				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Variational Gaussian Process (VGP) Sparse Variational Gaussian Process (SVGP) Gaussian Process Markov Chain Monte Carlo (GPMC) Online Sparse Variational Gaussian Process (OnlineSVGP) Multi-output Gaussian Process (MOGP) Variational Student-T Process (VStP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(M^3) \)	Zero Constant Empirical Linear	Isotropic Anisotropic	Squared Exponential Exponential Gamma Exponential Matern Matern12 Matern32 Matern52 Rational Quadratic Rational Gamma Rational Linear Polynomial Piecewise Polynomial Periodic Cosine Constant White noise Exponentiated Fractional Brownian Motion Gabor Gibbs Neural Network Wiener Spectral Mixture Independent Multi-output Intrinsic Coregionalization Latent Factor Linear Mixing Model		Sum Product Scale Tensor Product	Gaussian Student-T Laplace Heteroskedastic Noise Bernoulli Bayesian SVM Poisson Negative Binomial Softmax Logistic-Softmax		Inferable	Exact inference Variational Inference (VI) Stochastic Variational Inference (SVI) Evidence Lower Bound (ELBO) Markov Chain Monte Carlo (MCMC)	Flux.jl optimizer Adam Gradient Descent Momentum Robbins-Monro Natural Gradient Descent (NGD)
AutoGP Krauth et al. (2017)	Python	Apache-2.0	ebonilla/AutoGP	master (2019-07-19)		The University of New South Wales EURECOM AutoGP contributors	docs		TensorFlow		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Variational Gaussian Process (SVGP) Multi-output Gaussian Process (MOGP)		Zero	Isotropic Anisotropic	Squared Exponential ArcCosine			Gaussian Logit Softmax Regression Network			Stochastic Variational Inference (SVI) Evidence Lower Bound (ELBO) Leave-One-Out Cross-Validation (LOOCV)	TensorFlow optimizer RMSProp
AutoGP.jl Saad et al. (2023)	julia	Apache-2.0	probsys/AutoGP.jl	v0.1.19	Pkg.jl	Carnegie Mellon University Google Research Massachusetts Institute of Technology	docs tutorials API		Distributions.jl		Gaussian Process Regression (GPR) Automatic Kernel Structure Discovery		Zero	Isotropic	White noise Constant Linear Squared Exponential Gamma Exponential Periodic		Sum Product Change Points	Gaussian	Inferable Custom	Inferable Custom	Sequential Monte Carlo (SMC) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC)	Greedy Search
BayesianOptimization Nogueira (2014)	Python	MIT	bayesian-optimization/BayesianOptimization	v3.3.0	PyPI conda	BayesianOptimization contributors	docs API tutorials examples		NumPy SciPy		Gaussian Process Regression (GPR) scikit-learn GaussianProcessRegressor			Isotropic Anisotropic	Matern52 Custom		Sum Product Exponentiation	Gaussian	Custom default value: 1e-6		Maximum Likelihood Estimation (MLE)	L-BFGS-B Custom
BayesianOptimization.jl jbrea (2018)	julia	MIT	jbrea/BayesianOptimization.jl	v0.2.5	Pkg.jl	EPFL BayesianOptimization.jl contributors	docs				Gaussian Process Regression (GPR) Elastic Gaussian Process (ElasticGPE)		Constant	Anisotropic	Squared Exponential			Gaussian		Inferable	Maximum A Posteriori (MAP)	NLopt L-BFGS
Bayes-Newton Wilkinson et al. (2023)	Python	Apache-2.0	AaltoML/BayesNewton	v1.3.4	PyPI	Aalto University Bayes-Newton contributors	docs examples		JAX		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Variational Gaussian Process (VGP) Sparse Variational Gaussian Process (SVGP) Markov (State Space) Gaussian Process Sparse Markov Gaussian Process Spatio-Temporal Gaussian Process Expectation Propagation GP Laplace / Newton GP Posterior Linearisation GP Taylor / Extended Kalman Smoother GP Gauss-Newton GP Quasi-Newton GP Riemannian Gradient GP Infinite Horizon GP Parallel Markov GP Multi-output Gaussian Process (MOGP)			Isotropic Anisotropic	Matern12 Matern32 Matern52 Matern72 Spatio-Temporal Matern Cosine Periodic Quasi-Periodic Matern Subband Matern Spectro-Temporal Latent Exponentially Generated Divergence-Free Oscillator Independent		Sum Product	Gaussian Bernoulli Poisson Student-T Beta Gamma Negative Binomial Zero-Inflated Negative Binomial Heteroskedastic Noise Heteroskedastic Student-T Positive Positive Student-T Gaussian Multivariate Student-T Multivariate Softmax Multi-Stage Nonnegative Matrix Factorisation Audio Amplitude Demodulation Linear Coregionalisation Regression Network		Inferable	Maximum Likelihood Estimation (MLE) Variational Inference (VI) Evidence Lower Bound (ELBO) Expectation Propagation (EP) Power Expectation Propagation (PEP) Laplace Approximation (LA) Newton's Method Posterior Linearisation (PL) Taylor Expansion / Analytical Linearisation Gauss-Newton Quasi-Newton Riemannian Gradients	Adam		Negative Log Predictive Density (NLPD)
celerite Foreman-Mackey et al. (2017)	C++ julia Python	MIT	dfm/celerite	v0.4.3	PyPI conda	University of Washington Flatiron Institute Indian Institute of Science Columbia University celerite contributors	docs API		NumPy		Gaussian Process Regression (GPR)	\( \mathcal{O}(N) \)	Zero Constant Custom		Real Term Complex Term SHO Term Matern32 White noise Custom		Sum Product	Gaussian	Custom Inferable	Inferable Custom	Maximum Likelihood Estimation (MLE) Markov Chain Monte Carlo (MCMC)	L-BFGS-B SciPy optimizer
celerite2 Gordon et al. (2020)	C++ Python	MIT	exoplanet-dev/celerite2	v0.3.3	PyPI conda	University of Washington Flatiron Institute celerite2 contributors	docs tutorials		JAX NumPyro		Gaussian Process Regression (GPR)		Zero Constant		SHO Term Rotation Term Matern32 Real Term Complex Term Custom		Sum Product Derivative Convolution	Gaussian	Custom Inferable	Inferable Custom	Maximum Likelihood Estimation (MLE) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC)	L-BFGS-B SciPy optimizer
CppGPs Winovich (2019)	C++	MIT	nw2190/CppGPs	master (2019-04-24)		Nick Winovich	docs examples				Gaussian Process Regression (GPR)			Isotropic	Squared Exponential			Gaussian	default value: 1e-10	Inferable	Maximum Likelihood Estimation (MLE)	L-BFGS
DACE Nielsen et al. (2002)	MATLAB	Custom	n/a	v2.5	add to the path	Technical University of Denmark (DTU)	docs user manuals				Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Constant Linear Quadratic	Isotropic Anisotropic	Gaussian Exponential Linear Spherical Cubic Spline			Gaussian		Inferable	Maximum Likelihood Estimation (MLE)	Matlab Optimization Toolbox
Dakota Adams et al. (2026)	C++ Python	LGPL	snl-dakota/dakota	v6.24.0	conda	Sandia National Laboratories Dakota contributors	docs API examples tutorials	GitHub discussions			Gaussian Process Regression (GPR) Gradient-enhanced Kriging (GEK)		Constant Linear Reduced Quadratic Quadratic	Anisotropic	Squared Exponential Matern32 Matern52			Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE)	DIRECT CONMIN Random sampling L-BFGS-B		Root Mean Squared Error (RMSE) Mean Squared Error (MSE) Mean Absolute Error (MAE) Coefficient of determination (\( R^2 \)) Leave-One-Out Cross-Validation (LOOCV)
deepgp Sauer et al. (2023)	R	LGPL	cran/deepgp	1.2.3	CRAN	Virginia Polytechnic Institute and State University	docs tutorials				Gaussian Process Regression (GPR) Deep Gaussian Processes (DGP) Vecchia-approximated GP/DGP Gradient-enhanced GP/DGP Monotonically-warped DGP	\( \mathcal{O}(N^3) \)	Zero	Isotropic Anisotropic	Matern Squared Exponential			Gaussian	Custom Inferable	Inferable	Markov Chain Monte Carlo (MCMC) Metropolis-Hastings (MH) Elliptical Slice Sampling (ESS)			Root Mean Squared Error (RMSE)
DiceKriging Roustant et al. (2012)	R	GPL-2.0	cran/DiceKriging	1.6.1	CRAN	INSA Toulouse Ecole des Mines de St-Etienne Universitat Bern Alpestat	docs	blog			Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Zero Constant Polynomial Custom	Isotropic Anisotropic	Gaussian Exponential Matern32 Matern52 Power Exponential			Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE)	BFGS genoud
egobox-gp Lafage (2022)	Rust Python	Apache-2.0	relf/egobox	0.37.9	cargo PyPI	ONERA University of Toulouse egobox contributors	docs				Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Constant Linear Quadratic	Isotropic Anisotropic	Squared Exponential Absolute Exponential Matern32 Matern52			Gaussian			Maximum Likelihood Estimation (MLE) Fully Independent Training Conditional (FITC)	COBYLA SLSQP		Leave-One-Out Cross-Validation (LOOCV) Leave-One-Out Cross-Validation (CV)
Emukit Paleyes et al. (2019)	Python	Apache-2.0	EmuKit/emukit	0.5.1	PyPI	Amazon University of Cambridge Emukit contributors	docs API tutorials jupyter notebooks		NumPy SciPy		Gaussian Process Regression (GPR) Multi-output Gaussian Process (MOGP) Linear Multi-fidelity GP Nonlinear Multi-fidelity GP			Isotropic Anisotropic	Squared Exponential Matern12 Matern32 Matern52 Brownian Custom		Product	Gaussian		Inferable	Markov Chain Monte Carlo (MCMC)
fbm Neal (1996)	C	BSL-1.0	radfordneal/fbm	fbm.2022-04-21		University of Toronto	docs				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Multi-class Classification (softmax) Poisson Regression (count data)		Zero	Isotropic Anisotropic	Constant Linear Squared Exponential Power Exponential Cauchy (power -1) White noise			Gaussian Student-T Logit Softmax Poisson	default value: 0 Custom Inferable Fixed Non-Trainable	Inferable	Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) Gibbs sampling Metropolis-Hastings			Mean Squared Error (MSE) Mean Absolute Error (MAE) Negative Log Predictive Density (NLPD)
fdagstat Grujic et al. (2017)	R	GPL-2.0	ogru/fdagstat	1.0		Stanford University Politecnico di Milano	tutorials				Gaussian Process Regression (GPR) Multi-output Gaussian Process (MOGP) Ordinary Trace Kriging Universal Trace Kriging Universal Trace Co-Kriging Co-Kriging of FPC scores		Constant Linear	Isotropic Anisotropic	Gaussian Matern Custom		Sum Product Product-Sum Separable	Gaussian	Custom Inferable		Ordinary Least Squares (OLS) Generalised Least Squares (GLS)
friedrich Demeure (2019)	Rust	Apache-2.0	nestordemeure/friedrich	0.6.0	cargo	friedrich contributors	docs				Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Zero Constant Linear Custom	Isotropic	Squared Exponential Exponential Matern32 Matern52 Rational Quadratic Linear Polynomial Multiquadric Hyperbolic Tangent Custom		Sum Product	Gaussian	Custom	Custom Inferable	Maximum Likelihood Estimation (MLE)	Adam Gradient Descent
FRK Zammit-Mangion et al. (2021)	R	GPL-2.0	andrewzm/FRK	2.3.2	CRAN	University of Wollongong	docs r docs tutorials API				Gaussian Process Regression (GPR) Fixed Rank Kriging (FRK) Spatial Random Effects (SRE) model Spatio-Temporal Kriging Generalised Linear Mixed Model (GLMM)		Constant Linear Custom	Isotropic Anisotropic	Bisquare Gaussian Exponential Matern32			Gaussian Poisson Binomial Gamma Negative Binomial Inverse-Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE) Expectation Maximisation (EM) Laplace Approximation (LA)	nlminb
gaussianproc RobinRCM (2020)	GO	MIT	RobinRCM/sklearn	v0		RobinRCM	docs				Gaussian Process Regression (GPR)			Isotropic Anisotropic	Squared Exponential Constant Dot Product White noise		Sum Product Exponentiation	Gaussian		Inferable	Maximum Likelihood Estimation (MLE)	L-BFGS		Coefficient of determination (\( R^2 \))
GaussianProcesses.jl Fairbrother et al. (2022)	julia	MIT	STOR-i/GaussianProcesses.jl	v0.12.6	Pkg.jl	Lancaster University EPFL GaussianProcesses.jl contributors	docs tutorials jupyter notebooks		Optim.jl Distributions.jl		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process (SGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Constant Linear Polynomial Sum Product Custom	Isotropic Anisotropic	Squared Exponential Matern12 Matern32 Matern52 Polynomial Periodic Rational Quadratic Fixed Masked		Sum Product	Gaussian Bernoulli Poisson Binomial Exponential Student-T	Custom	Inferable	Maximum Likelihood Estimation (MLE) Markov Chain Monte Carlo (MCMC) Variational Inference (VI) Fully Independent Training Conditional (FITC) Subset of Regressors (SoR) Deterministic Training Conditional (DTC) Full scale approximation (FSA)	Optim.jl optimizer L-BFGS Conjugate Gradient (CG)
george Ambikasaran et al. (2015)	Python	MIT	dfm/george	v0.4.4	PyPI conda	New York University Simons Foundation george contributors	docs tutorials		NumPy SciPy		Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \) O(N log^2 N)	Zero Constant Custom	Isotropic Anisotropic	Constant Dot Product Exponential Squared Exponential Matern32 Matern52 Rational Quadratic Exponential Sine Squared Cosine Local Gaussian Polynomial Linear Custom		Sum Product	Gaussian	Custom Inferable default value: log(TINY)	Inferable Custom	Maximum Likelihood Estimation (MLE) Markov Chain Monte Carlo (MCMC)	L-BFGS-B SciPy optimizer
GeoStats.jl Hoffimann (2018)	julia	MIT	JuliaEarth/GeoStats.jl	v0.90.2	Pkg.jl	Stanford University GeoStats.jl contributors	docs tutorials user manuals talk	chat GitHub discussions			Gaussian Process Regression (GPR) Simple Kriging (SK) Ordinary Kriging (OK) Universal Kriging (UK) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \)	Constant Linear Quadratic Polynomial Custom	Isotropic Anisotropic	Gaussian Spherical Exponential Matern Cubic Penta-Spherical Sine Hole Circular		Sum Scale	Gaussian	Custom Inferable	Inferable	Weighted Least Squares (WLS)			Leave-One-Out Cross-Validation (LOOCV) Validation Error
go-bayesopt Rice (2017)	GO	MIT	d4l3k/go-bayesopt	master (2024-05-31)		go-bayesopt contributors	API				Gaussian Process Regression (GPR)			Isotropic	Matern52 Custom			Gaussian	Custom default value: 0
go-kriging lvisei (2020)	GO	MIT	lvisei/go-kriging	v0.0.1-alpha.15		lvisei	docs				Ordinary Kriging (OK)			Isotropic	Gaussian Exponential Spherical			Gaussian	Inferable	Custom	Variogram fitting (Bayesian priors)
goptuna-bayesopt Shibata (2020)	GO	MIT	c-bata/goptuna-bayesopt	master (2020-07-29)		goptuna-bayesopt contributors	API examples				Gaussian Process Regression (GPR) go-bayesopt GP			Isotropic	Matern52			Gaussian	default value: 0
GPax Ziatdinov et al. (2021)	Python	MIT	ziatdinovmax/gpax	0.1.8	PyPI	Oak Ridge National Laboratory GPax contributors	docs tutorials API colab notebooks jupyter notebooks	GitHub discussions	JAX NumPyro		Gaussian Process Regression (GPR) Structured Gaussian Process (sGP) GP with Uncertain Inputs (UIGP) Heteroskedastic GP (VarNoiseGP) Measured-Noise GP Vector-valued GP (vExactGP) Variational Gaussian Process (VGP) Sparse Variational Gaussian Process (SVGP) Deep Kernel Learning (DKL) Variational Deep Kernel Learning (viDKL) Infinite-width Bayesian Neural Network (iBNN) Multi-output Gaussian Process (MOGP) Multi-task Deep Kernel Learning (viMTDKL) Structured Probabilistic Model (sPM)		Zero Custom	Isotropic Anisotropic	Squared Exponential Matern52 Periodic NNGP Multitask LCMK Custom			Gaussian Heteroskedastic Noise	Custom default value: 1e-6	Inferable	Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) Stochastic Variational Inference (SVI) Evidence Lower Bound (ELBO) Maximum A Posteriori (MAP)	Adam
GPc SheffieldML (2014)	C++	MIT	SheffieldML/GPc	master (2021-09-16)		University of Sheffield GPc contributors	docs examples				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process Regression (SGPR) Informative Vector Machine (IVM) Gaussian Process Latent Variable Model (GPLVM) Back constrained Gaussian Process Latent Variable Model (BCGPLVM) Gaussian Process Dynamical Model (GPDM)			Isotropic Anisotropic	Squared Exponential Exponential Rational Quadratic Matern32 Matern52 Linear Polynomial MLP Bias White noise		Sum Product	Gaussian Probit Ordered Categorical Null Category Noise Model (NCNM)	Inferable	Inferable	Maximum Likelihood Estimation (MLE) Deterministic Training Conditional (DTC) Variational Free Energy (VFE)	Scaled Conjugate Gradient (SCG) Conjugate Gradient (CG) Gradient Descent
GPEXP Gorodetsky et al. (2016)	Python	GPL-2.0	goroda/GPEXP	pre-refactor		Massachusetts Institute of Technology GPEXP contributors	examples		NumPy SciPy		Gaussian Process Regression (GPR)			Isotropic Anisotropic	Squared Exponential Matern Mehler
GPflow Matthews et al. (2017)	Python	Apache-2.0	GPflow/GPflow	v2.11.1	PyPI	University of Cambridge University of Oxford Kyoto University University of Edinburgh The University of Manchester Lancaster University GPflow contributors	docs	slack GitHub discussions stackoverflow	TensorFlow		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process Regression (SGPR) GPR with Fully Independent Training Conditional (FITC) Variational Gaussian Process (VGP) Sparse Variational Gaussian Process (SVGP) Gaussian Process Latent Variable Model (GPLVM) Conjugate Gradient Lower Bound (CGLB) Gaussian Process Markov Chain Monte Carlo (GPMC) Sparse Gaussian Process Markov Chain Monte Carlo (SGPMC) Convolutional Gaussian Process Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Sum Polynomial Constant Identity Linear Product Switched Function Custom	Isotropic Anisotropic	ArcCosine Bias Change Points Constant Convolutional Coregion Cosine Exponential Independent Latent Linear Linear Coregionalization Matern12 Matern32 Matern52 Multioutput Periodic Polynomial Squared Exponential Rational Quadratic Separate Independent Shared Independent Static Stationary White noise Custom		Sum Product Combination	Bernoulli Beta Exponential Gamma Gaussian Gaussian MC Heteroskedastic TFP Conditional Monte Carlo Likelihood Multi Latent Likelihood Student-T Poisson Softmax Switched Likelihood Scalar Custom	Custom Fixed Non-Trainable default value: 1e-6	Inferable	Maximum Likelihood Estimation (MLE) Variational Free Energy (VFE) Evidence Lower Bound (ELBO) Markov Chain Monte Carlo (MCMC) Expectation Propagation (EP) Laplace Approximation (LA)	Natural Gradient Descent (NGD) Adam SciPy optimizer Keras optimizer
GPflux Dutordoir et al. (2021)	Python	Apache-2.0	secondmind-labs/GPflux	v0.4.5	PyPI	University of Cambridge Imperial College London University College London Secondimind labs GPflux contributors	docs tutorials API	slack	TensorFlow		Deep Gaussian Processes (DGP) Sparse Variational Gaussian Process (SVGP)	\( \mathcal{O}(M^3) \)	Identity Linear Zero	Anisotropic	Squared Exponential Matern12 Linear Periodic Separate Independent Custom		Sum	Gaussian Bernoulli Softmax RobustMax Custom		Inferable	Evidence Lower Bound (ELBO) Variational Inference (VI)	Adam Keras optimizer Natural Gradient Descent (NGD)
GpGp Guinness et al. (2018)	R	MIT	cran/GpGp	1.0.0	CRAN	Cornell University GpGp contributors	docs tutorials				Gaussian Process Regression (GPR) Vecchia-approximated Gaussian Process Spatio-Temporal Gaussian Process Gaussian Process on the Sphere Nonstationary-variance Gaussian Process		Constant Linear	Isotropic Anisotropic	Matern Matern32 Matern52 Matern72 Matern92 Exponential Spatio-Temporal Matern Matern on Sphere Nonstationary-Variance Matern Categorical Random-Effects Matern			Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE) Vecchia Likelihood	Fisher Scoring
GPJax Pinder et al. (2022)	Python	Apache-2.0	QuantClimate/GPJax	v1.0.0	PyPI	Lancaster University GPJax contributors	docs tutorials API	GitHub discussions contact form	JAX		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Deep Gaussian Processes (DGP) Sparse Gaussian Process Regression (SGPR) Sparse Variational Gaussian Process (SVGP) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Constant Combination	Isotropic Anisotropic	Matern12 Matern32 Matern52 Squared Exponential Rational Quadratic Power Exponential Periodic White noise Linear Polynomial Graph kernels Non-stationary ArcCosine Non-stationary Linear Non-stationary Polynomial Custom		Sum Product	Gaussian Bernoulli Poisson	Custom Inferable default value: 1e-6	Inferable	Maximum Likelihood Estimation (MLE) Leave-One-Out Cross-Validation (LOOCV) Markov Chain Monte Carlo (MCMC) Stochastic Variational Inference (SVI) Evidence Lower Bound (ELBO) Variational Expectation (VE)	Optax SciPy optimizer		Leave-One-Out Cross-Validation (LOOCV) Conjugate Marginal Log-Likelihood (MLL) Log-Posterior Density
GPmat SheffieldML (2013)	MATLAB	BSD-3-Clause	SheffieldML/GPmat	v1.0.0	add to the path	University of Sheffield GPmat contributors	docs examples				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process Regression (SGPR) Informative Vector Machine (IVM) Gaussian Process Latent Variable Model (GPLVM) Back constrained Gaussian Process Latent Variable Model (BCGPLVM) Hierarchical Gaussian Process Latent Variable Model (HGPLVM) Gaussian Process Dynamical Model (GPDM)		Zero Custom	Isotropic Anisotropic	Squared Exponential Gaussian Matern32 Matern52 Rational Quadratic Linear Polynomial Periodic Gibbs MLP Ornstein-Uhlenbeck (OU) Wiener Single Input Motif (SIM) Latent Force Model (LFM) Bias White noise		Sum Product	Gaussian Probit Ordered Categorical Null Category Noise Model (NCNM)	Inferable Fixed Non-Trainable	Inferable	Maximum Likelihood Estimation (MLE) Deterministic Training Conditional (DTC) Fully Independent Training Conditional (FITC) Partially Independent Training Conditional (PITC) Variational Free Energy (VFE)	Scaled Conjugate Gradient (SCG) Conjugate Gradient (CG)
GPML Rasmussen et al. (2010)	MATLAB GNU Octave	FreeBSD	hnickisch/gpml-matlab	v4.2+dev2	add to the path	University of Cambridge Max Planck Institute	docs user manuals				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero One Constant Linear Polynomial Discrete Precomputed mean Predictive Nearest neighbor Weighted sum of projected cosines Scaled Sum Product Power Mask Difference Warped	Isotropic Anisotropic	Constant White noise Piecewise Polynomial Matern12 Matern32 Matern52 Rational Quadratic Squared Exponential Linear		Sum Product Scale Mask	Probit Logit Uniform Gaussian Gumbel Laplace Sech-square Student-T Poisson Negative Binomial Gamma Exponential Log Gaussian Beta Mixture	Custom Inferable Fixed Non-Trainable	Inferable	Exact inference Laplace Approximation (LA) Expectation Propagation (EP) Variational Bayes Approximation (VB) Kullback-Leibler Approximation (KL) Markov Chain Monte Carlo (MCMC) Leave-One-Out Cross-Validation (LOOCV)	Conjugate Gradient (CG) L-BFGS-B minFunc
GPmp Vazquez (2026)	Python	GPL-3.0	gpmp-dev/gpmp	v0.9.31	PyPI	CentraleSupélec GPmp contributors	docs tutorials examples API		NumPy SciPy PyTorch		Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Zero Constant Linear Predictor (Universal Kriging) Custom	Anisotropic	Squared Exponential Exponential Matern12 Matern32 Matern52 Matern Custom			Gaussian	Custom default value: 10sigma2eps_mach	Custom	Maximum Likelihood Estimation (MLE) Restricted Maximum Likelihood Estimation (REMLE) Restricted Maximum A Posteriori (REMAP) Markov Chain Monte Carlo (MCMC) Sequential Monte Carlo (SMC)	SLSQP L-BFGS-B SciPy optimizer		Root Mean Squared Error (RMSE) Coefficient of determination (\( R^2 \)) Leave-One-Out Cross-Validation (LOOCV)
GPRust KentaKato (2024)	Rust	N/A	KentaKato/GPRust	main (2024-03-22)		GPRust contributors	examples				Gaussian Process Regression (GPR)										Maximum Likelihood Estimation (MLE)	Grid Search
GPstuff Vanhatalo et al. (2017)	R MATLAB GNU Octave	GPL-3.0	gpstuff-dev/gpstuff	v4.7	add to the path CRAN	University of Helsinki Aalto University of Science GPstuff contributors	docs				Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process (SGP) GPR with Fully Independent Training Conditional (FITC) GPR with Partial Independent Training Conditional (PITC) Sparse Variational Gaussian Process (SVGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Constant Linear Squared	Isotropic Anisotropic	Categorical Constant Squared Exponential Linear Matern32 Matern52 NN Periodic Piecewise Polynomial Rational Quadratic		Sum Product Scale	Gaussian Gaussian scale mixture Student-T Logit Probit Softmax Binomial Poisson Negative Binomial Hurdle model Weibull	Custom	Inferable	Maximum Likelihood Estimation (MLE) Deviance information criterion (DIC) Leave-One-Out Cross-Validation (LOOCV) Widely Applicable Information Criterion (WAIC) Laplace Approximation (LA) Expectation Propagation (EP) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC)	fminscg fminlbfgs fminunc		Euclidean distance
gptk Kalaitzis et al. (2014)	R	FreeBSD	cran/gptk	1.08		University of Sheffield University of Cambridge Aalto University	docs examples				Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) GPR with Fully Independent Training Conditional (FITC) GPR with Partial Independent Training Conditional (PITC) GPR with Deterministic Training Conditional (DTC)			Isotropic	Squared Exponential White noise		Sum	Gaussian		Inferable	Maximum Likelihood Estimation (MLE)	Scaled Conjugate Gradient (SCG) Conjugate Gradient (CG)
GPvecchia Katzfuss et al. (2017)	R	GPL-2.0 GPL-3.0	katzfuss-group/GPvecchia	0.1.8	CRAN	Texas A&M University Cornell University GPvecchia contributors	docs tutorials				Gaussian Process Regression (GPR) Vecchia-approximated Gaussian Process Sparse General Vecchia (SGV) Vecchia-Laplace Generalised Gaussian Process Nearest Neighbour Gaussian Process (NNGP) Multi-Resolution Approximation (MRA) Modified Predictive Process (MPP) Full-Scale Approximation (FSA)		Zero Constant Linear	Isotropic	Matern Exponential + Squared Exponential (esqe) Custom			Gaussian Logit Poisson Gamma Beta	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE) Vecchia Likelihood Laplace Approximation (LA)	optim Nelder-Mead
GPy GPy (2012)	Python	BSD-3-Clause	SheffieldML/GPy	v1.14.2	PyPI	University of Sheffield GPy contributors	docs jupyter notebooks	GitHub discussions	NumPy SciPy		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Sparse Gaussian Process Regression (SGPR) Sparse Gaussian Process Classification (SGPC) Variational Gaussian Process (VGP) Gaussian Process Latent Variable Model (GPLVM) Sparse Gaussian Process Latent Variable Model (SGPLVM) Spike-and-Slab Gaussian Process Latent Variable Model (SSGPLVM) Back constrained Gaussian Process Latent Variable Model (BCGPLVM) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Constant Linear Polynomial Custom	Isotropic Anisotropic	Squared Exponential Matern Brownian Linear Bias Periodic Polynomial MLP Coregionalized White noise Cosine Exponential Rational Quadratic		Sum Product Coregionalization Active Dimensions	Gaussian Bernoulli Binomial Exponential Gamma Log Logistic Log Gaussian Mixed Noise Poisson Student-T Weibull	Custom Inferable default value: 1e-6	Inferable	Maximum Likelihood Estimation (MLE) Evidence Lower Bound (ELBO) Variational Free Energy (VFE) Laplace Approximation (LA) Variational Inference (VI)	L-BFGS Scaled Conjugate Gradient (SCG) Gradient Descent SciPy optimizer
GPyTorch Gardner et al. (2018)	Python	MIT	cornellius-gp/gpytorch	v1.15.2	PyPI conda	Cornell University The University of British Columbia Meta New York University University of Pennsylvania GPyTorch contributors	docs examples	stackoverflow GitHub discussions	PyTorch		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) GPR with BlackBox Matrix-Matrix Inference (BBMM) GPR with LancZos Variance Estimates (LOVE) Sparse Gaussian Process Regression (SGPR) Structured Kernel Interpolation (SKI/KISS-GP) Structured Kernel Interpolation for Products (SKIP) Structure-Exploiting Kernels Approximate GP Inference Deep Gaussian Processes (DGP) Gaussian Process Latent Variable Model (GPLVM) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(N^2) \) \( \mathcal{O}(NM^2) \) \( \mathcal{O}(N) \) \( \mathcal{O}(N + M \log M) \)	Zero Constant Linear	Isotropic Anisotropic	Cosine Constant Cylindrical Linear Matern Periodic Piecewise Polynomial Polynomial Squared Exponential Rational Quadratic Spectral Delta Spectral Mixture Arc Index LCMK Multitask Grid Grid Interpolation Inducing Point RFFK Hamming IMQ Gaussian Symmetrized KL Distributional Input		Sum Product Scale Spectral Mixture	Gaussian Gaussian With Missing Values Fixed Noise Gaussian Dirichlet Classification Bernoulli Beta Laplace Student-T Multitask Gaussian Softmax Heteroskedastic Noise	Custom Fixed Non-Trainable default value: 1e-6 for float default value: 1e-8 for double	Inferable	Maximum Likelihood Estimation (MLE) Leave-One-Out Cross-Validation (LOOCV) Evidence Lower Bound (ELBO) Variational Inference (VI) Predictive Log Likelihood Gamma Robust Variational ELBO Deep Approximate MLL Inducing Point Kernel Added Loss Term KL Gaussian Added Loss Term	Natural Gradient Descent (NGD) PyTorch optimizer Adam L-BFGS SGD		Negative Log Predictive Density (NLPD) Meas Standardized Log Loss (MSLL) Mean Absolute Error (MAE) Mean Squared Error (MSE)
GSTools Müller et al. (2022)	Python	LGPL	GeoStat-Framework/GSTools	v1.7.0	PyPI conda	UFZ University of Potsdam CASUS Utrecht University GSTools contributors	docs tutorials API	GitHub discussions	NumPy SciPy		Gaussian Process Regression (GPR) Simple Kriging (SK) Ordinary Kriging (OK) Universal Kriging (UK) External Drift Kriging Detrended Kriging		Constant Linear Quadratic Polynomial External Drift Custom	Isotropic Anisotropic	Gaussian Exponential Matern Exponential Integral Stable Rational Quadratic Cubic Linear Circular Spherical HyperSpherical SuperSpherical J-Bessel Truncated Power Law (TPLGaussian, TPLExponential, TPLStable, TPLSimple) White noise Custom		Sum	Gaussian	Custom Inferable	Custom	Variogram fitting (non-linear least squares) Weighted Least Squares (WLS)	SciPy optimizer Trust Region Reflective (trf) Dogleg (dogbox)		Coefficient of determination (\( R^2 \))
IterGP Wenger et al. (2022)	Python	MIT	JonathanWenger/itergp	main (2023-04-12)		University of Tübingen Columbia University Max Planck Institute for Intelligent Systems IterGP contributors	docs tutorials API jupyter notebooks				Gaussian Process Regression (GPR) Computation-aware Gaussian Process (IterGP) IterGP-Cholesky IterGP-CG (Conjugate Gradient) IterGP-PI (Pseudo-Input / Inducing Points) Auto-Preconditioned Conjugate Gradient Projected Bayes Regressor Mixed Strategy	\( \mathcal{O}(N^2) \)	Zero Custom	Isotropic	Squared Exponential Matern White noise		Sum Scale	Gaussian
Keras-GP Al-Shedivat et al. (2017)	Python	MIT	alshedivat/keras-gp	0.3.2		Carnegie Mellon University Cornell University Keras-GP contributors	examples tutorials		TensorFlow		Gaussian Process Regression (GPR) Deep Kernel Learning (DKL) GP-RNN / GP-LSTM / GP-GRU Structured Kernel Interpolation (SKI/KISS-GP) Massively Scalable Gaussian Process (MSGP)		Zero Constant Linear Sum	Isotropic	Squared Exponential Spectral Mixture			Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE) Exact inference	Adam Keras optimizer		Root Mean Squared Error (RMSE) Mean Squared Error (MSE)
libgp Blum & Riedmiller (2013)	C++	BSD-3-Clause	mblum/libgp	v0.3.0		Manuel Blum	docs				Gaussian Process Regression (GPR)		Zero	Isotropic Anisotropic	Squared Exponential Matern32 Matern52 Rational Quadratic Linear Periodic White noise Custom		Sum Product	Gaussian	Custom	Inferable Custom	Maximum Likelihood Estimation (MLE)	Conjugate Gradient (CG) Rprop
libKriging Richet et al. (2023)	C++ Python R MATLAB GNU Octave	Apache-2.0	libKriging/libKriging	v1.2.2	PyPI CRAN	libKriging contributors	docs r docs API colab notebooks	GitHub discussions			Gaussian Process Regression (GPR) Ordinary Kriging (OK) Universal Kriging (UK) Input-warped Kriging (WarpKriging) Deep Kernel Learning (DKL) Nested Kriging (NK / PoE / gPoE / BCM / rBCM)	\( \mathcal{O}(N^3) \)	Constant Linear Interactive Quadratic	Anisotropic	Gaussian Exponential Matern32 Matern52			Gaussian	Inferable	Custom	Maximum Likelihood Estimation (MLE) Leave-One-Out Cross-Validation (LOOCV) Log-Marginal Posterior (LMP) Vecchia approximated log-likelihood (LLVecchia) Nystrom approximated log-likelihood (LLNystrom)	BFGS Multi-start BFGS Newton		Leave-One-Out Cross-Validation (LOOCV)
mogptk de Wolff et al. (2020)	Python	MIT	GAMES-UChile/mogptk	v0.5.3	PyPI	GAMES Universidad de Chile mogptk contributors	docs tutorials examples		PyTorch		Gaussian Process Regression (GPR) Multi-output Gaussian Process (MOGP) Spectral Mixture (SM) Multi-Output Spectral Mixture (MOSM) Cross Spectral Mixture (CSM) Spectral Mixture Linear Model of Coregionalization (SM-LMC) Convolutional Gaussian (CONV) Multi-Output Harmonizable Spectral Mixture (MOHSM) Sparse Gaussian Process Regression (SGPR) Sparse Variational Gaussian Process (SVGP) Variational Gaussian Process (VGP) Sparse Pseudo-input GP (Snelson and Ghahramani)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(N^2) \)	Constant Linear Multi-Output Mean Custom	Isotropic Anisotropic	Constant Cosine Exponential Function Linear Locally Periodic Matern Periodic Polynomial Rational Quadratic Sinc Spectral Spectral Mixture Squared Exponential White noise Change Points Cross Spectral (CSM) Gaussian Convolution Process (CONV) Independent Multi-output Linear Coregionalization Multi-Output Harmonizable Spectral (MOHSM) Multi-Output Spectral (MOSM) Multi-Output Spectral Mixture Uncoupled Multi-Output Spectral (uMOSM) Custom		Sum Product Mixture Automatic Relevance Determination	Bernoulli Beta Chi-Squared Exponential Gamma Gaussian Laplace Log Gaussian Log Logistic Multi-Output Likelihood Poisson Student-T Weibull Custom	Custom Fixed Non-Trainable default value: 1e-8 default value: 1e-6	Inferable Custom	Maximum Likelihood Estimation (MLE) Exact inference Evidence Lower Bound (ELBO) Variational Inference (VI)	Adam L-BFGS Adagrad SGD PyTorch optimizer		Mean Absolute Error (MAE) Mean Absolute Percentage Error (MAPE) Mean Squared Error (MSE) Root Mean Squared Error (RMSE)
MUQ Parno et al. (2021)	C++ Python	BSD-3-Clause	mituq/muq2	v0.5.0	conda	Massachusetts Institute of Technology Dartmouth College New York University Heidelberg University National Science Foundation US Department of Energy	docs examples py examples	slack			Gaussian Process Regression (GPR) Markov (State Space) Gaussian Process		Zero Constant Linear Linear Transform Sum	Isotropic Anisotropic	Squared Exponential Matern Periodic Linear Constant White noise Linear Transform		Sum Product Concatenate	Gaussian	default value: 1e-14	Custom
Neural Tangents Novak et al. (2020)	Python	Apache-2.0	google/neural-tangents	v0.6.5	PyPI	Google Brain University of Cambridge Neural Tangents contributors	docs colab notebooks talk	GitHub discussions	JAX		Gaussian Process Regression (GPR) Neural Network Gaussian Process (NNGP) Neural Tangent Kernel (NTK) NTK Gaussian Process (NTKGP)				NNGP NTK		Sum Product Concatenation Serial composition Parallel composition		Custom default value: 0.0		Exact inference Infinite-time Gradient Flow (NTK)
ooDACE Couckuyt et al. (2014)	MATLAB	GPL-3.0	n/a	v1.4	add to the path	Ghent University	docs				Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Zero Constant Linear Polynomial	Isotropic Anisotropic	Gaussian Matern32 Matern52 Exponential			Gaussian		Inferable	Maximum Likelihood Estimation (MLE) Cross-validation estimation (CV)	NLopt PCTOptimizer		Mean Squared Error (MSE) Leave-One-Out Cross-Validation (CV)
OpenCossan Patelli (2017)	MATLAB	LGPL	cossan-working-group/OpenCossan	v1.1.2	add to the path	University of Liverpool Leibniz University Hannover OpenCossan contributors	docs tutorials				Gaussian Process Regression (GPR)		Constant Linear Quadratic	Anisotropic	Exponential Power Exponential Gaussian Linear Spherical Spline									Coefficient of determination (\( R^2 \))
OpenTURNS Baudin et al. (2016)	C++ Python	LGPL	openturns/openturns	v1.26	PyPI conda	Airbus Group EDF R&D Phimeca Engineering IMACS ONERA OpenTURNS contributors	docs	chat forum stackoverflow			Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Constant Linear Quadratic Custom	Isotropic Anisotropic	Squared Exponential Exponential Matern Kronecker Rank-M Spherical Tensorized Custom		Product	Gaussian	Custom Inferable	Inferable	Maximum Likelihood Estimation (MLE)	NLopt COBYLA L-BFGS-B TNC		Coefficient of determination (\( R^2 \)) Mean Squared Error (MSE)
PyDeepGP SheffieldML (2016)	Python	BSD-3-Clause	SheffieldML/PyDeepGP	master (2021-05-04)		University of Sheffield PyDeepGP contributors	examples jupyter notebooks		NumPy SciPy		Deep Gaussian Processes (DGP) Variational Auto-encoded Deep GPs	\( \mathcal{O}(NM^2) \)		Isotropic Anisotropic	Squared Exponential Bias		Sum	Gaussian		Inferable	Variational Inference (VI) Stochastic Variational Inference (SVI)	GPy optimizer
pyGPs Neumann et al. (2015)	Python	FreeBSD	marionmari/pyGPs	v1.3.5	PyPI	Washington University Fraunhofer IAIS TU Dortmund Sproutling pyGPs contributors	docs examples		NumPy SciPy		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) GPR with Fully Independent Training Conditional (FITC) GPC with Fully Independent Training Conditional (FITC) Multi-class Gaussian Process Classification (one-vs-one)		Zero One Constant Linear Sum Product Scaled Power Custom	Isotropic Anisotropic	Constant Linear Matern Periodic Polynomial Piecewise Polynomial Squared Exponential Rational Quadratic Gabor Spectral Mixture White noise Graph kernels Precomputed Custom		Sum Product Scale	Gaussian Probit Laplace	Custom Inferable default value: 0.1	Inferable	Maximum Likelihood Estimation (MLE) Exact inference Expectation Propagation (EP) Laplace Approximation (LA) Fully Independent Training Conditional (FITC)	Minimize Conjugate Gradient (CG) BFGS Scaled Conjugate Gradient (SCG)		Root Mean Squared Error (RMSE) Negative Log Predictive Density (NLPD)
pyinterpolate Moliński (2022)	Python	BSD-3-Clause	DataverseLabs/pyinterpolate	v1.2.1	PyPI conda	Dataverse Labs pyinterpolate contributors	docs tutorials jupyter notebooks API	GitHub discussions chat	NumPy SciPy		Gaussian Process Regression (GPR) Indicator Kriging Poisson Kriging Block Kriging (area-to-area, area-to-point)		Constant Linear	Isotropic Anisotropic	Circular Cubic Exponential Gaussian Linear Power Spherical			Gaussian	Custom Inferable		Variogram autofit (RMSE/MAE/Bias/SMAPE)	Grid Search		Root Mean Squared Error (RMSE) Mean Absolute Error (MAE)
PyKrige Müller et al. (2022)	Python	BSD-3-Clause	GeoStat-Framework/PyKrige	v1.7.3	PyPI conda	UFZ University of Potsdam CASUS Utrecht University PyKrige contributors	docs examples API	GitHub discussions	NumPy SciPy		Gaussian Process Regression (GPR) Ordinary Kriging (OK) Universal Kriging (UK) Regression Kriging Classification Kriging (Simplicial Indicator Kriging)		Constant Linear Point Logarithmic External Drift Custom	Isotropic Anisotropic	Linear Power Gaussian Spherical Exponential Hole-Effect Custom			Gaussian	Custom Inferable		Variogram fitting (soft L1 norm minimization)			Coefficient of determination (\( R^2 \)) Leave-One-Out Cross-Validation (CV)
PyMC Abril-Pla et al. (2023)	Python	Apache-2.0	pymc-devs/pymc	v6.3.2	PyPI conda	ArviZ-Devs Boston University Google Research University of Toronto The Hospital for Sick Children Philadelphia Phillies Baseball Operations Department PyMC Labs Stony Brook University Universidad Nacional de San Luis Forschungszentrum Jülich University of Oxford NumFOCUS Mistplay ODSC ADIA Lab PyMC contributors	docs examples API	forum GitHub discussions	JAX Numba		Gaussian Process Regression (GPR) Latent Gaussian Process Sparse Gaussian Process Regression (SGPR) Kronecker Structured Gaussian Process Hilbert Space Gaussian Process (HSGP) Student-T Process (TP) Gaussian Process Classification (GPC) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) O(NM + M)	Zero Constant Linear Custom	Isotropic Anisotropic	Constant White noise Squared Exponential Rational Quadratic Exponential Matern12 Matern32 Matern52 Linear Polynomial Cosine Periodic Circular Gibbs Warped Input Scaled Covariance Kronecker Coregion Custom		Sum Product Scale Exponentiation	Gaussian Student-T Bernoulli Custom	Custom default value: 1e-6	Inferable	Markov Chain Monte Carlo (MCMC) No-U-Turn Sampler (NUTS) Maximum A Posteriori (MAP) Automatic Differentiation Variational Inference (ADVI) Variational Free Energy (VFE) Fully Independent Training Conditional (FITC) Deterministic Training Conditional (DTC)	L-BFGS-B BFGS Powell SciPy optimizer
pymc-learn Emaasit et al. (2018)	Python	BSD-3-Clause	pymc-learn/pymc-learn	v0.0.1rc3	PyPI	pymc-learn contributors	docs user manuals examples API jupyter notebooks	stackoverflow			Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) Student-T Process Regression (STPR)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Zero Constant	Isotropic Anisotropic	Squared Exponential Dot Product White noise		Sum	Gaussian Student-T		Inferable	Variational Inference (VI) Automatic Differentiation Variational Inference (ADVI) Markov Chain Monte Carlo (MCMC) No-U-Turn Sampler (NUTS)			Coefficient of determination (\( R^2 \))
PYRO Bingham et al. (2019)	Python	Apache-2.0	pyro-ppl/pyro	1.9.1	PyPI conda	Uber AI Stanford University Broad Institute Linux Foundation PYRO contributors	docs examples	forum	PyTorch		Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) Variational Gaussian Process (VGP) Sparse Variational Gaussian Process (SVGP) Gaussian Process Classification (GPC) Gaussian Process Latent Variable Model (GPLVM) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \) \( \mathcal{O}(M^3) \)	Zero Custom	Isotropic Anisotropic	Squared Exponential Matern32 Matern52 Exponential Rational Quadratic Periodic Cosine Linear Polynomial Constant White noise Brownian Coregionalize Custom		Sum Product Exponent Vertical Scaling Warping	Gaussian Bernoulli Softmax Poisson Custom	Custom default value: 1e-6	Inferable	Maximum Likelihood Estimation (MLE) Maximum A Posteriori (MAP) Evidence Lower Bound (ELBO) Variational Inference (VI) Stochastic Variational Inference (SVI) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) Variational Free Energy (VFE) Fully Independent Training Conditional (FITC) Deterministic Training Conditional (DTC)	Adam PyTorch optimizer
scikit-learn Pedregosa et al. (2011)	Python	BSD-3-Clause	scikit-learn/scikit-learn	1.9.1	PyPI conda	Community driven NVIDIA INRIA Hugging Face Microsoft Quansight Labs sci-kit-learn contributors	docs examples tutorials API	blog stackoverflow GitHub discussions	NumPy SciPy		Gaussian Process Regression (GPR) Gaussian Process Classification (GPC)	\( \mathcal{O}(N^3) \)	Zero	Isotropic Anisotropic	Matern Constant Dot Product Squared Exponential Rational Quadratic White noise		Sum Product Exponentiation Compound	Gaussian Bernoulli	Custom default value: 1e-10	Inferable	Maximum Likelihood Estimation (MLE) Laplace Approximation (LA) Expectation Propagation (EP)	L-BFGS-B SciPy optimizer		Mean Squared Error (MSE) Mean Squared Log Error (MSLE) Root Mean Squared Error (RMSE) Mean Absolute Error (MAE) Mean Absolute Percentage Error (MAPE) Median Absolute Error (MedAE) Coefficient of determination (\( R^2 \)) Explained Variance Max Error
SMT Saves et al. (2024)	Python	BSD-3-Clause	SMTorg/smt	v2.15.0	PyPI	ISAE SUPEAERO NASA ONERA University of Michigan University of San Diego Polytechnique Montréal SMT contributors	docs tutorials	GitHub discussions	NumPy Numba SciPy		Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) Marginal GP Inference Kriging with Partial Least Squares (KPLS / KPLSK) Gradient-enhanced Kriging (GEK)	\( \mathcal{O}(N^3) \) \( \mathcal{O}(NM^2) \)	Constant Linear Quadratic	Isotropic Anisotropic	Power Exponential Absolute Exponential Squared Exponential Matern32 Matern52 Categorical Hierarchical			Gaussian	Custom Inferable default value: 2.22e-14	Inferable	Maximum Likelihood Estimation (MLE) Fully Independent Training Conditional (FITC) Variational Free Energy (VFE)	COBYLA TNC
STAN Stan Development Team (2017)	R C++ julia Python MATLAB	BSD-3-Clause	brian-lau/MatlabStan	v2.15.1.0	CRAN PyPI Pkg.jl conda	Stan Development Team NumFOCUS Stan contributors MatlabStan contributors RStan contributors pyStan contributors Stan.jl contributors	docs r docs mat docs py docs jl docs	forum slack			Gaussian Process Regression (GPR) Gaussian Process Classification (GPC) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \)	Zero Custom	Isotropic Anisotropic	Squared Exponential Dot Product Exponential Matern32 Matern52 Periodic Custom			Gaussian Poisson Bernoulli Custom	Custom	Inferable	Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) No-U-Turn Sampler (NUTS) Maximum A Posteriori (MAP) Automatic Differentiation Variational Inference (ADVI) Pathfinder Laplace Approximation (LA)	L-BFGS BFGS Newton
Stheno Tebbutt et al. (2019)	julia Python	MIT	JuliaGaussianProcesses/Stheno.jl	v0.8.2	Pkg.jl PyPI	University of Cambridge Stheno.jl contributors Stheno py contributors	py docs jl docs py examples jl examples py API jl API talk	GitHub discussions	NumPy TensorFlow PyTorch JAX		Gaussian Process Regression (GPR) Gaussian Process Probabilistic Programme (GPPP) Multi-output Gaussian Process (MOGP) Sparse Gaussian Process Regression (SGPR) GPR with Fully Independent Training Conditional (FITC) GPR with Deterministic Training Conditional (DTC) Bayesian Linear Regression		Zero Constant Custom	Isotropic Anisotropic	Squared Exponential Exponential Gamma Exponential Matern Matern12 Matern32 Matern52 Matern72 Rational Quadratic Rational Gamma Rational Linear Polynomial Piecewise Polynomial Periodic Cosine Constant White noise Exponentiated Fractional Brownian Motion Gabor Gibbs Neural Network Wiener Spectral Mixture Independent Multi-output Intrinsic Coregionalization Latent Factor Linear Mixing Model Causal Exponentiated Quadratic (CEQ) Decaying Log		Sum Product Scale Tensor Product	Gaussian	Custom default value: 1e-12	Inferable Custom	Maximum Likelihood Estimation (MLE) Markov Chain Monte Carlo (MCMC) Hamiltonian Monte Carlo (HMC) Evidence Lower Bound (ELBO) Variational Free Energy (VFE) Fully Independent Training Conditional (FITC) Deterministic Training Conditional (DTC)	Optim.jl optimizer BFGS Nelder-Mead L-BFGS-B PyTorch optimizer Adam
STK Bect et al. (2023)	MATLAB GNU Octave	GPL-3.0	stk-kriging/stk	2.8.1	add to the path	CentraleSupélec STK contributors	docs examples	mailing-list			Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Zero Constant Linear	Isotropic Anisotropic	Gaussian Matern32 Matern52 Spherical Discrete			Gaussian		Inferable	Restricted Maximum Likelihood Estimation (REMLE)	fmincon fminsearch		Leave-One-Out Cross-Validation (LOOCV)
SuperGauss Ling et al. (2020)	R	GPL-3.0	mlysy/SuperGauss	2.0.4	CRAN	University of Waterloo SuperGauss contributors	docs tutorials				Stationary Gaussian Time Series (Toeplitz likelihood)	\( \mathcal{O}(N^2) \) O(N log^2 N)	Zero Custom	Isotropic	Fractional Brownian Motion Matern Power Exponential Exponential			Gaussian			Maximum Likelihood Estimation (MLE)	optimize nlm Newton's Method
Surrogates.jl Rackauckas et al. (2024)	julia	MIT	SciML/Surrogates.jl	v8.0.0	Pkg.jl	Chan Zuckerberg Initiative Wellcome Trust Microsoft Surrogates.jl contributors	docs	chat			Gaussian Process Regression (GPR) Gradient-enhanced Kriging (GEK) Kriging with Partial Least Squares (KPLS / KPLSK) Gradient-enhanced KPLS (GEKPLS)	\( \mathcal{O}(N^3) \)	Constant	Isotropic Anisotropic	Power Exponential Gaussian Matern52 Polynomial		Sum Product Scale Tensor Product	Gaussian	Custom default value: 10*eps()	Custom	Maximum Likelihood Estimation (MLE)	Nelder-Mead
TemporalGPs.jl Tebbutt et al. (2021)	julia	MIT	JuliaGaussianProcesses/TemporalGPs.jl	v0.7.3	Pkg.jl	University of Cambridge Aalto University TemporalGPs.jl contributors	examples talk		Distributions.jl		Gaussian Process Regression (GPR) Markov (State Space) Gaussian Process Spatio-Temporal Gaussian Process Sparse Markov Gaussian Process Gaussian Process Classification (GPC)	\( \mathcal{O}(N) \)	Zero Constant	Isotropic	Matern12 Matern32 Matern52 Cosine Approximate Periodic Constant Squared Exponential		Sum Product Scale Separable	Gaussian Bernoulli	Custom	Inferable Custom	Maximum Likelihood Estimation (MLE) Evidence Lower Bound (ELBO) Deterministic Training Conditional (DTC)	Optim.jl optimizer BFGS
TensorFlow Probability Dillon et al. (2017)	Python	Apache-2.0	tensorflow/probability	v0.25.0	PyPI conda	Google Columbia University TensorFlow Probability contributors	docs API tutorials examples jupyter notebooks	stackoverflow mailing-list blog	TensorFlow JAX		Gaussian Process Regression (GPR) Variational Gaussian Process (VGP) Student-T Process Regression Gaussian Process Latent Variable Model (GPLVM) Multi-output Gaussian Process (MOGP)		Zero Custom	Isotropic Anisotropic	Squared Exponential Matern12 Matern32 Matern52 Matern Periodic Rational Quadratic Constant Linear Polynomial Gamma Exponential Exponential Curve Parabolic Pointwise Exponential Spectral Mixture Change Points Schur Complement Feature Scaled Feature Transformed Kumaraswamy Transformed Custom		Sum Product	Gaussian Custom	Custom default value: 1e-6	Inferable	Maximum Likelihood Estimation (MLE) Evidence Lower Bound (ELBO) Variational Inference (VI) Markov Chain Monte Carlo (MCMC)	Adam L-BFGS BFGS Nelder-Mead Differential Evolution Stochastic Gradient Langevin Dynamics (SGLD) Variational SGD
tinygp Foreman-Mackey et al. (2024)	Python	MIT	dfm/tinygp	v0.3.1	PyPI	Simons Foundation tinygp contributors	docs tutorials API	GitHub discussions	JAX NumPyro		Gaussian Process Regression (GPR) Scalable Gaussian Processes	\( \mathcal{O}(N^3) \)	Custom	Isotropic Anisotropic	Constant Polynomial Dot Product Exponential Squared Exponential Matern32 Matern52 Cosine Exponential Sine Squared Rational Quadratic Custom		Sum Product	Gaussian Non-Gaussian	Custom	Inferable	Maximum Likelihood Estimation (MLE)	jaxopt
Trieste Picheny et al. (2023)	Python	Apache-2.0	secondmind-labs/trieste	v4.6.0	PyPI	Secondmind Labs Trieste contributors	docs tutorials API jupyter notebooks	slack GitHub discussions	TensorFlow		Gaussian Process Regression (GPR) Sparse Gaussian Process Regression (SGPR) Sparse Variational Gaussian Process (SVGP) Variational Gaussian Process (VGP) Gaussian Process Classification (GPC) Multi-fidelity Autoregressive GP Multi-fidelity Nonlinear Autoregressive GP Deep Gaussian Processes (DGP)		Constant		Matern52 Matern32 Custom			Gaussian Bernoulli		Inferable	Maximum Likelihood Estimation (MLE) Variational Inference (VI)	SciPy optimizer Adam Natural Gradient Descent (NGD)
UQLab Marelli et al. (2014)	MATLAB	BSD-3-Clause	n/a	v2.1.0	add to the path	RSUQ ETH Zürich UQLab contributors	docs user manuals examples	contact form forum			Gaussian Process Regression (GPR) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \)	Zero Constant Linear Quadratic Polynomial Custom	Isotropic Anisotropic	Linear Exponential Gaussian Matern32 Matern52 Custom			Gaussian	Custom default value: 1e-10	Inferable	Maximum Likelihood Estimation (MLE) Cross-validation estimation (CV)	L-BFGS GA HGA CMA-ES HCMA-ES		Leave-One-Out Cross-Validation (LOOCV) Validation Error
UQpy Olivier et al. (2020)	Python	MIT	SURGroup/UQpy	v4.2.1	PyPI conda	Johns Hopkins University UQpy contributors	docs examples	GitHub discussions	NumPy SciPy		Gaussian Process Regression (GPR)	\( \mathcal{O}(N^3) \)	Constant Linear Quadratic Custom	Isotropic Anisotropic	Squared Exponential Matern Custom			Gaussian		Inferable	Maximum Likelihood Estimation (MLE)	SciPy optimizer MinimizeOptimizer COBYLA
UQ[py]Lab Lataniotis et al. (2021)	Python	BSD-3-Clause	n/a	v1.0.2	PyPI	RSUQ ETH Zürich UQ[py]Lab contributors	docs user manuals examples	contact form forum			Gaussian Process Regression (GPR) Multi-output Gaussian Process (MOGP)	\( \mathcal{O}(N^3) \)	Zero Constant Linear Quadratic Polynomial Custom	Isotropic Anisotropic	Linear Exponential Gaussian Matern32 Matern52 Custom			Gaussian	Custom default value: 1e-10	Inferable	Maximum Likelihood Estimation (MLE) Cross-validation estimation (CV)	L-BFGS GA HGA CMA-ES HCMA-ES		Leave-One-Out Cross-Validation (LOOCV) Validation Error
UQTk Debusschere et al. (2017)	C++	BSD-3-Clause	sandialabs/UQTk	v3.1.5		Sandia National Laboratories UQTk contributors	docs user manuals API examples	GitHub discussions			Gaussian Process Regression (GPR)		Polynomial	Anisotropic	Squared Exponential			Gaussian	default value: 1e-6 Custom		Exact inference Maximum A Posteriori (MAP)	L-BFGS

Source: © A. Faraci, P. Beaurepaire, N. Gayton; A comprehensive guide to Gaussian Process libraries: bridging theory with practice through features, limitations, and performance.

This Project has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie project GREYDIENT – Grant Agreement n°955393