
 Description:
If you use GPstuff, please use the reference: Jarno Vanhatalo, Jaakko Riihimäki, Jouni Hartikainen, Pasi Jylänki, Ville Tolvanen, Aki Vehtari (2013). GPstuff: Bayesian Modeling with Gaussian Processes. In Journal of Machine Learning Research, 14:11751179.
See also user guide at http://arxiv.org/abs/1206.5754
GPstuff is a toolbox for Bayesian Modeling with Gaussian Processes with following features and more:

Several covariance functions (e.g. squared exponential, exponential, Matérn, periodic and a compactly supported piece wise polynomial function)
 Sums, products and scaling of covariance functions
 Euclidean and delta distance
 Several mean functions with marginalized parameters

Several likelihood/observation models
 Continuous observations: Gaussian, Gaussian scale mixture (MCMC only), Student'st, quantile regression
 Classification: Logit, Probit, multinomial logit (softmax), multinomial probit
 Count data: Binomial, Poisson, (Zero truncated) NegativeBinomial, Hurdle model, Zeroinflated NegativeBinomial, Multinomial
 Survival: CoxPH, Weibull, logGaussian, loglogistic
 Point process: LogGaussian Cox process
 Density estimation and regression: logistic GP
 Other: derivative observations (for sexp covariance function only)
 Monotonicity information
 Hierarchical priors for hyperparameters

Sparse models
 Sparse matrix routines for compactly supported covariance functions
 Fully and partially independent conditional (FIC, PIC)
 Compactly supported plus FIC (CS+FIC)
 Variational sparse (VAR), Deterministic training conditional (DTC), Subset of regressors (SOR) (Gaussian/EP only)
 PASSGP

Latent inference
 Exact (Gaussian only)
 Laplace, Expectation propagation (EP), Parallel EP, RobustEP
 marginal posterior corrections (cm2 and fact)
 Scaled Metropolis, Hamiltonian Monte Carlo (HMC), Scaled HMC, Elliptical slice sampling
 State space inference (1D for some covariance functions)

Hyperparameter inference
 Type II ML/MAP
 Leaveoneout crossvalidation (LOOCV), Laplace/EP LOOCV
 Metropolis, HMC, NoUTurnSampler (NUTS), Slice Sampling (SLS), Surrogate SLS, Shrinkingrank SLS, Covariancematching SLS
 Grid, CCD, Importance sampling

Model assessment
 LOOCV, Laplace/EP LOOCV, ISLOOCV, kfoldCV
 WAIC, DIC
 Average predictive comparison

Several covariance functions (e.g. squared exponential, exponential, Matérn, periodic and a compactly supported piece wise polynomial function)
 Changes to previous version:
20160609 Version 4.7
Development and release branches available at https://github.com/gpstuffdev/gpstuff
New features
 Simple Bayesian Optimization demo
Improvements
 Improved use of PSIS
 More options added to gp_monotonic
 Monotonicity now works for additive covariance functions with selected variables
 Possibility to use gpcf_squared.mcovariance function with derivative observations/monotonicity
 Default behaviour made more robust by changing default jitter from 1e9 to 1e6
 LALOO uses the cavity method as the default (see Vehtari et al (2016). Bayesian leaveoneout crossvalidation approximations for Gaussian latent variable models. JMLR, accpeted for publication)
 Selected variables option works now better with monotonicity
Bugfixes
 small error in derivative observation computation fixed
 several minor bug fixes
 BibTeX Entry: Download
 Corresponding Paper BibTeX Entry: Download
 URL: Project Homepage
 JMLR MLOSS PaperURL: JMLRMLOSS Paper Homepage
 Supported Operating Systems: Agnostic, Platform Independent
 Data Formats: Matlab, Octave
 Tags: Classification, Regression, Machine Learning, Nonparametric Bayes, Gaussian Process, Bayesian Inference
 Archive: download here
Other available revisons

Version Changelog Date 4.7 20160609 Version 4.7
Development and release branches available at https://github.com/gpstuffdev/gpstuff
New features
 Simple Bayesian Optimization demo
Improvements
 Improved use of PSIS
 More options added to gp_monotonic
 Monotonicity now works for additive covariance functions with selected variables
 Possibility to use gpcf_squared.mcovariance function with derivative observations/monotonicity
 Default behaviour made more robust by changing default jitter from 1e9 to 1e6
 LALOO uses the cavity method as the default (see Vehtari et al (2016). Bayesian leaveoneout crossvalidation approximations for Gaussian latent variable models. JMLR, accpeted for publication)
 Selected variables option works now better with monotonicity
Bugfixes
 small error in derivative observation computation fixed
 several minor bug fixes
June 9, 2016, 17:45:15 4.6 20150709 Version 4.6
Development and release branches available at https://github.com/gpstuffdev/gpstuff
New features
Use Pareto smoothed importance sampling (Vehtari & Gelman, 2015) for
importance sampling leaveoneout crossvalidation (gpmc_loopred.m)
importance sampling integration over hyperparameters (gp_ia.m)
importance sampling part of the logistic Gaussian process density estimation (lgpdens.m)
references:
 Aki Vehtari and Andrew Gelman (2015). Pareto smoothed importance sampling. arXiv preprint arXiv:1507.02646.
 Aki Vehtari, Andrew Gelman and Jonah Gabry (2015). Efficient implementation of leaveoneout crossvalidation and WAIC for evaluating fitted Bayesian models.
New covariance functions
 gpcf_additive creates a mixture over products of kernels for each dimension reference: Duvenaud, D. K., Nickisch, H., & Rasmussen, C. E. (2011). Additive Gaussian processes. In Advances in neural information processing systems, pp. 226234.
 gpcf_linearLogistic corresponds to logistic mean function
 gpcf_linearMichelismenten correpsonds Michelis Menten mean function
Improvements  faster EP moment calculation for lik_logit
Several minor bugfixes
July 15, 2015, 15:08:06 4.5 20140722 Version 4.5
New features
Input dependent noise and signal variance.
 Tolvanen, V., Jylänki, P. and Vehtari, A. (2014). Expectation Propagation for Nonstationary Heteroscedastic Gaussian Process Regression. In Proceedings of IEEE International Workshop on Machine Learning for Signal Processing, accepted for publication. Preprint http://arxiv.org/abs/1404.5443
Sparse stochastic variational inference model.
 Hensman, J., Fusi, N. and Lawrence, N. D. (2013). Gaussian processes for big data. arXiv preprint http://arxiv.org/abs/1309.6835.
Option 'autoscale' in the gp_rnd.m to get split normal approximated samples from the posterior predictive distribution of the latent variable.
Geweke, J. (1989). Bayesian Inference in Econometric Models Using Monte Carlo Integration. Econometrica, 57(6):13171339.
Villani, M. and Larsson, R. (2006). The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis. Communications in Statistics  Theory and Methods, 35(6):11231140.
Improvements
 New unit test environment using the Matlab builtin test framework (the old Xunit package is still also supported).
 Precomputed demo results (including the figures) are now available in the folder tests/realValues.

New demos demonstrating new features etc.
 demo_epinf, demonstrating the input dependent noise and signal variance model
 demo_svi_regression, demo_svi_classification
 demo_modelcomparison2, demo_survival_comparison
Several minor bugfixes
July 22, 2014, 14:03:11 4.4 20140411 Version 4.4
New features
Monotonicity constraint for the latent function.
 Riihimäki and Vehtari (2010). Gaussian processes with monotonicity information. Journal of Machine Learning Research: Workshop and Conference Proceedings, 9:645652.
State space implementation for GP inference (1D) using Kalman filtering.
 For the following covariance functions: SquaredExponential, Matérn3/2 & 5/2, Exponential, Periodic, Constant

Särkkä, S., Solin, A., Hartikainen, J. (2013).
Spatiotemporal learning via infinitedimensional Bayesian filtering and smoothing. IEEE Signal Processing Magazine, 30(4):5161.
 Simo Sarkka (2013). Bayesian filtering and smoothing. Cambridge University Press.
 Solin, A. and Särkkä, S. (2014). Explicit link between periodic covariance functions and state space models. AISTATS 2014.
Improvements
 GP_PLOT function for quick plotting of GP predictions
 GP_IA now warns if it detects multimodal posterior distributions
 much faster EP with logGaussian likelihood (numerical integrals > analytical results)
 faster WAIC with GP_IA array (numerical integrals > analytical results)

New demos demonstrating new features etc.
 demo_minimal, minimal demo for regression and classification
 demo_kalman1, demo_kalman2
 demo_monotonic, demo_monotonic2
Plus bug fixes
April 15, 2014, 15:26:49 4.3.1 20131126 Version 4.3.1
Improvements:

Updated cpsrf and psrf to follow BDA3: split each chain to two halves and use Geyer's IPSE for n_eff
 Multilatent models for Octave
November 29, 2013, 14:10:59 4.3 20131014 Version 4.3
Improvements:
 lgpdens.m: better default estimation using importance and rejection sampling, better default priors (see updated paper http://arxiv.org/abs/1211.0174)
 RobustEP for zero truncated negativebinomial likelihood
 If moment computations in EP return NaN, return NaN energy (handled gracefully by fminlbfgs and fminscg)
 gp_cpred.m: new option 'target'
 gp_ia.m: Changed Hessian computation stepsize to 1e3
 gpstuff_version.m: function for returning current GPstuff version
 gpia_jpreds.m: a new function
 demo_survival_weibull.m > demo_survival_aft.m
Bug fixes:
 build suitesparse path correctly if it includes spaces
 gp_avpredcomp.m: fixed for CoxPH
 gp_cpred.m: fixed for CoxPH
 esls.m: don't accept a step to a point with infinite log likelihood
 gp_ia.m: removed some redundant computation
 gp_rnd.m: works now for multilatent models also
 bugfixes for setrandstream
 other bugfixes
October 16, 2013, 13:27:09 4.2 20130614 Version 4.2
Improvements
 Crossvalidation much faster if no biascorrections are needed (computes only the necessary predictions)
 Marginal posterior corrections with loopred (Laplace) and crossvalidation
 More robust computation of marginal posterior corrections
 More robust density estimation in lgpdens (default parameters changed)
Bug fixes
 Mex files now in correct folders if compiled with SuiteSparse (covariance matrix computation now much faster)
 Fixed bug with default marginal posterior correction when using gp_predcm
 Fixed conditions in likelihood functions for grid approximation of predictions with marginal posterior corrections
 Fixed outputs of gpmc_preds with multilatent models (thanks to Mahdi Biparva for pointing this out)
 and some minor bug fixes
June 14, 2013, 12:30:18 4.1 20130424 Version 4.1
New features:
 Multinomial probit classification with nestedEP. Jaakko Riihimäki, Pasi Jylänki and Aki Vehtari (2013). Nested Expectation Propagation for Gaussian Process Classification with a Multinomial Probit Likelihood. Journal of Machine Learning Research 14:75109, 2013.

Marginal posterior corrections for latent values. Cseke & Heskes
(2011). Approximate Marginals in Latent Gaussian Models. Journal of Machine Learning Research 12 (2011), 417454
 Laplace: cm2 and fact
 EP: fact
Improvements
 lgpdens ignores now NaNs instead of giving error
 gp_cpred has a new option 'target' accpeting values 'f' or 'mu'

unified gp_waic and gp_dic
 by default return mlpd
 option 'form' accetps now values 'mean' 'all' 'sum' and 'dic'

improved survival demo demo_survival_aft (accalerated failure time)
 renamed and improved from demo_survival_weibull
 rearranged some files to more logical directories
 bug fixes
New files
 gp_predcm: marginal posterior corrections for latent values.
 demo_improvedmarginals: demonstration of marginal posterior corrections
 demo_improvedmarginals2: demonstration of marginal posterior corrections
 lik_multinomprobit: multinomial probit likelihood
 demo_multiclass_nested_ep: demonstration of nested EP with multinomprobit
April 25, 2013, 11:07:06 4.0 Initial Announcement on mloss.org.
March 22, 2013, 08:14:05
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