GAUSSIAN PROCESS REGRESSION AND CLASSIFICATION Toolbox version 4.2 for GNU Octave 3.2.x and Matlab 7.x and higher
Copyright (c) by Carl Edward Rasmussen and Hannes Nickisch, 2018-06-11.
If you want to get started without further delay, then read section 1) below and jump right to the examples in doc/index.html.
This collection of matlab programs implements and demonstrates some of the algorithms described in a) the book by Rasmussen and Williams: "Gaussian Processes for Machine Learning", the MIT Press 2006, in b) the article by Nickisch and Rasmussen: "Approximations for Binary Gaussian Process Classification", JMLR 2008, in c) the article by Candela and Rasmussen: "A Unifying View of Sparse Approximate Gaussian Process Regression", JMLR 2005, in d) the paper by Murray, Adams and Mackay: "Elliptical slice sampling", AISTATS 2010, in e) the report by Neal: "Annealed Importance Sampling", UToronto 1998, in f) the paper by Naish-Guzman and Holden: "The Generalized FITC Approximation", NIPS, 2007, in g) the paper by Duvenaud, Nickisch and Rasmussen: "Additive Gaussian Processes", NIPS, 2011, in h) the paper by Wilson and Adams: "Gaussian Process Kernels for Pattern Discovery and Extrapolation", ICML, 2013, in i) the paper by Snelson, Rasmussen and Ghahramani: "Warped Gaussian Processes", NIPS, 2003, and in j) the paper by Wilson and Nickisch: "Kernel interpolation for scalable structured Gaussian processes (KISS-GP)", ICLM, 2015, k) the paper by Nickisch, Solin and Grigorievskiy: "State Space Gaussian Processes with Non-Gaussian Likelihood", ICLM, 2018, and l) the paper by Pleiss, Gardner, Weinberger and Wilson "Constant-Time Predictive Distributions for Gaussian Processes", ICLM, 2018.
There are 7 code subdirectories: cov, doc, inf, lik, mean, prior and util.
cov/ contains covariance functions cov*.m => see covFunctions.m
doc/ contains an index.html file providing documentation. This information is also available from http://www.GaussianProcess.org/gpml/code. Usage of mean, cov, classification and regression is demonstrated in usage*.m. Further details can be found in the developer documentation manual.pdf.
inf/ contains the inference algorithms inf*.m => see infMethods.m
lik/ contains the likelihood functions lik*.m => see likFunctions.m
mean/ contains the mean functions mean*.m => see meanFunctions.m
prior/ contains the hyperparameter prior distributions prior*.m => see priorDistributions.m
util/ contains optimisation routines, backward compatibility programs and small auxiliary scripts
Before running the demos or any other part of the code, you should execute startup.m to add all necessary directories to your path. In Octave, you can also use the .octaverc file.
Some of the programs make use of the MEX facility in matlab for more efficient implementation. However, if you don't know about how to compile MEX files, you do not need to worry about this -- the code runs anyway. If you do compile the MEX files, this is automatically detected, and the program will run more efficiently. If you do not have a compiler installed on your system, you might want to consult [3].
Two components of the toolbox can be accelerated by MEX.
First, there is an auxiliary functions solve_chol.m having a MEX equivalent. This can be compiled by either executing util/make.m from the Matlab/Octave command line. In addition to that, we provide a Makefile for Matlab in util/ that you can run by simply typing make in your shell after having supplied your Matlab path and your operating system. We recommend the make.m script because it works both under Matlab and Octave.
Second, in order to use the L-BFGS minimiser for hyperparameter optimisation as an equivalent to minimize.m, you have to compile Peter Carbonetto's "Matlab interface for L-BFGS-B" [1] which was extended to also work for Octave by José Vallet. The challenge here is the Fortran 77 code. We provide a Makefile suitable for Linux 32/64 bit and Mac whenever you have 1) g77 or 2) gfortran properly set up. The latter is prefered on current Ubuntu systems. Under Ubuntu, you can achieve this by installing the packages fort77 and gfortran, respectively. Note that the code is GNU licensed.
Compilation is done by editing util/lbfgsb/Makefile. In any case, you need to provide $MATLAB_HOME which can be found by the commands 'locate matlab' or 'find / -name "matlab"'. You can choose between two compilation modes: a) without mex utility by Matlab [default] provide $MEX_SUFFIX and $MATLAB_LIB, then type 'make nomex' b) using the mex utility by Matlab provide $MEX, then type 'make mex' c) compilation for Octave provide Octave variables and type 'make oct'
In Ubuntu 10.04 LTS, the libg2c library needed for both 1)+a) and 1)+b) is not included per default. If 'ls /usr/lib/libg2c.*' does not list anything this is the case on your machine. You then whant to install the packages gcc-3.4-base and libg2c0 e.g. from http://packages.ubuntu.com/hardy/gcc-3.4-base and http://packages.ubuntu.com/hardy/libg2c0. After installation, you have to create a symbolic link by 'cd /usr/lib' and 'ln -s libg2c.so.0 libg2c.so'.
There were reports of problems running the mex files on recent 64bit Ubuntu since the libgfortran.3.0.0 that comes with matlab ($(MATLAB_HOME)/sys/os/glnxa64/libgfortran.so.3.0.0) is not the same as the libgfortran.3.0.0 that comes with the ubuntu package libgfortran3 and that is used when linking. So running the mex file results in a version mismatch error. The issue can be solved by changing the name of to the matlab file and linking to the ubuntu file instead: in $(MATLAB_HOME)/sys/os/glnxa64 run 'sudo mv libgfortran.3.0.0 libgfortran.3.0.0_matlab' 'sudo ln -s /usr/lib/x86_64-linux-gnu/libgfortran.so.3.0.0 libgfortran.3.0.0' Thanks to Giampiero Salvi for posting the workaround.
[1] https://github.com/pcarbo/lbfgsb-matlab [2] http://www.mathworks.com/support/compilers/R2010a
The current version of the programs is 4.2. Previous versions of the code are available at http://www.gaussianprocess.org/gpml/code/oldcode.html.
State space covariance approximation apxState, infState
Fast predictive variance estimation for grid-based approximate covariances
Bugfixes
Little features
Logdet-estimation functionality for grid-based approximate covariances
More generic infEP functionality
New infKL function contributed by Emtiyaz Khan and Wu Lin
Time-series covariance functions on the positive real line
New covariance functions
A major code restructuring effort did take place in the current release unifying certain inference functions and allowing more flexibility in covariance function composition. We also redesigned the whole derivative computation pipeline to strongly improve the overall runtime. We finally include grid-based covariance approximations natively.
More generic sparse approximation using Power EP
Approximate covariance object unifying sparse approximations, grid-based approximations and exact covariance computations
Hiearchical structure of covariance functions
Faster derivative computations for mean and cov functions
New mean functions
New optimizer
New prior
New GLM link function
Smaller fixes
New likelihood functions in lik/:
New inference functions in inf/:
New covariance functions in cov/:
A major code reorganisation effort did take place in the current release. First, classification and regression are now done by a single file gp.m which is completely generic in the likelihood. The previous regression program gpr.m corresponds to gp.m with Gaussian likelihood. Several other likelihoods for robust regresssion were added. Further, the code now supports mean functions with a similar specification mechanism as already used by the covariance functions. Previous implementations correspond to using meanZero.m. We merged the covariance functions covMatern3iso.m and covMatern5.iso into a single covMaterniso.m and added a covariance function for additive functions as well as the possibility to use only certain components of the data. Finally, we included covPPiso.m a piecewise polynomial covariance function with compact support.
New likelihood functions in lik/: likGauss.m, likLaplace.m, likLogistic.m and likT.m
New mean functions in mean/: meanConst.m, meanLinear.m, meanPow.m, meanProd.m, meanSum.m and meanZero.m
New covariance functions in cov/: covADD.m, covMask.m, covPPiso.m
The gprSRPP.m function which previously provided "Subset of Regressors" and the "Projected Process" approximation has now been removed.
covConst.m: fixed a bug which caused an error in the derivative of the log marginal likelihood for certain combinations of covariance functions and approximation methods. (Thanks to Antonio Eleuteri for reporting the problem)
gauher.m: added the function "gauher.m" which was mistakenly missing from the previous release. This caused an error for certain combinations of approximation method and likelihood function.
logistic.m: modified the approximation of moments calculation to use a mixture of cumulative Gaussian, rather than Gauss-Hermite quadrature, as the former turns out to be more accurate.
Some code restructuring has taken place for the classification code to make it more modular, to facilitate addition of new likelihood functions and approximations methods. Now, all classification is done using the binaryGP function, which (among other things) takes an approximation method and a likelihood function as an arguments. Thus, binaryGP replaces both binaryEPGP and binaryLapaceGP, although wrapper functions are still provided for backward compatibility. This gives added flexibility: now EP can also be used wth the logistic likelihood function (implemented using Gauss-Hermite quadrature).
approxEP.m: New file, containing the Expectation Propagation approximation method, which was previously contained in binaryEPGP.m
approxLA.m: New file, containing Laplaces approximation method, which was previously contained in binaryLaplace.m
approximations.m: New file, help for the approximation methods.
binaryEPGP.m: This file has been replaced by a wrapper (for backward compatibility) which calls the more general binaryGP function.
binaryGP.m: New general function to do binary classification.
binaryLaplaceGP.m: This file has been replaced by a wrapper (for backward compatibility) which calls the more general binaryGP function.
covMatern3iso.m, covMatern5iso.m, covNNone.m, covRQard.m, covRQiso.m, cosSEard, covSEiso: now check more carefully, that persistent variables have the correct sizes, and some variable names have been modified.
cumGauss.m: New file, containing code for the cumulative Gaussian likelihood function
likelihoods.m: New file, help for likelihood functions
logistic.m: New file, logistic likelihood
covRQard.m: bugfix: replaced x with x' and z with z' in line 36
covRQiso.m: bugfix: replaced x with x' and z with z' in line 28
minimize.m: correction: replaced "error()" with "error('')", and made a few cosmetic changes
binaryEPGP.m: added the line "lml = -n*log(2);" in line 77. This change should be largely inconsequential, but occationally may save things when the covariance matrix is exceptionally badly conditioned.
added the "erfint" function to "binaryLaplaceGP.m". The erfint function was missing by mistake, preventing the use of the "logistic" likelihood.
added files: "covProd.m" and "covPeriodic.m"
changes: "covSEiso.m" was changed slightly to avoid the use of persistent variables
initial version shipped with the book