A Gaussian Processes package for Julia.
This package is still under development. If you have any suggestions to improve the package, or if you've noticed a bug, then please post an issue for us and we'll get to it as quickly as we can. Pull requests are also welcome.
Gaussian processes are a family of stochastic processes which provide a flexible nonparametric tool for modelling data. A Gaussian Process places a prior over functions, and can be described as an infinite dimensional generalisation of a multivariate Normal distribution. Moreover, the joint distribution of any finite collection of points is a multivariate Normal. This process can be fully characterised by its mean and covariance functions, where the mean of any point in the process is described by the mean function and the covariance between any two observations is specified by the kernel. Given a set of observed real-valued points over a space, the Gaussian Process is used to make inference on the values at the remaining points in the space.
For an extensive review of Gaussian Processes there is an excellent book Gaussian Processes for Machine Learning by Rasmussen and Williams, (2006)
GaussianProcesses.jl requires Julia version 0.7 or above. To install GaussianProcesses.jl run the following command inside a Julia session:
julia> using Pkg julia> Pkg.add("GaussianProcesses")
The package allows the user to fit exact Gaussian process models when the observations are Gaussian distributed about the latent function. In the case where the observations are non-Gaussian, the posterior distribution of the latent function is intractable. The package allows for Monte Carlo sampling from the posterior.
The main function of the package is
GP, which fits the Gaussian process
gp = GP(x, y, mean, kernel) gp = GP(x, y, mean, kernel, likelihood)
for Gaussian and non-Gaussian data respectively.
The package has a number of mean, kernel and likelihood functions available. See the documentation for further details.
The parameters of the model can be estimated by maximizing the log-likelihood (where the latent function is integrated out) using the
optimize! function, or in the case of non-Gaussian data, an
mcmc function is available, utilizing the Hamiltonian Monte Carlo sampler, and can be used to infer the model parameters and latent function values.
optimize!(gp) # Find parameters which maximize the log-likelihood mcmc(gp) # Sample from the GP posterior
See the notebooks for examples of the functions used in the package.
Documentation is accessible in the Julia REPL in help mode. Help mode can be started by typing '?' at the prompt.
julia> ?GP search: GP GPE GPMC GPBase gperm log1p getpid getproperty MissingException GP(x, y, mean::Mean, kernel::Kernel[, logNoise::Float64=-2.0]) Fit a Gaussian process that is defined by its mean, its kernel, and the logarithm logNoise of the standard deviation of its observation noise to a set of training points x and y. See also: GPE ──────────────────────────────────────────────────────────────────────────── GP(x, y, mean::Mean, kernel::Kernel, lik::Likelihood) Fit a Gaussian process that is defined by its mean, its kernel, and its likelihood function lik to a set of training points x and y. See also: GPMC
Alternatively, online documentation and is under development
Sample code is available from the notebooks
GeoStats - High-performance implementations of geostatistical algorithms for the Julia programming language. This package is in its initial development, and currently only contains Kriging estimation methods. More features will be added as the Julia type system matures.
This package also supports the ScikitLearn interface. ScikitLearn provides many tools for machine learning such as hyperparameter tuning and cross-validation. See here for an example of its usage with this package.
4 days ago