3.0 API Reference

GaussianKernelHyperparameters

This contains the hyperparameters for the gaussian kernel. The functional form for correlation between xp and xq is w0 exp( -0.5 * \sum{d=1}^D ((x{p,d} - x{q,d})/wd)^2) where D is the number of dimensions. and each term of the summation is a different dimension of xp and x_q.

RProp_params

K_matrix(X::Array{Float64,2}, cov_func::Function, cov_func_parameters::GaussianKernelHyperparameters, noise::Float64 = 0.0)

Returns a Kmatrix together with marginal K matrices (marginal over each hyperparameter). THe covfunc should be a function with a signature like that of gaussian_kernel.

K_matrix_with_marginals(X::Array{Float64,2}, cov_func::Function, cov_func_parameters::GaussianKernelHyperparameters, noise::Float64 = 0.0)

Returns a K_matrix together with marginal K matrices (marginal over each hyperparameter)

calibrate_by_ML_with_Rprop(X, y, cov_func_parameters, MaxIter, noise, params)

Trains kriging hyperparameters by maximising marginal likelihood with RProp.

calibrate_by_ML_with_SGD(X, y, cov_func_parameters, steps, batch_size, step_multiple, noise, twister)

Trains kriging hyperparameters by maximising marginal likelihood with stochastic gradient descent.

correlation_vector_of_a_point(x::AbstractArray{T,1},X::AbstractArray{R,2}, cov_func::Function, cov_func_parameters::GaussianKernelHyperparameters) where T<:Real where R<:Real

This calculates the correlations of a point with each point in the X array.

evaluate(modl::KrigingModel, PointToExamine::AbstractArray{T,1}) where T<:Real

Returns the kriging predictor value (ordinary kriging estimate) at the given point.

expected_improvement(modl::KrigingModel, fmin::Real, PointToExamine::AbstractArray{<:Real,1})

Computes the expected improvement (Jones, Schonlau, Welch Equation 15) at a point. Returns how much improvement over the current best value fmin is expected.

gaussian_kernel(x1::Array{Float64,1}, x2::Array{Float64,1}, cov_func_parameters::GaussianKernelHyperparameters)

Returns a covariance estimated with a gaussian kernel.

get_next_query_point_through_expected_improvement(modl::KrigingModel, lower, upper)

Finds the point that maximises expected improvement over the current best observed value. Uses SAMIN optimisation over the box [lower, upper].

get_predicted_minimum(modl::KrigingModel, lower, upper)

Finds the predicted minimum of the kriging model over the box [lower, upper]. Uses SAMIN optimisation.

integrate(modl::KrigingModel, prob_means::AbstractArray{U,1}, covar::Hermitian) where U<:Real

Returns the expectation and variance of the integral of a kriging model given the probabilities described by a multivariate normal with means (in each dimension) of probmeans and covariance matrix covar. The integration performed is: int{x in X} f(x) p(x) dx Where f(x) is the function which is approximated in the kriging map by an exponential covariance function and p(x) is the pdf which is multivariate gaussian.

log_likelihood( y::Array{Float64,1},  K::Hermitian{Float64,Array{Float64,2}}; invK::Hermitian{Float64,Array{Float64,2}} = inv(K), determinant = det(K))

The log likelihood of a kriging model with values y and covariances K. invK and the determinant can be fed in as well to prevent additional operations. Note that the normalising constant is excluded from the log likelihood here because it is not relevent for optimising hyperparameters.

marginal_gaussian_kernel(x1::Array{Float64}, x2::Array{Float64}, cov_func_parameters::GaussianKernelHyperparameters)

Returns a covariance estimated with a gaussian kernel. Also returns the marginal covariances (how does each covariance change by bumping each hyperparameter).

marginal_likelihood_gaussian_derivatives(X::Array{Float64,2}, y::Array{Float64,1}, w_0::Float64, w_i::Array{Float64,1}, noise::Float64 = 0.0)

The marginal likelihoods (along each parameter) of a kriging model are returned. In addition the K matrix and the inverse K matrix are returned (to allow programers to use them as generated here and no redo them).

predicted_error(modl::KrigingModel, PointToExamine::AbstractArray{T,1}) where T<:Real

Returns the predicted standard error (square root of kriging variance) at the given point. Uses Equation 9 of Jones, Schonlau, Welch with ordinary kriging correction.

sample(twister::MersenneTwister, dim::Integer, batch_size::Integer)

This does sampling with or without replacement.