Software documentation

High Level functions

gpoptSequential or batch optimization using GP algorithms
bfgs_search_priorOptimize prior hyper-parameter with respect to the pseudo-likelihood using the BFGS algorithm

Chaining procedures

chaining_treeCompute the chaining tree given the distance matrix
chaining_ucbCompute the chaining UCB given the distance matrix
enet_greedyCompute an $\epsilon$-net given the distance matrix

GP computing

gp_distCanonical GP distance $d^2(x,y)=V[f(x)-f(y)\mid X_t, Y_t]$
gp_downdatePosterior $\mu(x_i)$ and $\sigma^2(x_i)$ given $X_t\setminus\{x_i\}$
gp_infBayesian system resolution for computing posterior of GP given observations
gp_inf_updateBayesian system update with new observations
gp_likNegative log likelihood
gp_loolikNegative log pseudo-likelihood
gp_predPosterior mean and variance of GP given the kernel matrices and the Bayesian inferance
gp_sampleSample a Gaussian process in a hypercube and perform Bayesian inferance

Predefined basis and kernel functions

basis_cstConstant mean function
basis_noneZero mean function
kernel_maternMatern covariance function for $ u \in\{1/2,3/2,5/2\}$
kernel_seSquared exponential covariance function
kernel_se_normisoIsotropic squared exponential covariance function


cholpsdUpper Cholesky decomposition of psd matrix
cummaxCumulative maximum as used in simple regrets
solve_cholLinear system resolution $MX=Y$ given upper Cholesky decomposition $M=R^\top R$