gp_optim | R Documentation |

This function can be used to optimize the hyperparameters of the model to the maximum marginal likelihood (or maximum marginal posterior if priors are used), using Nelder-Mead algorithm.

gp_optim( gp, x, y, tol = 1e-04, tol_param = 0.1, maxiter = 500, restarts = 1, verbose = TRUE, warnings = TRUE, ... )

`gp` |
The gp model object to be fitted. |

`x` |
n-by-d matrix of input values (n is the number of observations and d the input dimension). Can also be a vector of length n if the model has only a single input. |

`y` |
Vector of n output (target) values. |

`tol` |
Relative change in the objective function value (marginal log posterior) after which the optimization is terminated. This will be passed to the function stats::optim as a convergence criterion. |

`tol_param` |
After the optimizer (Nelder-Mead) has terminated, the found hyperparameter values will be checked for convergence within tolerance tol_param. More precisely, if we perturb any of the hyperparameters by the amount tol_param or -tol_param, then the resulting log posterior must be smaller than the value with the found hyperparameter values. If not, then the optimizer will automatically attempt a restart (see argument restarts). Note: tol_param will be applied for the logarithms of the parameters (e.g. log length-scale), not for the native parameter values. |

`maxiter` |
Maximum number of iterations. |

`restarts` |
Number of possible restarts during optimization. The Nelder-Mead iteration can sometimes terminate prematurely before a local optimum is found, and this argument can be used to specify how many times the optimization is allowed to restart from where it left when Nelder-Mead terminated. By setting restarts > 0, one can often find local optimum without having to call gp_optim several times. Note: usually there is no need to allow more than a few (say 1-3) restarts; if the optimization does not converge with a few restarts, then one usually must try to reduce argument tol in order to achieve convergence. If this does not help either, then the optimization problem is usually ill-conditioned somehow. |

`verbose` |
If TRUE, then some information about the progress of the optimization is printed to the console. |

`warnings` |
Whether to print out some potential warnings (such as maximum number of iterations reached) during the optimization. |

`...` |
Further arguments to be passed to |

An updated GP model object.

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

# Generate some toy data set.seed(1242) n <- 50 x <- matrix(rnorm(n * 3), nrow = n) f <- sin(x[, 1]) + 0.5 * x[, 2]^2 + x[, 3] y <- f + 0.5 * rnorm(n) x <- data.frame(x1 = x[, 1], x2 = x[, 2], x3 = x[, 3]) # Basic usage cf <- cf_sexp() lik <- lik_gaussian() gp <- gp_init(cf, lik) gp <- gp_optim(gp, x, y)

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