method | R Documentation |

Functions for initializing the method or type of the model, which can then be passed to
`gp_init`

.
The supported methods are:

`method_full`

Full GP, so full exact covariance function is used, meaning that the inference will be for the

`n`

latent function values (fitting time scales cubicly in`n`

).`method_fitc`

Fully independent training (and test) conditional, or FITC, approximation (see QuiĆ±onero-Candela and Rasmussen, 2005; Snelson and Ghahramani, 2006). The fitting time scales

`O(n*m^2)`

, where n is the number of data points and m the number of inducing points`num_inducing`

. The inducing point locations are chosen using the k-means algorithm.`method_rf`

Random features, that is, linearized GP. Uses random features (or basis functions) for approximating the covariance function, which means the inference time scales cubicly in the number of approximating basis functions

`num_basis`

. For stationary covariance functions random Fourier features (Rahimi and Recht, 2007) is used, and for non-stationary kernels using case specific method when possible (for example, drawing the hidden layer parameters randomly for`cf_nn`

). For`cf_const`

and`cf_lin`

this means using standard linear model, and the inference is performed on the weight space (not in the function space). Thus if the model is linear (only`cf_const`

and`cf_lin`

are used), this will give a potentially huge speed-up if the number of features is considerably smaller than the number of data points.

method_full() method_fitc( inducing = NULL, num_inducing = 100, bin_along = NULL, bin_count = 10, seed = 12345 ) method_rf(num_basis = 400, seed = 12345)

`inducing` |
Inducing points to use. If not given, then |

`num_inducing` |
Number of inducing points for the approximation. Will be ignored if the inducing points are given by the user. |

`bin_along` |
Either an index or a name of the input variable along which to bin the
values before placing the inducing inputs. For example, if |

`bin_count` |
The number of bins to use if |

`seed` |
Random seed for reproducible results. |

`num_basis` |
Number of basis functions for the approximation. |

The method object.

Rahimi, A. and Recht, B. (2008). Random features for large-scale kernel machines. In Advances in Neural Information Processing Systems 20.

QuiĆ±onero-Candela, J. and Rasmussen, C. E (2005). A unifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research 6:1939-1959.

Snelson, E. and Ghahramani, Z. (2006). Sparse Gaussian processes using pseudo-inputs. In Advances in Neural Information Processing Systems 18.

#' # Generate some toy data # NOTE: this is so small dataset that in reality there would be no point # use sparse approximation here; we use this small dataset only to make this # example run fast 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]) # Full exact GP with Gaussian likelihood gp <- gp_init(cf_sexp()) gp <- gp_optim(gp, x, y) # Approximate solution using random features (here we use a very small # number of random features only to make this example run fast) gp <- gp_init(cf_sexp(), method = method_rf(num_basis = 30)) gp <- gp_optim(gp, x, y) # Approximate solution using FITC (here we use a very small # number of incuding points only to make this example run fast) gp <- gp_init(cf_sexp(), method = method_fitc(num_inducing = 10)) gp <- gp_optim(gp, x, y)

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