# Create A New GP Object Build a Gaussian process C-side object based on the `X`-`Z` data and parameters provided, and augment those objects with new data ```r newGP(X, Z, d, g, dK = FALSE) newGPsep(X, Z, d, g, dK = FALSE) updateGP(gpi, X, Z, verb = 0) updateGPsep(gpsepi, X, Z, verb = 0) ``` ## Arguments - `X`: a `matrix` or `data.frame` containing the full (large) design matrix of input locations - `Z`: a vector of responses/dependent values with `length(Z) = nrow(X)` - `d`: a positive scalar lengthscale parameter for an isotropic Gaussian correlation function (`newGP`); or a vector for a separable version (`newGPsep`) - `g`: a positive scalar nugget parameter - `dK`: a scalar logical indicating whether or not derivative information (for the lengthscale) should be maintained by the GP object; this is required for calculating MLEs/MAPs of the lengthscale parameter(s) via `mleGP` and `jmleGP` - `gpi`: a C-side GP object identifier (positive integer); e.g., as returned by `newGP` - `gpsepi`: similar to `gpi` but indicating a separable GP object, as returned by `newGPsep` - `verb`: a non-negative integer indicating the verbosity level. A positive value causes progress statements to be printed to the screen for each update of `i in 1:nrow(X)` ## Details `newGP` allocates a new GP object on the C-side and returns its unique integer identifier (`gpi`), taking time which is cubic on `nrow(X)`; allocated GP objects must (eventually) be destroyed with `deleteGP` or `deleteGPs` or memory will leak. The same applies for `newGPsep`, except deploying a separable correlation with limited feature set; see `deleteGPsep` and `deleteGPseps` `updateGP` takes `gpi` identifier as input and augments that GP with new data. A sequence of updates is performed, for each `i in 1:nrow(X)`, each taking time which is quadratic in the number of data points. `updateGP` also updates any statistics needed in order to quickly search for new local design candidates via `laGP`. The same applies to `updateGPsep` on `gpsepi` objects ## Returns `newGP` and `newGPsep` create a unique GP indicator (`gpi` or `gpsepi`) referencing a C-side object; `updateGP` and `updateGPsep` do not return anything, but yields a modified C-side object as a side effect ## References For standard GP inference, refer to any graduate text, e.g., Rasmussen & Williams **Gaussian Processes for Machine Learning**, or Gramacy, R. B. (2020) **Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences**. Boca Raton, Florida: Chapman Hall/CRC. (See Chapter 6.) [https://bobby.gramacy.com/surrogates/](https://bobby.gramacy.com/surrogates/) For efficient updates of GPs, see: R.B. Gramacy and D.W. Apley (2015). **Local Gaussian process approximation for large computer experiments.** Journal of Computational and Graphical Statistics, 24(2), pp. 561-678; preprint on arXiv:1303.0383; [https://arxiv.org/abs/1303.0383](https://arxiv.org/abs/1303.0383) ## Author(s) Robert B. Gramacy rbg@vt.edu ## See Also `vignette("laGP")`, `deleteGP`, `mleGP`, `predGP`, `laGP` ## Examples ```r ## for more examples, see predGP and mleGP docs ## simple sine data X <- matrix(seq(0,2*pi,length=7), ncol=1) Z <- sin(X) ## new GP fit gpi <- newGP(X, Z, 2, 0.000001) ## make predictions XX <- matrix(seq(-1,2*pi+1, length=499), ncol=ncol(X)) p <- predGP(gpi, XX) ## sample from the predictive distribution if(require(mvtnorm)) { N <- 100 ZZ <- rmvt(N, p$Sigma, p$df) ZZ <- ZZ + t(matrix(rep(p$mean, N), ncol=N)) matplot(XX, t(ZZ), col="gray", lwd=0.5, lty=1, type="l", xlab="x", ylab="f-hat(x)", bty="n") points(X, Z, pch=19, cex=2) } ## update with four more points X2 <- matrix(c(pi/2, 3*pi/2, -0.5, 2*pi+0.5), ncol=1) Z2 <- sin(X2) updateGP(gpi, X2, Z2) ## make a new set of predictions p2 <- predGP(gpi, XX) if(require(mvtnorm)) { ZZ <- rmvt(N, p2$Sigma, p2$df) ZZ <- ZZ + t(matrix(rep(p2$mean, N), ncol=N)) matplot(XX, t(ZZ), col="gray", lwd=0.5, lty=1, type="l", xlab="x", ylab="f-hat(x)", bty="n") points(X, Z, pch=19, cex=2) points(X2, Z2, pch=19, cex=2, col=2) } ## clean up deleteGP(gpi) ```

newGP function