S4 class for funGp Gaussian process models

This is the formal representation of Gaussian process models within the funGp package. Gaussian process models are useful statistical tools in the modeling of complex input-output relationships.

• Main methods
  fgpm: creation of funGp regression models
  predict,fgpm-method: output estimation at new input points based on a fgpm model
  simulate,fgpm-method: random sampling from a fgpm model
  update,fgpm-method: modification of data and hyperparameters of a fgpm model

• Plotters
  plot,fgpm-method: validation plot for a fgpm model
  plot.predict.fgpm: plot of predictions based on a fgpm model
  plot.simulate.fgpm: plot of simulations based on a fgpm model

Slots

howCalled

Object of class "modelCall". User call reminder.

type

Object of class "character". Type of model based on type of inputs. To be set from "scalar", "functional", "hybrid".

ds

Object of class "numeric". Number of scalar inputs.

df

Object of class "numeric". Number of functional inputs.

f_dims

Object of class "numeric". An array with the original dimension of each functional input.

sIn

Object of class "matrix". The scalar input points. Variables are arranged by columns and coordinates by rows.

fIn

Object of class "list". The functional input points. Each element of the list contains a functional input in the form of a matrix. In each matrix, curves representing functional coordinates are arranged by rows.

sOut

Object of class "matrix". The scalar output values at the coordinates specified by sIn and/or fIn.

n.tot

Object of class "integer". Number of observed points used to compute the training-training and training-prediction covariance matrices.

n.tr

Object of class "integer". Among all the points loaded in the model, the amount used for training.

f_proj

Object of class "fgpProj". Data structures related to the projection of functional inputs. Check fgpProj for more details.

kern

Object of class "fgpKern". Data structures related to the kernel of the Gaussian process model. Check fgpKern for more details.

nugget

Object of class "numeric". Variance parameter standing for the homogeneous nugget effect.

preMats

Object of class "list". L and LInvY matrices pre-computed for prediction. L is a lower diagonal matrix such that \(L'L\) equals the training auto-covariance matrix \(K.tt\). On the other hand, \(LInvY = L^(-1) * sOut\).

convergence

Object of class "numeric". Integer code either confirming convergence or indicating an error. Check the convergence component of the Value returned by optim.

negLogLik

Object of class "numeric". Negated log-likelihood obained by optim during hyperparameter optimization.

Useful material

• Manual Gaussian Process Regression for Scalar and Functional Inputs with funGp - The in-depth tour

Author

José Betancourt, François Bachoc, Thierry Klein and Jérémy Rohmer