A cokriging surrogate model. More...
Public Member Functions | |
function | CoKriging (var varargin) |
function | getSamplesIdx (var t) |
Returns samples of dataset t. | |
function | getValuesIdx (var t) |
Returns values of dataset t. | |
function | fit (var samples, var values) |
Fits a gaussian process for multi-fidelity datasets. | |
function | regressionFunction (var varargin) |
Returns the regression function. | |
function | correlationFunction (var varargin) |
Returns the internal correlation function handle. | |
function | getHyperparameters () |
Returns the hyperparameters. | |
function | getRho () |
Returns the rho parameter (only valid for CoKriging ) | |
function | getProcessVariance () |
Returns the process variance (sigma2) | |
function | getCorrelationMatrix () |
Returns the full extrinsic correlation matrix. | |
function | getSigma () |
Returns the intrinsic covariance matrix. | |
function | getRegressionMatrix () |
Returns the model matrix (Vandermonde matrix) | |
function | getSamples () |
Returns the input sample matrix. | |
function | getValues () |
Returns the output value matrix. | |
function | setOption (var key, var value) |
Sets a value in the options structure. | |
function | cleanup () |
Clears some unused variables. | |
function | display () |
Returns user-friendly description of the class instance. | |
function | predict (var points) |
Predict the mean and/or variance for one or more points x. | |
function | predict_derivatives (var point) |
Predict the derivatives of the mean and/or variance for a points. | |
function | predict_limit (var points) |
Limit predictor of kriging (EXPERIMENTAL) | |
function | getExpression (var options) |
Returns the Matlab expression of this Gaussian Process model. | |
function | cvpe () |
Calculates the log of the leave-one-out cross validation error (LOO-CV) | |
function | marginalLikelihood (var dpsi, var dsigma2) |
Marginal likelihood function. | |
function | pseudoLikelihood (var dpsi, var dsigma2) |
Leave-one-out predictive log probability (pseudo-likelihood) | |
function | mseTestset (var testx, var testy) |
Calculates error on holdout set. | |
function | imse () |
Calculates the log of the integrated mean squared error. | |
function | rcValues () |
Quantifies magnification of noise (lower is better) | |
function | plotVariogram () |
Variogram plot (EXPERIMENTAL) | |
Static Public Member Functions | |
static function | getDefaultOptions () |
Returns a default options structure. | |
Public Attributes | |
const var | RHO |
index of the rho parameter | |
const var | LAMBDA |
index of the lambda parameter | |
const var | SIGMA2 |
index of the sigma2 parameter | |
const var | HP |
index of the correlation function parameters | |
Protected Member Functions | |
function | setData (var samples, var values) |
Sets samples and values matrix. | |
function | extrinsicCorrelationMatrix (var points1, var points2) |
Constructs extrinsic correlation matrix. | |
function | intrinsicCovarianceMatrix (var points1, var points2) |
Constructs intrinsic covariance matrix (stochastic kriging/regression kriging) | |
function | regressionMatrix (var points) |
Constructs regression matrix. | |
function | updateModel (var F, var hp) |
Constructs model. | |
function | updateRegression (var F, var hp) |
Constructs regression part. | |
function | updateStochasticProcess (var hp) |
Constructs correlation part. | |
function | tuneParameters (var F) |
Hyperparameter optimization. | |
function | generateDegrees (var dj) |
Generate degrees matrix from individual ones. | |
Protected Attributes | |
var | options |
var | regressionFcn |
degrees matrix (strings are converted) | |
var | correlationFcn |
string -> function handle | |
var | hyperparameters0 |
initial hp values OR the real ones (if optimization is done outside the class) | |
var | dist |
sample inter-distance | |
var | distIdxPsi |
indexing needed to calculate psi from D | |
var | optimIdx |
logical indices to parameters that are optimized | |
var | optimNrParameters |
number of optimization parameter (vector; one entry per type of parameter) | |
var | alpha |
Regression coefficients. | |
var | gamma |
'Correlation part' coefficients | |
var | hyperparameters |
correlation parameters | |
var | rho |
var | C |
Choleski Decomposition of extrinsic + intrinsic matrices. | |
var | sigma2 |
process variance of the GP (extrinsic variance ) | |
var | tau2 |
intrinsic variance | |
var | Sigma |
intrinsic covariance matrix (amount of regression of stochastic part) | |
var | Ft |
decorrelated model matrix | |
var | R |
from QR decomposition of regression part | |
var | sigma2_reinterp |
Reinterpolation version of sigma2 . | |
var | C_reinterp |
Reinterpolation version of C . | |
var | Ft_reinterp |
Reinterpolation version of Ft . | |
var | R_reinterp |
Reinterpolation version of R . | |
A cokriging surrogate model.
Papers:
Limitations:
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inline |
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inlineinherited |
Clears some unused variables.
function correlationFunction | ( | var | varargin | ) |
Returns the internal correlation function handle.
Symbolic expression not supported for cokriging.
varargin | Options |
correlationFcn | String of correlation function |
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inherited |
Calculates the log of the leave-one-out cross validation error (LOO-CV)
Error function used is the Mean Squared Error (MSE)
out | log(loo-cv) score |
Papers:
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inlineinherited |
Returns user-friendly description of the class instance.
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protected |
Constructs extrinsic correlation matrix.
Generate correlation matrix of points1 vs points2 using the current hyperparameters as followed:
points1 | input point matrix (optional) |
points2 | input point matrix (optional) |
psi | Correlation matrix |
dpsi | Derivative of correlation matrix w.r.t. the hyperparameters |
NOTE: The first case returns derivatives w.r.t. X The latter two cases returns derivatives w.r.t. the hyperparameters
Issues:
function fit | ( | var | samples, |
var | values | ||
) |
Fits a gaussian process for multi-fidelity datasets.
Need to be invoked before calling any of the prediction methods.
samples | input sample matrix (cell array) |
values | output value matrix (cell array) |
samples/values are (columnwise!) cell arrays. {1} is cheap data ... more expensive ... {end} is most expensive NOTE: though only 2 datasets are supported atm (length of samples/values must be 2)
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protectedinherited |
Generate degrees matrix from individual ones.
Generates a (full) degree matrix based on one or more degree matrices for variable j The option 'regressionMaxLevelInteractions' determines the maximum level of interactions (BasicGaussianProcess::getDefaultOptions)
dj | Cell array of degree matrices (for each dimension) |
degrees | Full degrees matrix |
idx | Cell array of indices (used by blind kriging) |
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inlineinherited |
Returns the full extrinsic correlation matrix.
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inlinestatic |
Returns a default options structure.
options | Options structure |
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inherited |
Returns the Matlab expression of this Gaussian Process model.
Example: expression = getExpression( this )
options | Options struct |
expression | Symbolic expression |
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inlineinherited |
Returns the hyperparameters.
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inlineinherited |
Returns the process variance (sigma2)
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inlineinherited |
Returns the model matrix (Vandermonde matrix)
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inlineinherited |
Returns the rho parameter (only valid for CoKriging
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inlineinherited |
Returns the input sample matrix.
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inline |
Returns samples of dataset t.
t | index of dataset to retrieve |
samples | samples of dataset t |
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inlineinherited |
Returns the intrinsic covariance matrix.
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inlineinherited |
Returns the output value matrix.
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inline |
Returns values of dataset t.
t | index of dataset to retrieve |
values | values of dataset t |
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inherited |
Calculates the log of the integrated mean squared error.
Only supported for 1D and 2D problems.
out | log(imse) score |
Papers:
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protected |
Constructs intrinsic covariance matrix (stochastic kriging/regression kriging)
Generate covariance matrix matrix of points1 vs points2 using the current hyperparameters as followed:
points1 | input point matrix (optional) |
points2 | input point matrix (optional) |
psi | Covariance matrix |
dpsi | Derivative of covariance matrix w.r.t. the hyperparameters OR the input points |
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inherited |
Marginal likelihood function.
Used for Maximum Likelihood Estimation (MLE)
dpsi | cell array of derivative matrices (optional; for internal use only) |
out | score |
dout | Derivatives w.r.t. hyperparameters |
Papers:
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inherited |
Calculates error on holdout set.
Error function used is the Mean Squared Error (MSE) function.
testx | input samples of the test set |
testy | output samples of the test set |
out | mse error on test set |
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inherited |
Variogram plot (EXPERIMENTAL)
Plots the experimental (semi-)variogram (based on the data) as well as the theoretical kriging (semi-)variogram (defined by the correlation function).
h | Figure handle |
Empirical variogram:
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inherited |
Predict the mean and/or variance for one or more points x.
points | Matrix of input points to be predicted |
values | predicted output values |
sigma2 | predicted variance of the output values (optional) |
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inherited |
Predict the derivatives of the mean and/or variance for a points.
NOTE:
point | input point to calculate the derivative of |
dvalues | Derivative w.r.t. the output |
sigma2 | Derivative w.r.t. the output variance (optional) |
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inherited |
Limit predictor of kriging (EXPERIMENTAL)
points | Matrix of input points to be predicted |
values | predicted output values |
sigma2 | predicted variance of the output values (optional) |
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inherited |
Leave-one-out predictive log probability (pseudo-likelihood)
Calculates the leave-one-out predictive log probability.
dpsi | cell array of derivative matrices (optional; for internal use only) |
out | score |
dout | Derivatives w.r.t. hyperparameters |
Papers:
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inherited |
Quantifies magnification of noise (lower is better)
Robustness-criterion (In theory useful only for ordinary kriging).
rc | robustness-criterion |
Returns a 2xn matrix:
function regressionFunction | ( | var | varargin | ) |
Returns the regression function.
Symbolic expression and terms not supported for cokriging.
varargin | Options |
regressionFcn | Degree matrix representing the regression function |
expression | Symbolic expression |
terms | Cell array of the individual terms |
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protected |
Constructs regression matrix.
Regression matrix (model matrix, Vandermonde matrix, ...) for a set of points Based on this.regressionFcn.
points | input point matrix (optional) |
F | Model matrix |
dF | Derivative of model matrix w.r.t. the hyperparameters OR the input points |
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protected |
Sets samples and values matrix.
Concatenate sample/values cell array to numeric array passing the resulting dataset to the underlying base method.
samples | input sample matrix (cell array) |
values | output value matrix (cell array) |
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inlineinherited |
Sets a value in the options structure.
key | option name |
value | option value |
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protectedinherited |
Hyperparameter optimization.
Setups and invokes the optimizer.
F | model matrix |
optimHp | optimized hyperparameters |
perf | Performance score (likelihood score) |
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protectedinherited |
Constructs model.
Full update of the model (regression + correlation part)
F | model matrix |
hp | new hyperparameters |
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protectedinherited |
Constructs regression part.
Updates regression part of the model.
F | model matrix |
hp | new hyperparameters |
err | error string (if any) |
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protectedinherited |
Constructs correlation part.
Updates correlation part of the model.
hp | hyperparameters |
err | error string (if any) |
dpsi | Derivative of correlation matrix w.r.t. the hyperparameters |
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protectedinherited |
Regression coefficients.
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protectedinherited |
Choleski Decomposition of extrinsic + intrinsic matrices.
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protectedinherited |
Reinterpolation version of C
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protectedinherited |
string -> function handle
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protectedinherited |
sample inter-distance
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protectedinherited |
indexing needed to calculate psi from D
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protectedinherited |
decorrelated model matrix
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protectedinherited |
Reinterpolation version of Ft
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protectedinherited |
'Correlation part' coefficients
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inherited |
index of the correlation function parameters
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protectedinherited |
correlation parameters
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protectedinherited |
initial hp values OR the real ones (if optimization is done outside the class)
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inherited |
index of the lambda parameter
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protectedinherited |
logical indices to parameters that are optimized
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protectedinherited |
number of optimization parameter (vector; one entry per type of parameter)
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protectedinherited |
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protectedinherited |
from QR decomposition of regression part
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protectedinherited |
Reinterpolation version of R
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protectedinherited |
degrees matrix (strings are converted)
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inherited |
index of the rho parameter
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protectedinherited |
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protectedinherited |
intrinsic covariance matrix (amount of regression of stochastic part)
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inherited |
index of the sigma2 parameter
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protectedinherited |
process variance of the GP (extrinsic variance )
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protectedinherited |
Reinterpolation version of sigma2
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protectedinherited |
intrinsic variance