MATLAB: Prediction without prior fitting in GPR

gpr

We can use fitrgp to fit a Gaussian process regression model, then use this model to predict the output on new input. The process of fitting model is to find the optimal hyperparameters of kernel. My question is: does Matlab previde GPR prediction without prior fitting model. That is if I already have optimal hyperparameters, is there any way (function) to predict new output directly.

Best Answer

Set the initial parameter values and also pass 'FitMethod','None'

http://www.mathworks.com/help/stats/fitrgp.html?searchHighlight=fitrgp&s_tid=doc_srchtitle#input_argument_d0e334513

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MATLAB: Matlab GPR -> equation for prediction

Found a solution myself. Here is the code if someone else needs it:

clc
load('my_GPR')
RegObj = obj_TrainedSet1.RegressionGP;
SigmaL = RegObj.KernelInformation.KernelParameters(1);  %length scale
SigmaF = RegObj.KernelInformation.KernelParameters(2);  %kernel scale
Sigma = RegObj.Sigma; %measurement noise
Alpha = RegObj.Alpha; % precomputed (K + Sigma*I)^-1*Y
Xraw = table2array(RegObj.X);
Yraw = RegObj.Y;
offsetX = RegObj.PredictorLocation'; % X offset
scaleX = RegObj.PredictorScale';     % X scaling
offsetY = RegObj.Beta;                  % Y offset
% after scaling (this is what goes into the GP)
X = repmat(scaleX,size(Xraw,1),1).\(Xraw - offsetX);
Y = Yraw - offsetY;
dist = @ (x1,x2) sqrt(sum((x1-x2).*(x1-x2),2)); %euclidean distance sqrt(x1-x2)'*(x1-x2)
matern52 = @(x1,x2) SigmaF^2*(1+ sqrt(5)*dist(x1,x2)/SigmaL + 5*dist(x1,x2).^2/(3*SigmaL^2)).*exp(-sqrt(5)*dist(x1,x2)/SigmaL);
K = [];
for i=1:size(X,1)
    K(:,i) = matern52(X(i,:),X); % K matrix
end
Alpha_reconstructed = (K + Sigma^2*eye(size(X,1)))\Y; % this is already computed in Alpha
norm(Alpha-Alpha_reconstructed);
% test prediction of training data
for i=1:size(X,1)
   pred_test(i) = matern52(X(i,:),X)'*Alpha;
end
% hold off
% plot(pred_test)
% hold on
% plot(Y) % fits the training data quite well
% for a general test point
x_new_raw = rand(1,3);
x_new = scaleX.*(x_new_raw - offsetX);
x_new = scaleX.\(rand_Input - offsetX);
mean_prediction = matern52(x_new,X)'*Alpha + offsetY;
var_prediction = matern52(x_new,x_new) + matern52(x_new,X)'*((K + Sigma*eye(size(X,1)))\matern52(x_new,X));

MATLAB: Crossval and regressiontree.fit – how does crossval works

What does KFold 10 means?

https://en.wikipedia.org/wiki/Cross-validation_(statistics)

matlab has done exactly?

MATLAB has performed kfold cross-validation and returned a partitioned model instead of a single regression tree. Crossvalidation allows you to assess the predictive performance of model on cross-validated data. You can access these methods using the output of a cross validated model: kfoldfun, kfoldLoss, kfoldPredict.

Alternatively you can fit a model and then call cross val this way:

rtree = RegressionTree.fit(X,price);
rcrossvaltree = crossval(rtree);

Read more here (also includes examples):

http://www.mathworks.com/help/stats/regressionpartitionedmodel-class.html

http://www.mathworks.com/help/stats/regressiontree.crossval.html

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MATLAB: Matlab GPR -> equation for prediction

MATLAB: Crossval and regressiontree.fit – how does crossval works

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