Surface plot using fitrpg

Dear all,

I tried to make a surface plot of the gaussian process function with the following code:

gprMdl = fitrgp(X,Y1,'KernelFunction','squaredexponential','OptimizeHyperparameters','auto','HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'));
ypred = predict(gprMdl,X);
[X1,X2] = meshgrid(0.1:0.1:0.9,0.1:0.1:0.9);
surf(X1,X2,reshape(ypred,9,9));
hold on
plot3(X(:,1),X(:,2),Y1,'.r','DisplayName','Observations')

Where the result is presented below.

However, I would expect something more like this. Because the surface plot I have now doesn't fit the data properly and the contour lines are widespread. What am I doing wrong here?

I also tried the following with the help of another post (https://nl.mathworks.com/matlabcentral/answers/407736-plot-3d-hyperplane-from-fitcsvm-results#answer_326570)

But this doens't seem sufficient either.

[x,y]=meshgrid(0.1:0.01:0.9,0.1:0.01:0.9);
xGrid = [x(:),y(:)];
gprMdl = fitrgp(X,Y1,'KernelFunction','squaredexponential','OptimizeHyperparameters','auto','HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'));
[~,f]=predict(gprMdl2,xGrid);
f=reshape(f(:,1),size(x));
figure
surf(x,y,f)
hold on
plot3(X(:,1),X(:,2),Y1,'.r','DisplayName','Observations')

Answer 1

[Mario Malic]

Hello,

Take a look at the code below, unfortunately I can't find the link where I found an example I took the code from, but look for scatteredInterpolant function. I am not sure whether this is applicable, so, please verify.

clc;
clear;
close all;

load data.mat

gprMdl = fitrgp(X,Y1,'KernelFunction','squaredexponential','OptimizeHyperparameters','auto','HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'));
ypred = predict(gprMdl,X);

% so I don't write indexes below
x_data = X(:,1);
y_data = X(:,2);

% Getting the 2d grid
Num_Points = 50;
X_Lin = linspace(min(x_data),max(x_data),Num_Points);
Y_Lin = linspace(min(y_data),max(y_data),Num_Points);
[X,Y] = meshgrid(X_Lin,Y_Lin);

% Interpolating the surface from ypred
f = scatteredInterpolant(x_data, y_data, ypred);
Z = f(X,Y);
surf(X,Y,Z);

% plotting the observed points
hold on;
plot3(x_data,y_data, Y1,'.r','DisplayName','Observations');

[Tessa Kol]

Thank you for your solution. It really helped.

Is it possible to do some cubic interpolation instead of the linear?

[Mario Malic]

Function griddedInterpolant offers cubic interpolation method.

[Tessa Kol]

I tried that function, but it gives errors saying: "The sample points arrays must have the same size

as the sample values array."

[Mario Malic]

I am not completely sure whether it's possible to do the griddedInterpolation as you need values for your objective function across the grid. Let's say your grid is 50x50, you would need values for your objective function at each grid point. Maybe you could use the scatteredInterpolation to get grid values and interpolated values for obj. fun., but I don't know if this is a silly thing to do.

Answer 2

[VBBV]

Change the limits of the meshgrid and try

 % if true
    % code
  %end
gprMdl = fitrgp(X,Y1,'KernelFunction','squaredexponential','OptimizeHyperparameters','auto','HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'));
ypred = predict(gprMdl,X);
[X1,X2] = meshgrid(-5:0.1:5,-5:0.1:5); % change the limits 
surf(X1,X2,reshape(ypred,9,9));
hold on
plot3(X(:,1),X(:,2),Y1,'.r','DisplayName','Observations')

[Tessa Kol]

Thank you for the reply. I think I was not clear enough. My question is how to make a surface plot of gaussian process regression function? I think I did not get the correct meshgrid. I got my observation data (81 points) from the plot below. With fitrgp I try to fit a gaussian regression process through the data. And then I want to make a surface plot of my gaussian regression. If I look up how a gaussian process regression plot looks like I get the picture as in my post.

It is also challenging because I have 2 predictors and one output.