How to make a 2D Gaussian Process using GPML (Matlab) for regression?

Question

I have an Nx2 input matrix called X. I also have the output values Y which is a vector Nx1. I create some data to test as follows:

Xtest=linspace(x_min,x_max,n);
Ytest=linspace(y_min,y_max,n);

So, matrix Z is of nx2 dimensions and is going to be used as my test points. I use the default tuning of the parameters found in the demo provided with the GPML lib which is as follows:

covfunc = {@covMaterniso, 3}; 
ell = 1/4; sf = 1; 
hyp.cov = log([ell; sf]);
likfunc = @likGauss; 
sn = 0.1;
hyp.lik = log(sn);

and then use the gp function:

[ymu ys2 fmu fs2] = gp(hyp, @infExact, [], covfunc, likfunc, x, y, z);

I expected ymu to be the predicted value for each testing value in z. When I plot this like this:

[L1,L2]=meshgrid(Xtest',Ytest');
[mu,~]=meshgrid(ymu,ymu);
surf(L1,L2,ymu);

I get a strange surface. i.e i get stripes of coloured area rather some Gaussian like structure which is expected. The data in X and Y are real life data. This is what I get from my code

What I would expect:

can you upload a picture of the plot that you think is wrong? also, you don't have a mean function, so is your training data standardized to be approx standardized Gaussian? If you didn't, your hyperparameter fitting could be completely messed up. — Yanshuai Cao
– Yanshuai Cao, Commented Jan 23, 2014 at 23:01
how can i upload a picture here? I think it should work without the mean function since my data are good enough when observed with the eye. — JustCurious
– JustCurious, Commented Jan 23, 2014 at 23:26
edit your post, and there's a button for picture, click and upload. — Yanshuai Cao
– Yanshuai Cao, Commented Jan 23, 2014 at 23:28
if your Y has a large non zero mean, or its scale is large comparing to the initial scale hyperparameter you specified, then optimization of hyperparameter could run into numerical issues. report the learned hyperparameters and I can tell you if it's reasonable. — Yanshuai Cao
– Yanshuai Cao, Commented Jan 23, 2014 at 23:30

Patrick Mineault · Accepted Answer · 2014-01-23 23:48:37Z

3

You're using it wrong. Your z variable should be given by [L1(:),L2(:)]. Then what you should plot is:

surf(L1,L2,reshape(ymu,size(L1)));

answered Jan 23, 2014 at 23:48

Patrick Mineault

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4 Comments

JustCurious Over a year ago

Error using reshape To RESHAPE the number of elements must not change. Error in spatialGP (line 63) surf(L1,L2,reshape(ymu,size(L1)));

JustCurious Over a year ago

size(L1)=size(L2)=500x500 and size(ymu)=500x1

JustCurious Over a year ago

do I have to do this ([L1(:),L2(:)]) for X as well?

Patrick Mineault Over a year ago

If you wrote z the way I told you to, then ymu would be 25000x1. X and y can be anything, but X has to have size Nx2 and y has to be Nx1, where N is the number of data points.

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