如何使用GPML(Matlab)进行二维高斯过程回归?

问题描述

我有一个名为 X 的 Nx2 输入矩阵.我还有输出值 Y ，它是向量 Nx1 .我创建一些数据进行测试，如下所示:

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);

因此，矩阵 Z 的尺寸为 nx2 ，将用作我的测试点.我使用与GPML lib一起提供的演示中找到的参数的默认调整，如下所示:

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);

，然后使用gp函数:

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

我希望ymu是z中每个测试值的预测值.当我这样绘制时:

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);

我得到一个奇怪的表面.即我得到了彩色区域的条纹，而不是预期的某种高斯式结构. X 和 Y 中的数据是真实数据.

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.

我期望的是:

推荐答案

您使用的是错误的.您的z变量应由[L1(:)，L2(:)]给出.那么您应该绘制的是:

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)));

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