getting error in fitrgp with customized kernal function

x=[2.4994,3.1476,5.5532; 2.5086, 3.3894, 5.6874; 2.5315, 3.4528, 5.6087; 2.5383, 3.5921, 5.8071; 2.5638, 3.7242, 5.6367];

y=[0.9251; 0.9205; 0.9151; 0.9151; 0.9093];

n=5;

with this x and output y I have generated one customized kernel function

kfcn = @(sf,sn,l) (((0.5*y'*inv(((sf.^2)*exp(-(cov(x'))/(2*l.^2)+(sn.^2*eye(n,n)))))*y)+(0.5*log(det((sf.^2)*exp(-(cov(x'))/(2*l^2)+(sn.^2*eye(n,n))))))+((n/2)*log(2*pi))));

But whenever i am using the generated customized kernel function in the fitrgp function I am getting error.

I have three hyperparameters(sf,sn,l) of the kernel which I want to optimize using negative log marginal likelihood and for that reason I am using fminsearch.

sf0 = 0.1; sn0=0.1; l0=1;

gprMdl = fitrgp(x,y,'KernelFunction', kfcn, 'Verbose', 1, 'Optimizer','fminsearch','KernelParameters',[sf0,sn0,l0]);

Every matrix dimension I have given right but still I am getting this error that matrix dimension is mismatch

Error using /

Matrix dimensions must agree

Error in

trial>@(sf,sn,l)(((0.5*y'*inv(((sf.^2)*exp(-(cov(x'))/(2*l.^2)+(sn.^2*eye(n,n)))))*y)+(0.5*log(det((sf.^2)*exp(-(cov(x'))/(2*l^2)+(sn.^2*eye(n,n))))))+((n/2)*log(2*pi))))

Error in classreg.learning.gputils.CustomKernel/makeKernelAsFunctionOfTheta/f (line 138)

KNM = customFcn(XN,XM,theta);

Error in classreg.learning.impl.GPImpl/makeNegativeProfiledLogLikelihoodExact/f1 (line 922)

[V,DK] = kfcn(theta);

Error in fminsearch (line 189)

fv(:,1) = funfcn(x,varargin{:});

Error in classreg.learning.impl.GPImpl/doMinimization (line 2886)

[phiHat,fHat,exitFlag] = fminsearch(objFun,phi0,opts);

Error in classreg.learning.impl.GPImpl/estimateThetaHatSigmaHatExact (line 808)

[phiHat,nloglikHat,cause] = doMinimization(this,objFun,phi0,haveGrad);

Error in classreg.learning.impl.GPImpl/doFitMethodExact (line 382)

[this.ThetaHat,this.SigmaHat,this.LogLikelihoodHat] =

estimateThetaHatSigmaHatExact(this,this.X,this.y,this.Beta0,this.Theta0,this.Sigma0);

Error in classreg.learning.impl.GPImpl/doFit (line 322)

this = doFitMethodExact(this);

Error in classreg.learning.impl.GPImpl.make (line 226)

this = doFit(this);

Error in RegressionGP (line 277)

this.Impl = classreg.learning.impl.GPImpl.make(...

Error in classreg.learning.FitTemplate/fit (line 251)

obj = this.MakeFitObject(X,Y,W,this.ModelParams,fitArgs{:});

Error in RegressionGP.fit (line 303)

this = fit(temp,X,Y);

Error in fitrgp (line 380)

obj = RegressionGP.fit(X,Y,varargin{:})

Error in trial (line 14)

gprMdl = fitrgp(x,y,'KernelFunction', kfcn, 'Verbose', 1, 'Optimizer',...

kindly help

Answer 1

[sanidhyak]

Hi @ARPITA MONDAL,

I understand that you are facing a matrix dimension mismatch error while using a customized kernel function with MATLAB's “fitrgp” function.

When reviewing your code, I noticed that the issue arises because the “fitrgp” function expects the custom kernel function to accept two input matrices (“X1” and “X2”) and a parameter vector “theta”. The current implementation does not follow this structure, causing the dimension mismatch.

Kindly refer to the following corrected code:

function K = customKernel(X1, X2, theta) 
sf = theta(1); 
sn = theta(2); 
l = theta(3); 
D = pdist2(X1, X2, 'euclidean').^2; 
K = sf^2 * exp(-D / (2 * l^2)); 
if isequal(X1, X2) 
    K = K + sn^2 * eye(size(X1, 1)); 
end 
end 

Save this function as “customKernel.m”.

Then, use the following code in your main script:

x = [2.4994, 3.1476, 5.5532; 
    2.5086, 3.3894, 5.6874; 
    2.5315, 3.4528, 5.6087; 
    2.5383, 3.5921, 5.8071; 
    2.5638, 3.7242, 5.6367]; 
y = [0.9251; 0.9205; 0.9151; 0.9151; 0.9093]; 

initialTheta = [0.1, 0.1, 1]; 

gprMdl = fitrgp(x, y, ... 
    'KernelFunction', @(X1, X2, theta) customKernel(X1, X2, theta), ... 
    'KernelParameters', initialTheta, ... 
    'Verbose', 1, ... 
    'Optimizer', 'fminsearch'); 

This code ensures that your kernel function receives the correct inputs and returns a properly dimensioned covariance matrix, resolving the dimension mismatch error.

For further reference on the “fitrgp” function, kindly refer to the below documentation:

• https://www.mathworks.com/help/stats/fitrgp.html

I hope this helps!