Is it possible to construct gaussian processes custom kernels with built in functions?

I understand the way to construct custom kernels for gaussian processes, e.g.

kfcn = @(XN,XM,theta) exp(theta(1))^2*exp(-pdist2(XN,XM).^2/(2*exp(theta(2))^2)) 

I am wondering if it is possible to construct kernels from built in function names, e.g.

kfcn = 'exponential' + 'squaredexponential';

If not, does it mean we have to do it from scatch?

Any suggesion would be appreciated.

Answer 1

[Walter Roberson]

You can use str2func to convert a function name or text expression into a function handle.

kfcns = {'exponential','squaredexponential'};
KFCN = str2func("@(x) " + strjoin(string(kfcns(:)) + "(x)", " + "))

KFCN = function_handle with value:
    @(x)exponential(x)+squaredexponential(x)

[mono]

Thank you for the reply. Just did some tests.

Codes in similar shape works:

gpm1 = fitrgp(X_, y_, 'KernelFunction', 'squaredexponential');

but following with the same initial setup

kfcn = str2func("@(x) squaredexponential(x)");
gpm2 = fitrgp(X_, y_, 'KernelFunction', kfcn);

would get ouput:

So I assume, it does not support function handles from built-in function name.

[Walter Roberson]

I see what you mean now.

The function handle needs to accept three parameters.

But No, the options that can be named probably cannot be invoked as functions.

The following talks about the mathematics of some of those https://www.mathworks.com/help/stats/kernel-covariance-function-options.html

[mono]

Thanks for the information. Wish Matlab can add this functionality as well as kernel function operators etc. in the future release.

[Walter Roberson]

The actual functions called are several layers down and obviouslyly not intended to be directly invoked by the user. For example toolbox/stats/classreg/+classreg/+learning/+coder/+gputils/squaredExponentialKfun.m

[mono]

python scikit learn actually supports it. I feel it is quite convince as it is quite time consusing if constructing all the custom kernels from the scatch.