dlgradient: covariance matrix derivative.

Question

MA 2021-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/1610090-dlgradient-covariance-matrix-derivative

回答： MA 2021-12-16

Assuming I have a matrix x of size (mxn), the covariance matrix is of the size nxn. I want to find the gradient of the covariance matrix with respect to the input. So, starting with this code:

function [y,dx]=cov_der(x)
y=x'*x; 
dx=dlgradient(y,x,'EnableHigherDerivatives',true);
end

and evaluating it as:

[y,dx]=dlfeval(@cov_der,x)

This does not work for matrices but it works for scalars. So, is there anyway I could find the gradient with respect to every element in the matrix. THanks.

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Answer 1

MA 2021-12-16

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I actually solve it. For anyone looking for the same problem:

function [y,dx]=cov_der(x)
%simple example 
%x=dlarray(and(3,3)); 
%[y,dx]=dlfeval(@cov_der,x)
y=zeros(size(x,2),size(x,2)); 
z=size(x,1); 
y=dlarray(y); 
for  i=1:size(x,2)
    for j=1:size(x,2)
    y(i,j)=sum(x(:,i).*x(:,j))./z;
    end
end
dx=zeros(size(x,2)*size(x,2),size(x,1),size(x,2)); 
index=1; 
for i=1:size(x,2)
    for j=1:size(x,2)
    dx(index,:,:)=dlgradient(y(i,j),x,'EnableHigherDerivatives',true);
    index=index+1; 
    end
end
end

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Answer 2

yanqi liu 2021-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/1610090-dlgradient-covariance-matrix-derivative#answer_854715

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yes，sir，may be use loop for every element in matrix

clc; clear all; close all;
[X1, X2] = meshgrid(linspace(0,1,10));
X1 = dlarray(X1(:));
for i = 1:length(X1)
    [y(i),dx(i)]=dlfeval(@cov_der, dlarray(X1(i)));
end
% figure; plot(extractdata(X1),extractdata(y))
% hold on;
% plot(extractdata(X1),extractdata(dx))
function [y,dx]=cov_der(x)
y=x'*x; 
dx=dlgradient(y,x,'EnableHigherDerivatives',true);
end

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MA 2021-12-14

THanks for your answer, but in this example you gave the covariance is calculated for each point. I want to calculate the covariance matrix for a matrix of size mxn so the output (y) will be of size nxn.

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