Compute mean squared errors between data sets with the same vs different parameter values

Hello,

I have data stored in a n x n cell array. For example:

org_data = {rand(1000,1) rand(1000,1); rand(1000,1) rand(1000,1)};

In my data, the rows stand for different rounds and the columns stand for different parameter values. For example:

• data{1,1} would be the data set for the first round of the first parameter value
• data{2,1} would be the data set for the second round of the first parameter value
• data{2,3} would be the data set for the second round of the third parameter value
• etc.

My goal is to compute two things:

• The average mean squared error within data sets which have the same parameter value
• The average mean squared errors between data sets with different parameter values

To compute the two average mean squared errors I first need to compute it between every possible unique combination for the cells of my data. The resulting combinations in this case are:

• data{1,1} & data{1,2}
• data{1,1} & data{2,1}
• data{1,1} & data{2,2}
• data{1,2} & data{2,1}
• data{1,2} & data{2,2}
• data{2,1} & data{2,2}

To get all these combinations in MATLAB, I do the following:

org_data = {rand(1000,1) rand(1000,1); rand(1000,1) rand(1000,1)};
idx = 1:4;
c = nchoosek(idx,2);
data = org_data(c);

Now I want to compute the average mean squared error between all possible unique cell combinations. In this case, if computed manually, they would be the following:

% Compute mean squared errors between data sets with the same parameter values
a = immse(data{1,1}, data{2,1}); % parameter value #1
b = immse(data{1,2}, data{2,2}); % parameter value #2
same_par = mean([a b])
% Compute mean squared errors between data sets with different parameter values
c = immse(data{1,1}, data{1,2}); % parameter value #1 and #2, round 1 and round 1
d = immse(data{1,1}, data{2,2}); % parameter value #1 and #2, round 1 and round 2
e = immse(data{1,2}, data{2,1}); % parameter value #2 and #1, round 1 and round 2
f = immse(data{2,1}, data{2,2}); % parameter value #1 and #2, round 2 and round 2 
diff_par = mean([c d e f])

I will work with larger cell arrays than in this example (e.g., 10 x 10 instead of 2 x 2). In those cases, I do not want to type out the combinations manually.

I am therefore trying to find a way / a function to automatize the process to get to same_par and diff_par. Can anyone help?

Thanks a lot in advance.