K-Fold validation to compute bias correction.

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Ashfaq Ahmed on 23 Feb 2024
Answered: Chetan on 5 Mar 2024
Hi all!
Say, I have an in situ buoy data set in a variable called Tb. Now, I have corresponding satellite measurements for each buoy data, and the data are stored in the Ts variable. So, both Tb and Ts are of the same size.
Now, I am trying to calculate the error E. Where E = Tb - Ts -b.
Here, b = bias. This bias has two components, and we assume that b = m*Ts + n (m = temperature dependent bias component and n = the shift in the mean)
So, ultimately, E = Tb - Ts - m*Ts - n.
I want to use the K-fold validation operation to get the values for m and n.
Can anyone please suggest me some solution for it? Any feedback will be greatly appreciated!

Chetan on 5 Mar 2024
t seems like you are trying to do k- fold validation.To use K-Fold validation for bias correction with the given, follow these steps:
1. Prepare Data: Align and size-match your buoy "Tb" and satellite "Ts" data
2. Set Up K-Fold: Choose a number of folds, typically 5 or 10, based on your data size.
3. Split Data: Divide data into "K" non-overlapping folds.
• Validate in K-Folds:
• Treat one fold as validation and the rest as training.
• Use linear regression on the training set to model "Tb" from "Ts" accounting for bias.
• Estimate m and n to minimize E = Tb - Ts - m*Ts - n.
• Optionally, validate these estimates using the validation set.
4. Average Results: Calculate the mean of m and n estimates from all folds for final values.
Here is the MATLAB Code Sample for the same:
% Assuming Tb and Ts data are defined
K = 5; % Example fold number
cv = cvpartition(length(Tb), 'KFold', K);
m_values = zeros(K, 1);
n_values = zeros(K, 1);
for i = 1:K
trainIdx = training(cv, i);
model = fitlm(Ts(trainIdx), Tb(trainIdx), 'Intercept', true);
m_values(i) = model.Coefficients.Estimate(2); % m estimate
n_values(i) = model.Coefficients.Estimate(1); % n estimate
end
m_final = mean(m_values);
n_final = mean(n_values);
disp(['Estimated m: ', num2str(m_final)]);
disp(['Estimated n: ', num2str(n_final)]);
Additionally, you can refer the the following MATLAB fileexchange article:
I hope this helps!
Thanks
Chetan