K-Fold validation to compute bias correction.

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!

Answer 1

[Chetan]

Hi @Ashfaq Ahmed,

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:

https://www.mathworks.com/matlabcentral/fileexchange/46828-k-fold-cross-validation

I hope this helps!

Thanks

Chetan