Losses in forecasting _cosine similarity class ,mean square logarithmic error , and huber class

How can i write the code for calculating cosine similarity class ,mean square logarithmic error , and huber class in matlab code for Ypred and Ytrue.(prediction and actual value)

Answer 1

[Vaibhav]

Hi NN

Cosine similarity measures the cosine of the angle between two non-zero vectors. MSLE is a variant of the Mean Squared Error (MSE) that focuses on the logarithm of the predictions and actual values, penalizing underestimates more than overestimates. The Huber loss is less sensitive to outliers in data than the squared error loss. It’s quadratic for small errors and linear for large errors.

Here is the example code for your reference:

% Example data
Ytrue = [1, 2, 3, 4, 5];
Ypred = [1.1, 1.9, 3.2, 4.1, 4.9];

% Calculate losses
cosSim = cosine_similarity(Ytrue, Ypred);
msle = mean_square_logarithmic_error(Ytrue, Ypred);
huberL = huber_loss(Ytrue, Ypred, 1.35); % delta is a hyperparameter, adjust as needed

% Display results
fprintf('Cosine Similarity: %f\n', cosSim);

Cosine Similarity: 0.999310

fprintf('Mean Square Logarithmic Error: %f\n', msle);

Mean Square Logarithmic Error: 0.001317

fprintf('Huber Loss: %f\n', huberL);

Huber Loss: 0.008000

function huberLoss = huber_loss(Ytrue, Ypred, delta)
    % Calculate the absolute difference
    absDiff = abs(Ytrue - Ypred);
    
    % Calculate Huber loss
    huberLoss = zeros(size(absDiff));
    isSmallError = absDiff < delta;
    
    % Quadratic for small errors
    huberLoss(isSmallError) = 0.5 * absDiff(isSmallError).^2;
    
    % Linear for large errors
    huberLoss(~isSmallError) = delta * (absDiff(~isSmallError) - 0.5 * delta);
    
    % Mean of all losses
    huberLoss = mean(huberLoss);
end


function msle = mean_square_logarithmic_error(Ytrue, Ypred)
    % Ensure positive values, as logarithm of zero or negative numbers is undefined
    Ytrue(Ytrue <= 0) = eps; % eps is the smallest positive number in MATLAB
    Ypred(Ypred <= 0) = eps;
    
    % Calculate MSLE
    msle = mean((log(Ytrue + 1) - log(Ypred + 1)).^2);
end


function cosineSimilarity = cosine_similarity(Ytrue, Ypred)
    % Ensure the vectors are row vectors
    Ytrue = Ytrue(:)';
    Ypred = Ypred(:)';
    
    % Calculate the cosine similarity
    cosineSimilarity = dot(Ytrue, Ypred) / (norm(Ytrue) * norm(Ypred));
end

Hope it helps!