quadratic loss by solving a standard least squares problem over training data matrix in matlab

To solve a standard least squares problem over a training data matrix in MATLAB, you can use the "\ operator".

Assuming you have a training data matrix X and a target variable vector y, you can solve for the linear regression coefficients in the least squares sense using the following code:

main.m
% Generate a random training data matrix and target variable vector
X = randn(100,5);
y = randn(100,1);

% Solve for the linear regression coefficients using the "\" operator
beta = X\y;

% Predict the target variable using the learned coefficients
y_pred = X * beta;

% Calculate the residual sum of squares (RSS) and the mean squared error (MSE)
rss = sum((y - y_pred).^2);
mse = rss/length(y);
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The above code generates random training data and target variables, fits a linear regression using the "\ operator", makes predictions on the training data and calculates the residual sum of squares (RSS) and the mean squared error (MSE) measures of model performance. The "\ operator" solves the following standard least squares problem:

main.m
beta = argmin(||X*beta - y||^2)
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where ||.|| denotes the Euclidean norm.