gradient descent method in matlab

Here's an example implementation of gradient descent in MATLAB:

main.m
% Generate some sample data
x = 1:10;
y = 2*x + 5 + randn(size(x));

% Set hyperparameters
learning_rate = 0.001;
num_iterations = 1000;

% Initialize weights randomly
w0 = randn();
w1 = randn();

% Perform gradient descent
for i = 1:num_iterations
    % Compute gradient of loss function with respect to weights
    dw0 = sum(-2*(y - w1*x - w0));
    dw1 = sum(-2*x.*(y - w1*x - w0));
    
    % Update weights using gradient and learning rate
    w0 = w0 - learning_rate*dw0;
    w1 = w1 - learning_rate*dw1;
end

% Print final weights
fprintf('w0 = %f\n', w0);
fprintf('w1 = %f\n', w1);
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In this example, we generate some sample data (a set of 10 points on a line with some random noise) and then perform gradient descent to estimate the coefficients of a linear regression model. Specifically, we are trying to find the values of w0 and w1 that minimize the residual sum of squares between the predicted values (w1*x + w0) and the true values (y).

The learning_rate hyperparameter controls the step size in the gradient descent update rule, while num_iterations controls the number of iterations of gradient descent to perform. We initialize the weights w0 and w1 randomly and then update them using the gradient and learning rate until convergence.

At the end of the script, the final values of w0 and w1 are printed. These will be close to the true values of 5 and 2, respectively, that we used to generate the sample data.