1.2 Regularized linear regression cost function
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| J = 1/(2*m)*sum( (X*theta - y).^2 ) + lambda/(2*m)*sum(theta(2:end).^2);
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1.3 Regularized linear regression gradient
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| r = theta; r(1) = 0;
grad = 1/m*(X'*(X*theta-y)) + lambda/m*r;
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2.1 Learning curves
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| for i = 1:m
xi = X(1:i,:); yi = y(1:i);
theta = trainLinearReg(xi, yi, lambda);
error_train(i) = linearRegCostFunction(xi, yi, theta, 0)
error_val(i) = linearRegCostFunction(Xval, yval, theta, 0)
end
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3 Polynomial regression
$$ h_{\theta }(x) = \theta _{0} + \theta _{1}(waterLevel) + \theta _{2}(waterLevel)^{2} + … + \theta _{p}*(waterLevel)^{p} $$
3.3 Selecting λ using a cross validation set
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| for i = 1:length(lambda_vec)
lambda = lambda_vec(i);
theta = trainLinearReg(X, y, lambda);
error_train(i) = linearRegCostFunction(X, y, theta, 0)
error_val(i) = linearRegCostFunction(Xval, yval, theta, 0)
end
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