Regularized Linear Regression

We can apply regularization to both linear regression and logistic regression. We will approach linear regression first.

Gradient descent

We will modify our gradient descent function to separate out θ0​ from the rest of the parameters because we do not want to penalize θ0​.

Normal Equation

Now let’s approach regularization using the alternate method of the non-iterative normal equation.

To add in regularization, the equation is the same as our original, except that we add another term inside the parentheses:

L is a matrix with 0 at the top left and 1’s down the diagonal, with 0’s everywhere else. It should have a dimension (n+1)×(n+1). Intuitively, this is the identity matrix (though we are not including x0​), multiplied with a single real number λ.

Read Next -Regularized Logical Regression