Why is the regularization term *added* to the cost function (instead of mutiplied etc.)? – stats.stackexchange.com

Whenever regularization is used, it is often added onto the cost function such as in the following cost function. $$ J(\theta)=\frac 1 2(y-\theta X^T)(y-\theta X^T)^T+\alpha\|\theta\|_2^2 $$ This ...

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