线性回归和梯度下降

Question

In Linear Regression, we have formulas to calculate the slope and intercept, to find the best fit line; then why do we need to use Gradient Descent for calculating the optimum slope & intercept, which we already get by given formulas?

Answer 1

I guess you are referring to the closed form solution of the linear regression.

And yes - you can totally fine use it for that purpose. However, this only works as long as you have all your data being able to fit into memory, which you wouldn't necessarily need when using gradient descend: Since Gradient Descend is an iterative process you can swap in and out some data making it more appropriate for big data.

See the Cross Validated thread Solving for regression parameters in closed-form vs gradient descent for more details.