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Does linear regression need gradient descent?
Linear regression does provide a useful exercise for learning stochastic gradient descent which is an important algorithm used for minimizing cost functions by machine learning algorithms.
Why is gradient descent needed?
Gradient Descent is an optimization algorithm for finding a local minimum of a differentiable function. Gradient descent is simply used in machine learning to find the values of a function’s parameters (coefficients) that minimize a cost function as far as possible.
Does linear regression have closed form solution?
Normal Equation is the Closed-form solution for the Linear Regression algorithm which means that we can obtain the optimal parameters by just using a formula that includes a few matrix multiplications and inversions. Then, do a little bit of linear algebra to get the value of theta .
Why is gradient descent useful in linear regression?
This is why gradient descent is useful; not all basis functions give us a closed form solution like in the case of linear regression, but we can always minimize the squared loss given a differentiable basis function. The challenge is then choosing the correct basis function.
When to use gradient descent over closed form?
What is the advantage of using an iterative algorithm like gradient descent over a closed-form solution in general, when one is available? Unless the closed form solution is extremely expensive to compute, it generally is the way to go when it is available. However, For most nonlinear regression problems there is no closed form solution.
Why is gradient descent bad for convex optimization?
While there are methods of speeding this up (stochastic gradient descent, parallel computing, using other gradient methods), this is an inherently slow algorithm for general convex optimization. It does not arrive exactly at the minimum — with the gradient descent, you are guaranteed to never get to the exact minimum, be it local or global one.
When to use stochastic gradient descent in machine learning?
Iterative methods have some advantages when we have a large amount of data or the data is very sparse. Suppose our data matrix A is huge and it is not possible to fit in memory, stochastic gradient descent can be used. I have an answer to explain why How could stochastic gradient descent save time comparing to standard gradient descent?