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Okay, so let's take a moment to compare the two approaches that we've gone over,
either setting the gradient equal to zero or doing gradient descent.
Well, in the case of minimizing residual sum of squares,
we showed that both were fairly straight forward to do.
But in a lot of the machine learning method's that we're interested in
taking the gradient and setting it equal to zero,
well there's just no close form solution to that problem.
So, often we have to turn to method's like gradient descent.
And likewise, as we're gonna see in the next module, where we turn to having lots
of different inputs, lots of different features in our regression.
Even though there might be a close form solution to setting the gradient equal to
zero, sometimes in practice it can be much more efficient
computationally to implement the gradient descent approach.
And finally one thing that I should mention about the gradient descent
approach is the fact that in that case, we had to choose a stepsize and
a convergence criteria.
Whereas, of course, if we take the gradient and
are able to set it to zero, we don't have to make any of those choices.
So that is a downside to the gradient descent approach,
is having to specify these parameters of the algorithm.
But sometimes we're relying on these types of optimization algorithms to
solve our optimization objective.
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