[MUSIC] And now we're back. So, we computed the or we defined
the likelihood function for logistic regression, we computed its derivative, we
talked about simple real ascent algorithm for finding the best parameters and
for those who went through that full, kind of slow, mathematical revision you
saw where that gradient came from, but that was totally optional. We can go back and
summarize where we are right now. So now learning problem. We have some training data, we threw
this some feature extractor that gets us H of X, and we saw a discretion model
that says the probability that it's a positive review is one over one
plus E to the minus W transpose H. And then we define the quality metric
which is the likelihood function and we use gradient ascent to
optimize it to get w hat. And the gradient descent algorithm is
pretty simple and pretty intuitive. Now, you're able to define what the
quality metric is for logistic regression. You can interpret the likelihood function
as being kind of the probability that you get training data right. And you're going to maximize that. We talked about the gradient
ascent algorithm that does it with really simple updates, and
we had this optional section where we derived a gradient ascent
algorithm from scratch. Next module, we're going to
take this one step further and explore the idea of regularization and
over-fitting logistic regression, which is a really important
thing in practice. So that's where we're going to
go in the next module. But now you're ready, even at this point,
supplement your own logistic regression algorithm from scratch,
which is super exciting. [MUSIC]