[MUSIC] Now that we've seen the logistic
regression model and we understand it in quite a bit of detail, let's give a quick overview of what
learning means for this model. Although in the next module we're going
to go into quite a lot of detail to learning algorithm. This is just a little primer, a teaser for
what's coming in the next module. Now we're going to start
from some data and that data has inputs x and
outputs either plus one or minus one. As we said we're going to split that into
a training set and a validation set. And from the training set we're
going to run a learning algorithm that will output the parameter estimates w hat. And those w hats are going to
be plugged into the model. To estimate the probability that an input
sentence is either positive or negative. And, of course, we can use the learn
model to take the validation set and estimate how good it is, what the quality
metrics are, what the error is. Now to find the best classifier we
are going to define the quality metric. In this case the quality metric is going
to be called the likelihood function. So very possible parameters serve
coefficient w for example w0, w1, w2, we will be able to score it according to,
l of w to figure out how good it is. So for example if I take this data
set of plusses and minuses and learn the line shown in green,
we might get a particular likelihood. So, for example,
if the parameter w0 is 0, w1 is 1 but w2 is -1.5, the likelihood might
be 10 to the -6, pretty small. These numbers actually
tend to be pretty small. For this alternative line, where w0
is now 1, w1 is still 1, w2 is -1.5, the likelihood function is a little better
10 to the -5 instead of 10 to the -6. But perhaps for this best line over here,
where w0 is 1, w1 is 0.5 and w2 is -1.5. You get the best likelihood, 10 to the -4. So we'd like an approach that
would actually search for the possible values of w
to find the best line. And, as we will see in the next module,
we'll use a gradient ascent algorithm to find the set of parameters w that has
the highest likelihood best quality. [MUSIC]