[MUSIC] Now that we had the chance to
review the basics of probability, let's figure out how it can be useful
in the classification problem. So, if we take our two sentences,
one where was definite plus one, definite positive, the sushi and
everything were awesome! And the other one I was not sure,
the sushi was good, the service was okay. For the first one, you can say that the
probability that it's a positive review for this sentence is very high. So, the probability that y equals
plus one, given the sentence is 0.99. On the other one though, the probability
of y equals plus 1 given the sentence, given x equals the sushi was good,
the service was okay, that's only 0.55. And in general, many classifiers
output this degree of beliefs, or this probability. So the probability of the wide
output label y given input x, and it's going to be extremely
useful in practice. So let's go through a little bit
of an example of what that means. So let's say we're given an input
data set with N data points. They have inputs, number of awesomes,
number of awfuls and the labels y. And I use it to train the classifier
that outputs these probabilities, the predictions we're
going to call that P hat, or estimate of the predictions which are
going to spend on the parameters w hat, or the coefficients w hat for our model. And so P hat is going to be useful for
predicting y hat, the predictive class, which in our
case is the sentiment for senders. So, let's see how that works. What we're going to do is learn
this P hat estimated from data, and use it to predict
the most likely class. So in particular,
if I'm giving you some input sentence and I compute the probability the y is
plus one, it's a positive review given the sentence and that's greater then 0.5,
I say the y hat is plus one, its a positive sentence and
if you say that its less than 0.5, then we say it's a negative sentence,
so y hat is minus one. But we're not just going to get that, P hat is going to give us more
kind of interpretive output. So it's not going to say just plus one and
minus one, but it's going to tell us how sure we
are that this is a positive review. [MUSIC]