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The notation that we've used so far is
without features associated with it,

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but just like the regression course
we're going to focus on introducing

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features from the very beginning.

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So we're going to have these
functions h1 through h capital d.

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They've defined some features
we might extract from the data.

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and we are going to encode
the constant function that is h0.

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So in particular we are going
to have to discard is w0,

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h0, +w1, h1, w2, h2,
all the way to w capital d,

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hd so a feature could be a constant h0,

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it could be #awesome's for
h1, #aweful's for h2.

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It could be some translations like log of
number of awesome's times number of bad's.

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Or more realistically,
it could be the TFIDF of number

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awful's which help us emphasize more
words which are more distinctive, or

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important that we looked at PFIDF in the
first course, and explored it quite a bit.

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And we're going to revisit
that in the next course.

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So now we have this prediction score which
is based on the sum over the features

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of the coefficient wi,
wj times the feature hj.

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And we're going to use short hand a w
transposed hi(xi) to denote the scores.

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So you see me do that a lot.

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W transpose h(xi) denotes the score for

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that particular data point and if that
score is greater than 0 we're going to say

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positive and if the score is less than 0,
we're going to say it's negative.

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Very good, so now we introduce our
model in a little bit more detail.

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And I'm always going to
take the input data x,

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feed it through the feature
generating function,

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which might be counting the number of
awesomes or creating a TF-IDF model.

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I'm going to feed that to the machinery
model which is going to multiply

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the features with the learned weights that
you had an output of value a score which

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we're going to throw through the same
function an output item that Y had was

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plus one positive reviews of minus one,
negative reviews.

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