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So we talked about polynomial regression,

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where you have different
powers of your input.

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And we also talked about seasonality where
you have these sine and cosine bases.

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But we can really think about any
function of our single input.

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So let's write down our

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model a little bit more generically
in terms of some set of features.

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And I'm gonna denote each one of
my features with this function H.

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So H0 is gonna be my first feature,

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H1 my second feature,
H capital D, my last feature.

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So we can more compactly
represent this model

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using the sigma notation that
we introduced previously.

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Where we put an index I
equals one to capital D.

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Saying we're summing over each of
these capital D different features.

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And just to be very clear h
sub j of x is our jth feature,

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and wj is the regression coefficient or
weight associated with that feature.

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So just to give some examples that we've
gone through, this first feature might

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just be one, this constant feature that
we've used in all of the past examples.

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Or when we think about our second feature,
h1, maybe that's just our linear term, x.

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Our third feature might be x squared or
maybe it's our sine basis.

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Or we could think of lots of
other feature examples and

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when we get to our capital Dth feature,
maybe it's just our

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input raised to the pth power when we're
thinking about polynomial regression.

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So, going back to our
regression flow chart or

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block diagram here, we kinda swept
something under the rug before.

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We never really highlighted this
blue feature extraction box,

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and we just said the output of it was x.

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Really, now that we've learned a little
bit more about regression and this

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notion of features, really the output of
this feature extraction is not x but h(x).

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It's our features of our input x.

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So x is really the input to
our feature extractor, and

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the output is some set of functions of x.

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So for the remainder of this course,

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we're gonna assume that the output of
this feature extraction box is h of x.

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