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This next section will talk about
how to pick that threshold split,

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H equals 38 over income with 60,000 for
continuous valued features.

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We're going to make this
an optional session.

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Its not super complicated but
is that a little bit laborious?

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So, if you're interested,
definitely take a deep dive, but for

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those who want to skip it,
it's totally okay.

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So the goal here is to ask,
if I decide to split, on say income,

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how do I choose the splitting point,
p star, that we won't separate,

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now case of 60,000, but we want to split
the left and right side of the tree.

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Now, this infinite many values that t

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star could take, it could be $60,000,
$50,999.99, and if this

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is truly continuous it could go to
infinite remaining decimal places.

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The question is do we need
to consider all of those.

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And do all those decimal places really
effect the quality of our decision tree?

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Now if you think about it and

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if you look at the values that
income can take on the data so

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actual of income you'll see that if
you take two points of say VA, and VB.

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Let's say 60,000, and 65,000.

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If there are no points in between, whether
the split is at 61,000, 62,000, 63,000,

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64,000, you're still going to have
the same classification error.

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The points on the left of that
split always going to be the same,

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the points on the right of
the split cannot be the same.

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So all I have to do,

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is consider the middle point, between
any of the data points that we have, and

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just consider those to be
the possible splits for my data.

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And that's exactly what we're going to do.

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Let's now close the section by
walking through the algorithm for

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picking the best splitting point,
for a particular feature.

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So let's say that I'm considering
splitting, on the feature here, hj,

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which might be in our case, income, and,
what I can do is go through all my data,

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so the column of values of the income
might take, and sort them.

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Such that V1 is the lowest income,
V2 is the next lowest and

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VN is the highest income.

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And all I need to consider is the
splitting points right in between V1 and

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V2, V2 and V3 and so on.

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So I walk from i = 1 though N-1 and
then consider splitting point ti,

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which is the midpoint between Vi and
Vi+1, and I ask what is the classification

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error if I were to build a decision tree,
a decision stump in this case,

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that splits xj on ti,
on greater than ti and less than ti?

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So greater than 60,000 and
lower than 60,000.

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And then we'll pick.

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t star, to be the split that
leads to decision stump,

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with the lowest classification error.

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And that's it.

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Pretty simple algorithm,
pretty easy to take from here.

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