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This next section will talk about how to pick that threshold split,
H equals 38 over income with 60,000 for continuous valued features.
We're going to make this an optional session.
Its not super complicated but is that a little bit laborious?
So, if you're interested, definitely take a deep dive, but for
those who want to skip it, it's totally okay.
So the goal here is to ask, if I decide to split, on say income,
how do I choose the splitting point, p star, that we won't separate,
now case of 60,000, but we want to split the left and right side of the tree.
Now, this infinite many values that t
star could take, it could be $60,000, $50,999.99, and if this
is truly continuous it could go to infinite remaining decimal places.
The question is do we need to consider all of those.
And do all those decimal places really effect the quality of our decision tree?
Now if you think about it and
if you look at the values that income can take on the data so
actual of income you'll see that if you take two points of say VA, and VB.
Let's say 60,000, and 65,000.
If there are no points in between, whether the split is at 61,000, 62,000, 63,000,
64,000, you're still going to have the same classification error.
The points on the left of that split always going to be the same,
the points on the right of the split cannot be the same.
So all I have to do,
is consider the middle point, between any of the data points that we have, and
just consider those to be the possible splits for my data.
And that's exactly what we're going to do.
Let's now close the section by walking through the algorithm for
picking the best splitting point, for a particular feature.
So let's say that I'm considering splitting, on the feature here, hj,
which might be in our case, income, and, what I can do is go through all my data,
so the column of values of the income might take, and sort them.
Such that V1 is the lowest income, V2 is the next lowest and
VN is the highest income.
And all I need to consider is the splitting points right in between V1 and
V2, V2 and V3 and so on.
So I walk from i = 1 though N-1 and then consider splitting point ti,
which is the midpoint between Vi and Vi+1, and I ask what is the classification
error if I were to build a decision tree, a decision stump in this case,
that splits xj on ti, on greater than ti and less than ti?
So greater than 60,000 and lower than 60,000.
And then we'll pick.
t star, to be the split that leads to decision stump,
with the lowest classification error.
And that's it.
Pretty simple algorithm, pretty easy to take from here.
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