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In my opinion the best thing you can to do to deal with missing data is
to make your algorithm, machine learning algorithm, robust to missing data.
In other words, make sure that an algorithm adapt to missing data.
And that's exactly what we're going to do in this particular module.
And we're going to do it in the context of decision trees,
because a simple modification of decision trees, they can handle missing data.
So, how we going to deal with missing data?
Let us try to understand a little better
what happened in the context of the decision trees?
So I have this input xi where the credit was poor and income was unknown.
I go down the decision tree, I hit credit poor, so
I take the branch here, poor.
And then I hit income, but income was unknown.
Income was question mark.
So what do I do then?
So what we're going to do is assign a branch to follow
when the data is unknown, when the value is unknown.
And in this case, I'm going to associate all unknown data, for
example, with the branch where income was low.
So if your income was unknown, take the branch low and
from there I'm just going to predict that this loan was risky.
So in other words, in our decision tree we're going to make explicit decisions
as to where question marks or missing values, unknown values will go.
We've introduced a decision to what happens when we hit an unknown value
at this point of the decision tree.
But we may have unknown values any point of decision tree, so we're going to
make decisions everywhere as to what should happen when we see unknown values.
So for every decision known, when I choose one of them its right to absorb
the unknown values and notice that those are going to be specific
decisions we're going to make associated with every diamond known or
every decision known in the decision tree so for credit we're going to have
the unknowns or question marks going to the fair branch for
income, it was poor.
And we look at income, we're going to go down the lower branch.
When credit equals poor and income is high we look at term and,
in this case, when term is equal to five years,
we're going to put the unknowns, or the question marks, in the five year bunch.
However, note take a note of this,
we might choose to say that when credit goes fair and
we look at term the unknowns in this case will go to the term equals three years.
So the decision that we make about where unknowns go
does not need to be the same in different parts of the decision tree.
So we take different decisions here,
About the questions marks, or unknowns.
And that's the beauty of the approach that we're describing,
because we're going to optimize, just like we're optimizing of the decision trees,
we're going to optimize where the unknowns will go,
in order to minimize the classification error.
Now if a learning tree like this and we're given an input,
for example, where the credit is unknown and the income was high,
and the term was 5 years, we can go down this tree and traverse.
Well, credit was unknown, the term was 5 years, so
I'm going to predict it's a safe loan.
While if I have another input where the credit is poor,
the income is high, the term was question mark when the different
branch of the decision tree will go down credit poor, income high and
the term here unknown goes down the same as the five year loan and
again we'll predict safe.
In general, approaches that explicitly handle missing data
in the algorithm itself can be quite helpful.
They can help address missing data training time and prediction time.
And can make more accurate predictions in general.
And we just talked about an example in decision trees.
The downside though is that it requires it to modify the actual learning algorithm to
deal with missing data.
In the case of decision trees, I'm going to describe
kind of a very simple modification that can make this happen,
but this can be very complex for other algorithms.
And even for decision trees, if you're going to make it really, really good,
it might be more complex than what we're talking about next.
But the idea here is fundamentally important.
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