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Now that explored the idea of precision let's talk about the slightly more subtle
idea of recall, and recall has to do with out of the possible positive things
in the world, everything out there, did I find every possible positive?
Sentence about my restaurant.
So, more specifically, I might take all the restaurant reviews and
all the sentences and feed it through my classifier.
And then classify some of those as positive, and some of those as negative.
So, some might have, y hat = +1.
Some might have y hat = -1.
Now, if I look at the true label, the true class of each one of the sentences, so yi,
which ones have +1, you see that four of those were predicted to be positive,
and just like we talked earlier in the module.
But there turned out to be two other sentences, there were three positive
that my algorithm did not find that fell into the negative bin.
So those are missed out.
So in other words, we found the 4 positive sentences, but
we missed out on 2 positive sentences that could have shown in my website.
And maybe those two sentences were so
amazing they would change the history of my restaurant, but I missed it.
Because they did not have perfect recall.
So, more formally out of all the truly positive data points, so
the one's where yi is +1, we can have a subset on those that we do capture.
So where y hat is also +1 but there's a subset which we
don't capture where we think the y hat is -1, so y hat does not agree with y.
And so, that's the part that we missed.
So the recall is the fraction of the once that we actually get.
We want everything to be in the blue box here.
More formally, we can define recall as the fraction of true positives.
For these are the data points that we were positive and
we got them right divided by the true positives.
And the false negative.
So the data points that were true, but we labeled as negative.
So falsely labeled as negative.
And so, this is going to have value one if the false negatives are zero.
Which means we captured everything, we captured all the true positives.
And zero if we did not capture any true positives so
all the positive data went to the false negative bin.
So if we go back to the example that we have been looking at,
I want to show positive sentences on my website.
I've got four of them, in y hat i equals +1 but I missed out on two sentences.
So for example,
I missed out on the sentences that said my wife tried the ramen and it was delicious,
and so maybe somebody's interested in ramen they don't see that sentence,
they don't go to my website, and so I missed out on something really good.
So high recall means that you discover everything positive that's being
said about the restaurant or all of the positive data points.
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