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Now that we've seen the logistic regression model and
we understand it in quite a bit of detail,
let's give a quick overview of what learning means for this model.
Although in the next module we're going to go into quite a lot of detail to
learning algorithm.
This is just a little primer, a teaser for what's coming in the next module.
Now we're going to start from some data and
that data has inputs x and outputs either plus one or minus one.
As we said we're going to split that into a training set and a validation set.
And from the training set we're going to run a learning algorithm that
will output the parameter estimates w hat.
And those w hats are going to be plugged into the model.
To estimate the probability that an input sentence is either positive or negative.
And, of course, we can use the learn model to take the validation set and
estimate how good it is, what the quality metrics are, what the error is.
Now to find the best classifier we are going to define the quality metric.
In this case the quality metric is going to be called the likelihood function.
So very possible parameters serve coefficient w for example w0, w1, w2,
we will be able to score it according to, l of w to figure out how good it is.
So for example if I take this data set of plusses and minuses and
learn the line shown in green, we might get a particular likelihood.
So, for example, if the parameter w0 is 0, w1 is 1 but
w2 is -1.5, the likelihood might be 10 to the -6, pretty small.
These numbers actually tend to be pretty small.
For this alternative line, where w0 is now 1, w1 is still 1, w2 is -1.5,
the likelihood function is a little better 10 to the -5 instead of 10 to the -6.
But perhaps for this best line over here, where w0 is 1, w1 is 0.5 and w2 is -1.5.
You get the best likelihood, 10 to the -4.
So we'd like an approach that would actually search for
the possible values of w to find the best line.
And, as we will see in the next module, we'll use a gradient ascent algorithm to
find the set of parameters w that has the highest likelihood best quality.
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