"Sigmoid
Function," also called the "Logistic Function":
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hθ(x)=g(θTx)
z=θTx
g(z)=1/(1+e−z)
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The
following image shows us what the sigmoid function looks like:
The
function g(z), shown here, maps any real number to the (0, 1) interval, making
it useful for transforming an arbitrary-valued function into a function better
suited for classification.
hθ(x) will give us
the probability that our output is 1. For example, hθ(x)=0.7 gives us a
probability of 70% that our output is 1. Our probability that our prediction is
0 is just the complement of our probability that it is 1 (e.g. if probability
that it is 1 is 70%, then the probability that it is 0 is 30%).
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hθ(x)=P(y=1|x;θ)=1−P(y=0|x;θ)
P(y=0|x;θ)+P(y=1|x;θ)=1
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reference : Andrew Ug, Machine Learning
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