Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub

point to a discrete label (zero or one), we’ll compute the probability of a data
point’s belonging to the positive class.
Probabilities
If a data point has a logit that equals zero, it is exactly at the decision boundary
since it is neither positive nor negative. For the sake of completeness, we assigned
it to the positive class, but this assignment has maximum uncertainty, right? So,
the corresponding probability needs to be 0.5 (50%), since it could go either way.
Following this reasoning, we would like to have large positive logit values assigned
to higher probabilities (of being in the positive class) and large negative logit values
assigned to lower probabilities (of being in the positive class).
For really large positive and negative logit values (z), we would like to have:
Equation 3.4 - Probabilities assigned to different logit values (z)
We still need to figure out a function that maps logit values into probabilities.
We’ll get there soon enough, but first, we need to talk about…
Odds Ratio
"What are the odds?!"
This is a colloquial expression meaning something very unlikely has happened. But
odds do not have to refer to an unlikely event or a slim chance. The odds of getting
heads in a (fair) coin flip are 1 to 1 since there is a 50% chance of success and a 50%
chance of failure.
Let’s imagine we are betting on the winner of the World Cup final. There are two
countries: A and B. Country A is the favorite: It has a 75% chance of winning. So,
Country B has only a 25% chance of winning. If you bet on Country A, your chances
of winning—that is, your odds (in favor)—are 3 to 1 (75 to 25). If you decide to test
your luck and bet on Country B, your chances of winning—that is, your odds (in
favor)—are 1 to 3 (25 to 75), or 0.33 to 1.
212 | Chapter 3: A Simple Classification Problem