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

plot), they are. This serves us very well since we’re looking for a symmetrical
function that maps logit values into probabilities.
"Why does it need to be symmetrical?"
If the function weren’t symmetrical, different choices for the positive class would
produce models that were not equivalent. But, using a symmetrical function, we
could train two equivalent models using the same dataset, just flipping the classes:
• Blue Model (the positive class (y=1) corresponds to blue points)
◦ Data Point #1: P(y=1) = P(blue) = .83 (which is the same as P(red) = .17)
• Red Model (the positive class (y=1) corresponds to red points)
◦ Data Point #1: P(y=1) = P(red) = .17 (which is the same as P(blue) = .83)
Log Odds Ratio
By taking the logarithm of the odds ratio, the function is not only symmetrical, but
also maps probabilities into real numbers, instead of only the positive ones:
Equation 3.6 - Log odds ratio
In code, our log_odds_ratio() function looks like this:
def log_odds_ratio(prob):
return np.log(odds_ratio(prob))
p = .75
q = 1 - p
log_odds_ratio(p), log_odds_ratio(q)
Output
(1.0986122886681098, -1.0986122886681098)
214 | Chapter 3: A Simple Classification Problem