Instead of predicting exactly 0 or 1, logistic regression generates a
probability—a value between 0 and 1, exclusive. For example, consider a
logistic regression model for spam detection. If the model infers a value of
0.932 on a particular email message, it implies a 93.2% probability that the
email message is spam. More precisely, it means that in the limit of infinite
training examples, the set of examples for which the model predicts 0.932 will
actually be spam 93.2% of the time and the remaining 6.8% will not.

Logistic Regression

Predicting Coin Flips?

Imagine the problem of predicting probability of Heads for bent coins

You might use features like angle of bend, coin mass, etc.

What's the simplest model you could use?

What could go wrong?

Logistic Regression

Many problems require a probability estimate as output

Enter Logistic Regression

Logistic Regression

Many problems require a probability estimate as output

Enter Logistic Regression

Handy because the probability estimates are calibrated

for example, p(house will sell) * price = expected outcome

Logistic Regression

Many problems require a probability estimate as output

Enter Logistic Regression

Handy because the probability estimates are calibrated

for example, p(house will sell) * price = expected outcome

Also useful for when we need a binary classification

spam or not spam? → p(Spam)

Logistic Regression -- Predictions

$$ y' = \frac{1}{1 + e^{-(w^Tx+b)}} $$

\(\text{Where:} \)
\(x\text{: Provides the familiar linear model}\)
\(1+e^{-(...)}\text{: Squish through a sigmoid}\)