Logistic Regression

Question 1

What is logistic regression?

Answer 1

Logistic regression models the probability of an instance to belong to a given class as a linear combination of the inputs

Question 2

What is the formula for logit?

Answer 2

logit(p1) = ln(p1 / (1 − p1)) = wTx

Question 3

What are the boundaries for class 1 and class 0 when using logit?

Answer 3

Class 1 >= 0
Class 0 < 0

Question 4

Why do we use the logit function?

Answer 4

By taking logs in logit, we can map the space from [0,1] to [-infinity, infinity]

Question 5

What is the decision boundary?

Answer 5

The equation wTx = 0 is the decision boundary when the hyperplane is 2-dimensional

Question 6

What does the logit say about the position of the example according to the decision boundary?

Answer 6

Above the line if > 0
On the line if = 0
Below the line if < 0

Question 7

What is the formula for p1 and p0?

Answer 7

p1 = e(wTx) / (1 + e(wTx))
p0 = 1 - p1 = 1 / (1 + e(wTx))

Question 8

What are the boundaries for class 1 and class 0 when using p1?

Answer 8

Class 1 >= 0.5
Class 0 < 0.5