6.2 Logistic Regression

Question 1

Typically, logistic regression can be used when we are facing with ………. inputs and ……… outputs.

Answer 1

continuous; discrete

Typically inputs of a logistic regression are feature values that are continuous, and the output is the class label which is discrete

Question 2

In logistic regression, if β⋅X≫1 , the label would be:

Answer 2

1

In this case, the denominator of the logistic function approaches to 1 (refer to Slide 14), so the output will be 1.

Question 3

The overall likelihood function in logistic regression over a training dataset is the product of the likelihood of individual instances, because …

Answer 3

Features are assumed uncorrelated

The overall likelihood over a dataset is the product of individual likelihood when we assume that the training instances are independent, which means that observing one instance will not change the probability of another instance.

Question 4

Given multi-class classification problem with K classes, using multinomial logistic regression, how many logistic regression models do we need to build?

Answer 4

K-1

The multinomial logistic regression picks one class as the pivot, and then build K-1 models to separate this pivot class and one of the other classes (in total, K-1 of them).