# Logistic Regression — probabilistic interpretation

Let start with the assumptions that we need to make

- The class label Y takes only two outcomes+1, 0 like a coin toss and hence can be thought of as a Benoulli random variable. The first big assumption is that the class label Y has a Bernoulli distribution.
- We have features X= {x1,x2,x3,…xn) where each xi is a continous variable. The next assumption is that the conditional probability of these features are Gaussian distributed. for each xi P(xi|y=yk) is gaussian distributed
- For two features xi and xj where i not equal to j, then xi and xj are
**conditionally independent. T**his is the Naive Bayes assumption.

Logistic regression is Gaussian Naive Bayes plus Class labels are Bernouli distributed plus regularizer

**Case 1**

Let’s substitute y =+1 in the above two equations and simply them. The objective is to ensure that both produce the same formulae at the end.

**Case 2**

Let’s substitute y = -1 into the geometric equation and y = 0 in the probabilistic intrepretation equation we get