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. This 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 1 Geometric and probability interpretation equality

Case 2

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

Case 2 Geometric Interpretation equality

--

--

--

In the making Machine Learner programmer music lover

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Calculus: Differential Equations

Assume that students are distributed RANDOMLY in a college hallway.

The Cosine Rule: A Generalization of The Pythagorean Theorem

4 Proofs of Pythagorean Identity

The Best Websites to Solve Math Problems and Equations In 2020

The essence of Hypothesis Testing

Loci In The Argand Diagram

The Return of Beer Chess

The Return of Beer Chess

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Janardhanan a r

Janardhanan a r

In the making Machine Learner programmer music lover

More from Medium

Introduction to Splines

Regression to the mean

Feature selection for regression models on TIMMS

IEA IDB Analyzer screenshoot

ROC-AUC