Popular Courses
Beginner – Linear Regression
Introduction
Beginner – Decision Trees
Introduction
Beginner – Neural Networks
Introduction

Sign in to Curvingo

or

New Account     Reset Password     

Plans

Details
Logistic Regression
Introduction
How It Works
Scoring Our Model
Finding the Best S-Curve
Understanding Our S-Curve
Code with Python
Summary
Curvingo · Made in India

Share

Send us Feedback

Please let us know if you have any feedback and suggestions, or if you find any errors and bugs in our content.

Sorry, your message couldn’t be submitted. Please try again!

Thanks for your feedback!

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Logistic RegressionSummary

Reading time: ~5 min

One page to revise from — the ideas first, then every formula you need.

  • Classification predicts a group, not a number. Binary classification picks between two groups, written 1 and 0.
  • A straight line cannot give chances: it escapes below 0 and above 1. Logistic regression squashes the line z = wx + b with the sigmoid, so every output is a chance between 0 and 1.
  • A threshold turns a chance into a decision; the feature value where the chance equals the threshold is the decision boundary. Moving the threshold trades one kind of mistake for another.
  • Log-loss charges -\ln of the chance given to what really happened: right and sure costs almost nothing, wrong and sure costs a lot.
  • The best curve is found by gradient descent on the log-loss — or, equivalently, by maximum likelihood.
  • Odds are p \div (1 - p). One more unit of a feature multiplies the odds by e^w.

The model
p = \sigma(wx + b) = \dfrac{1}{1 + e^{-(wx + b)}}

Odds
\text{odds} = \dfrac{p}{1 - p}, \qquad \text{odds} \times e^{w} \text{ per unit of } x

Log-loss
-\dfrac{1}{n} \sum \Big[ y_i \ln p_i + (1 - y_i) \ln (1 - p_i) \Big]

Sina