Logistic Regression: Binary And Multinomial -

It outputs a vector of probabilities for all classes that sum up to 1.0. The class with the highest probability is the predicted outcome. Key Differences at a Glance Multinomial Outcome Classes Function Example Fraud vs. Not Fraud Red vs. Blue vs. Green Complexity Simple; one set of weights Higher; weights for each class When to Use Which?

Instead of one sigmoid function, it uses the Softmax function . It essentially runs multiple binary regressions comparing each category to a "reference" category.

Use if you are choosing between several distinct labels where one choice doesn't "outrank" another. Logistic Regression: Binary and Multinomial

This is used when your target variable has exactly (e.g., Yes/No, Pass/Fail, Spam/Not Spam).

Use if you are answering a "True/False" style question. It outputs a vector of probabilities for all

It uses the Sigmoid function to map any real-valued number into a value between 0 and 1. The Math: It models the "log-odds" of the probability

This is used when your target variable has (e.g., predicting if a user will choose Product A, B, or C). Not Fraud Red vs

ln(p1−p)=β0+β1x1+...+βnxnl n open paren the fraction with numerator p and denominator 1 minus p end-fraction close paren equals beta sub 0 plus beta sub 1 x sub 1 plus point point point plus beta sub n x sub n Usually, if the predicted probability is ≥0.5is greater than or equal to 0.5 , it’s classified as "1"; otherwise, it's "0." 2. Multinomial Logistic Regression