# multinomial logistic regression

(30 minutes to learn)

## Summary

Multinomial logistic regression is a generalization of logistic regression to the case where there are more than two categories.

## Context

This concept has the prerequisites:

- logistic regression
- maximum likelihood (Multinomial logistic regression can be fit using maximum likelihood.)
- optimization problems (Multinomial logistic regression is formulated as an optimization problem.)
- gradient descent (Multinomial logistic regression can be fit using gradient descent.)

## Goals

- Know what the multinomial logistic regression model is

- Derive the gradient descent update rule

## Core resources (read/watch one of the following)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 4.3.4, "Multiclass logistic regression," pages 209-210

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 8.3.7, "Multi-class logistic regression," pages 252-254

## See also

- Here are some other commonly used multiway classification algorithms: Multinomial logistic regression is a discriminative model .
- Multinomial logistic regression is a kind of generalized linear model .