# Multinomial Logit

In statistics, a multinomial logistic regression model, also known as softmax regression or multinomial logit, is a regression model which generalizes logistic regression by allowing more than two discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). The use of the term "multinomial" in the name arises from the common conflation between the categorical and multinomial distributions, as explained in the relevant articles. However, it should be kept in mind that the actual goal of the multinomial logit model is to predict categorical data.

In some fields of machine learning (e.g. natural language processing), when a classifier is implemented using a multinomial logit model, it is commonly known as a maximum entropy classifier, conditional maximum entropy model or MaxEnt model for short. Maximum entropy classifiers are commonly used as alternatives to Naive Bayes classifiers because they do not assume statistical independence of the independent variables (commonly known as features) that serve as predictors. However, learning in such a model is slower than for a Naive Bayes classifier, and thus may not be appropriate given a very large number of classes to learn. In particular, learning in a Naive Bayes classifier is a simple matter of counting up the number of cooccurrences of features and classes, while in a maximum entropy classifier the weights, which are typically maximized using maximum a posteriori (MAP) estimation, must be learned using an iterative procedure; see below.

Read more about Multinomial LogitIntroduction, Assumptions, Estimation of Intercept, Applications

### Other articles related to "multinomial logit, logit, multinomial":

Local Independence Of Irrelevant Alternatives - In Econometrics
... IIA is a property of the multinomial logit and the conditional logit models in econometrics outcomes that could theoretically violate this IIA (such as the outcome of multicandidate elections or any ... Generalized extreme value, multinomial probit (also called conditional probit) and mixed logit are alternative models for nominal outcomes which relax IIA ... The multinomial probit model has as a disadvantage that it makes calculation of maximum likelihood infeasible for more than five alternatives as it involves multiple integrals ...
Multinomial Logit - Applications
... Random multinomial logit models combine a random ensemble of multinomial logit models for use as a classifier ...
Random Multinomial Logit
... In statistics and machine learning, random multinomial logit (RMNL) is a technique for (multi-class) statistical classification using repeated multinomial logit analyses ...
Logistic Regression - Formal Mathematical Specification - As A "log-linear" Model
... provides a link to one of the standard formulations of the multinomial logit ... Here, instead of writing the logit of the probabilities pi as a linear predictor, we separate the linear predictor into two, one for each of the two outcomes Note that two ... shows clearly how to generalize this formulation to more than two outcomes, as in multinomial logit ...