Multinomial Logistic Regression Algorithm

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A Multinomial Logistic Regression Algorithm is a logistic regression algorithm that is a supervised multinomial classification algorithm and that fits a multinomial logistic function.



References

2017

2017

  • (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Multinomial_logistic_regression#Linear_predictor Retrieved:2017-7-24.
    • As in other forms of linear regression, multinomial logistic regression uses a linear predictor function [math]\displaystyle{ f(k,i) }[/math] to predict the probability that observation i has outcome k, of the following form: : [math]\displaystyle{ f(k,i) = \beta_{0,k} + \beta_{1,k} x_{1,i} + \beta_{2,k} x_{2,i} + \cdots + \beta_{M,k} x_{M,i}, }[/math] where [math]\displaystyle{ \beta_{m,k} }[/math] is a regression coefficient associated with the mth explanatory variable and the kth outcome. As explained in the logistic regression article, the regression coefficients and explanatory variables are normally grouped into vectors of size M+1, so that the predictor function can be written more compactly: : [math]\displaystyle{ f(k,i) = \boldsymbol\beta_k \cdot \mathbf{x}_i, }[/math] where [math]\displaystyle{ \boldsymbol\beta_k }[/math] is the set of regression coefficients associated with outcome k, and [math]\displaystyle{ \mathbf{x}_i }[/math] (a row vector) is the set of explanatory variables associated with observation i.

2012