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Refers generally to statistical procedures that utilize the logistic function, most commonly various forms of logistic regression

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Is logistic regression a generalized linear model for more than two classes?

Suppose that $K>2$ denote the number of classes and $Y$ be the class label that follows the logistic regression model for a given $X \in \mathbb{R}^d$ as follows: $$ P(Y=k|X)= \frac{e^{\beta_k^\top X}} … In other words, can we find an exponential family distribution, a link function and suitable set of parameters such that the logistic regression model above falls into a GLM category? …
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