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A set of distributions (eg, normal, $\chi^2$, Poisson, etc) that share a specific form. Many of the distributions in the exponential family are standard, workhorse distributions in statistics, w/ convenient statistical properties.

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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} …
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