Machine learning algorithm: Exponential family distribution and generalized linear model __ machine learning

>  Translation Summary by Joey Joseph Matthews

Reference Ng's lecture note1 part3
In this paper, we will first introduce the exponential family distribution, then introduce the generalized linear models (generalized linear model, GLM), and finally explain why logistic regression (logistic regression, LR) is one of the generalized linear models. Exponential family Distribution

The exponential family distribution (the exponential family distribution) differs from the exponential distribution (exponential distribution). In probability statistics, if a probability distribution satisfies the next formula, we call it the exponential family distribution.
P (y;η) =b (y) exp (ηtt (y) −a (η)) p (y; η) = B (y) exp (ηt t (y) −a (η)) p (Y;\eta) =b (y) \exp (\eta^t t (y)-A (\eta))

Where Ηη\eta is a natural parameter, T (y) t (y) T is a sufficient statistic, exp−a (η)) exp−a (η)) \exp^{-a (\eta))} is a normalized function. By determining the T,a,b T, a, b t,a,b, we can determine the exponential family distribution of a parameter ηη\eta.
Many familiar probability distributions in statistics are specific forms of exponential family distribution, such as Bernoulli distribution, Gaussian distribution, polynomial distribution (multionmal), Poisson distribution and so on. The Bernoulli distribution and the Gaussian distribution are described below. Bernoulli distribution
P (Y;ϕ) =ϕy (1−ϕ) 1−y=exp[ylogϕ+ (1−y) log (1−ϕ)]=exp[ylogϕ1−ϕ+log (1−ϕ)] p (y; ϕ) =ϕy (1−ϕ) 1−y = e x p [y logϕ+ (1−y) log (1−ϕ)] = e x p [y log