[LDA] LDA theme model notes - mainly Dirichlet

d To express an article ,z Show the theme ,w Means the word
This means , Dirichlet prior distribution produce A group of Polynomial distribution aggregate
in other words Dirichlet distribution produce Theme distribution ( That is to say doc-topic Distribution )（ Hyperparameters $\alpha$ Under the circumstances ）

In Bayesian thought ： Prior probability + Parameter estimation = Posterior probability

beta Distribution ：

stay beta Distribution in beta Distribution studies “ A length of k Disordered sequence of （ Each number in the sequence is uniformly distributed ） in , The first k What distribution does a large number satisfy ” The problem of .（ The vague self - generalization version of the corresponding part of the link ）,
in other words , For each number in the sequence ,beta We can give a distribution of this number ,
in other words , For each number in the sequence , Just know the sort size of this number in the set ,beta The distribution gives the probability distribution of this number , The probability distribution can give the range in which this number is most likely to exist .
Actually beta Distribution is , The number of , This sequence is Prior knowledge .

Dirichlet ：

Dirichlet is beta High dimensional version of distribution , You can get A priori distribution of polynomials .
Let's assume that , A set of polynomial distributions , Each distribution is different , You need to get these parameters that determine their differences ,（ The parameter of the polynomial should be p1,p2,p3…pn such ？）
Then the Dirichlet distribution produces these Parameters of polynomial distribution A priori of （ transcendental ： A possible probability distribution judged by experience ）, let me put it another way , The Dirichlet distribution has no other conditions , Generate the probability distribution of polynomial parameters （ A complex formula ）, Throw the dice at random under this probability distribution , Get the polynomial parameters （p1:0.5,p2:0.3）, So we find the corresponding polynomial distribution （ emotional ：0.5, economic ：0.3）, Then throw a dice from the corresponding polynomial distribution , Get specific topic Category （ emotional ）.

Reference link csdn_ Dirichlet …
Some detailed derivation about Dirichlet datalearner

Add ：
LDA The generation process ： source ：csdn_ Easy to understand lda( Giant length ）

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