Lucid LDA (2)

Read the beta distribution 1 Beta distribution 2 How to better understand the Beta distribution 21 the first kind of understanding is popular but not recommended 22 second understanding recommendation One solution two solution 33 Beta distribution nature conjugate prior 1 conjugate priori and conjugate distribution 2 Beta distribution with two-item distribution conjugate Relationship 3 Pseudo-count 4 the meaning of conjugate priori

0. Read the instructions

The necessary and minimal knowledge that is closely related to LDA is the body of the blog post. The contents of the gray box are expanded and supplemented, and skipping directly will not affect your understanding. A gray box refers to a paragraph of the following form:

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This part of the content is supplementary content, skipping directly does not affect your understanding 1β\beta distribution 1.1β\beta distribution

The probability density of the β\beta distribution is:
F (x) =⎧⎩⎨⎪⎪1b (β) xα−1 (1−x) β−1,0,x∈[0,1]others (1.1) F (x) =\left\{\begin{matrix} \frac{1}{b (\alpha,\beta)}x^{\alpha -1} (1-x) ^{\beta-1}, & x\in[0,1] \ 0, & others \end{matrix}\right. \tag{1.1}
which
B (β) =∫10xα−1 (1−x) β−1dx=γ (α) γ (beta) gamma (α + β) (1.2) B (\alpha,\beta) =\int_0^1x^{\alpha-1} (1-x) ^{\beta-1}dx=\frac{\gamma (\alpha) \gamma (\beta)}{\gamma (\alpha+\beta)}\tag{1.2}
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1.2 How to better understand the β\beta distribution.

The distribution of X (k) x_{(k)} at this point is the Β\beta distribution 1.2.1 First understanding (very popular but not recommended)

This way of understanding, I do not recommend, despite the online "scramble to copy"

The following items are from:
lda-math-Understanding Beta/dirichlet Distribution (1)