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The dirichlet distribution takes this form:

I'm trying to understand how we end up with a vector from this formula rather than a scalar. The only way I see how is that each x itself is a vector sampled from the simplex.

In particular, I'm trying to understand in the context of Latent Dirichlet Allocation. K would represent the number of topics we have (points on the simplex). So if we have 3 topics, do we sample three points in the simplex, multiply them, and then normalize them with the beta function?

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    $\begingroup$ The sum of the $x_i$'s is one. Meaning that the vector $(x_1,\ldots,x_K)$ belongs to the simplex of $\mathbb R^K$. $\endgroup$
    – Xi'an
    Feb 5 '21 at 16:17

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