#StackBounty: #expected-value #gamma-distribution #variational-bayes #dirichlet-distribution Using categorical data to build a Dirichle…

Bounty: 150

I am building a graphical model. I have some categorical data $boldsymbol{mu}$ where they are generated by $p(boldsymbol{mu}|boldsymbol{s},mathbf{A})=prod_kprod_jmathbf{A}_{ij}^{mu_is_j}$. I’d like to use $boldsymbol{mu}$ to be mapped to a Dirichlet distribution $P(boldsymbol{pi}|boldsymbol{alpha})=mathrm{Dir}(alpha)$.

I thought I can use the categorical distribution as a base distribution with some $alpha$ scalar value. But after investigating more, actually it is not possible because the concentration parameter vector $boldsymbol{alpha}$ must be values greater than zero.

Can anybody suggest how I can solve this problem?


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