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I'm doing dirichlet process clustering where dirichlet priors are used as:
with CRP representation as:

  • First customer will always choose first table.
  • Second will choose already occupied table with
  • probability c/α + n - 1
  • and will choose unoccupied table with
  • probability α / α + n - 1 where
  • α which is known as dirichlet prior and
  • c is # of customers at occupied table
  • n is total # of customers

Now if we use Collapsed Gibbs Sampling for initial assignments of group, α is also used as CRP probability in Collapased Gibbs Sampling. So the question is:

  • Should I myself assign a value to α or is there any technique to estimate α?

Thanks!

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  • $\begingroup$ Are you looking at a Chinese Restaurant process ? link $\endgroup$ – EngrStudent Mar 14 '16 at 12:58
  • $\begingroup$ @EngrStudent yeah absolutely I want to Dirichlet Clustering using CRP as what I know, Dirichlet Clustering using Stick Breaking Construction or using CRP is almost same. $\endgroup$ – maliks Mar 14 '16 at 13:03
  • $\begingroup$ @EngrStudent These both links shared by you are not downloadable for me here, can you please share at taufelaus@gmail.com $\endgroup$ – maliks Mar 14 '16 at 13:06
  • $\begingroup$ @EngrStudent can you help me in estimating or inferring a value for α please? $\endgroup$ – maliks Mar 14 '16 at 13:07
  • $\begingroup$ You can put a prior on alpha and make a draw from its conditional posterior on each sweep. $\endgroup$ – mef Mar 14 '16 at 13:41
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I assume by "Dirichlet Process Clustering Prior" you mean you are using a "Dirichlet Process Mixture Model" to model your data. This would be the simplest model with DP.

As @mef pointed out you can put a vague gamma prior on $\alpha$, $\alpha \sim Gamma(a, b)$ and resample $\alpha$ as well as your table assignments. You can find the details in Escobar and West 95 paper, or in this note by West.

Remember, these formulas are valid only if the conditional distribution of cluster labels follow a CRP. Otherwise they just give you an approximation.

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