I am looking for derivation of eqn 5 in C.Moody's paper https://arxiv.org/pdf/1605.02019.pdf where it says the loss function coming from dirichlet enforcement of sparsity is


When you look up a formal paper, such as https://tminka.github.io/papers/dirichlet/minka-dirichlet.pdf eqn 4

that term is only part of the whole formula. Can someone explain how the Moody is able to eliminate the two Gamma terms?


1 Answer 1


Equation $4$ from Minka's paper is

$$\log P(D|\alpha) = N\log\Gamma\left( \sum_k \alpha_k \right)-N\sum_k\log\Gamma\left( \alpha_k \right)+N\sum_k (\alpha_k - 1)\log \bar{p_k}$$

If $\alpha$ is fixed and the optimization variables are $\bar{p_k}$, the first two terms are just constant and they can be dropped for the purpose of such optimization, after all.

  • $\begingroup$ that was easy, and makes sense. $\endgroup$
    – bhomass
    Commented Sep 8, 2018 at 21:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.