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I am reading Variational Inference: A Review for Statisticians by Blei, Kucukelbir and McAuliffe. I am having a hard time following some of the steps in Section 3.2

More precisely, they state that $\phi_{ik}$ = $E$$[c_{ik};\phi_{i}$]. I am not sure I follow this. I understand that $c_{i}$ is an indicator vector and that $q(c_{i};\phi_{i})$ is the distribution on the mixture assignment of the $i$th observation vector. The statement in that particular statement goes onto say that because $c_{i}$ is an indicator vector, this follows. I am not sure I follow it.

Would appreciate an explanation of this.

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