Talk:Variational Bayesian methods

This article feels like a mess

I'm not sure where to begin. I feel that I've wasted several hours trying to understand the material in this article, and that I would have saved hours had the article been more clearly written. For instance, it appears - and I'm still not 100% clear on this - that the notation $E_{i\neq j}\log p(Z,X)$ is to be understood as an expectation with respect to the variational distribution $q(\cdot )$, as opposed to an expectation with respect to, say, the full conditional of $Z_{i}$. So maybe better notation would be $E_{q}[\log p(Z,X)|Z_{i}]$ or something similar; we are apparently supposed to be integrating out everything EXCEPT $Z_{i}$ and doing so with respect to the variational distribution (the fact that we are supposed to be using the variational distribution to do this isn't mentioned anywhere). Maybe the notation used in this article is standard somewhere, but coming at this from a math stat/probability background I find it confusing.

Maybe these things are obvious to the authors of this article, but it still took quite a bit of effort to get. It also seems like much effort could be saved in calculations if the full conditional distributions of $p(Z|X)$ were derived first in the examples, since the full conditionals in the examples are well known. Then one would have $q(Z_{i})\propto \exp \left\{\log E_{i\neq j}p(Z_{i}|X,Z_{-i})\right\}$ since all the terms not associated with the full conditional can be absorbed into the normalizing constant. The examples would appear less daunting if shortcuts like this were used.

--68.101.66.185 (talk) 19:46, 11 August 2012 (UTC)