# Online Stochastic Variational Inference for Dirichlet Process Mixture Models

There's a 2013 NeurIPS paper I'm trying to understand, Online Learning of Nonparametric Mixture Models via Sequential Variational Approximation. I have a few questions:

1. Equation 2, which defines a Dirichlet Process (DP) mixture model, doesn't use $$D$$ after drawing $$D$$ from the $$DP$$. I thought $$\theta_i$$ should be drawn from D, not from $$\mu$$. Could someone clarify?

1. Equation 14 says it uses Equation 10, but Equation 10 gives a variational distribution over the Dirichlet Process posterior $$q(D|\rho, \nu)$$ whereas the "Equation 10" used in Equation 14 is a variational distribution $$q(z_{i+1}|\rho_{1:i}, \nu^{(i)})$$. How does one convert the true Equation 10 into the form used in Equation 14?

1. The update rules are derived from minimizing a KL divergence. However, the direction of the KL divergence isn't clear, and one of the two terms, appears to rely on itself (i.e. the q distribution is conditioned on itself). Could someone clarify what the objective function is and show how the update rules can be derived?

Based on the paper's reviews, reviewer 4 had these same questions and I think the author intended to add answers to the supplement (the supplement starts with, "This document provides proofs of theorems presented in the paper") but never actually got around to adding the answers.

I've emailed the sole author but I have yet to hear back from him.