This paper introduces ASUGS (adaptive sequential updating and greedy search), building on the previous work on SUGS by Wang & Dunson 2011 \cite{10.1198/jcgs.2010.07081}, which is a sequential (ie online) MAP inference method for DPMMs.

The main contribution of the paper is to provide online updating for the concentration parameter, $\alpha$.

The paper shows that the posterior distribution on $\alpha$ can be expected to behave has a gamma distribution (that depends on the current number of clusters and on n) in the large-scale limit, assuming an exponential prior on $\alpha$.

ASUGS uses the mean of this gamma distribution as the $\alpha$ for updating cluster assignments, the remainder of the algorithm proceeding as in SUGS (ie using conjugacy to update model parameters in an online fashion, with hard assignments of data to clusters.)

The paper also shows that this choice of \alpha is bounded by $\log^\epsilon n$ for an arbitrarily small $\epsilon$, so that we may expect this process to converge, or at the very least be stable even in large settings.