  Time-varying mixture densities occur in many scenarios, for example, the
distributions of keywords that appear in publications may evolve from year to
year, video frame features associated with multiple targets may evolve in a
sequence. Any models that realistically cater to this phenomenon must exhibit
two important properties: the underlying mixture densities must have an unknown
number of mixtures, and there must be some "smoothness" constraints in place
for the adjacent mixture densities. The traditional Hierarchical Dirichlet
Process (HDP) may be suited to the first property, but certainly not the
second. This is due to how each random measure in the lower hierarchies is
sampled independent of each other and hence does not facilitate any temporal
correlations. To overcome such shortcomings, we proposed a new Smoothed
Hierarchical Dirichlet Process (sHDP). The key novelty of this model is that we
place a temporal constraint amongst the nearby discrete measures $\{G_j\}$ in
the form of symmetric Kullback-Leibler (KL) Divergence with a fixed bound $B$.
Although the constraint we place only involves a single scalar value, it
nonetheless allows for flexibility in the corresponding successive measures.
Remarkably, it also led us to infer the model within the stick-breaking process
where the traditional Beta distribution used in stick-breaking is now replaced
by a new constraint calculated from $B$. We present the inference algorithm and
elaborate on its solutions. Our experiment using NIPS keywords has shown the
desirable effect of the model.
