  We present a "pull" approach to approximate products of Gaussian mixtures
within message updates for Nonparametric Belief Propagation (NBP) inference.
Existing NBP methods often represent messages between continuous-valued latent
variables as Gaussian mixture models. To avoid computational intractability in
loopy graphs, NBP necessitates an approximation of the product of such
mixtures. Sampling-based product approximations have shown effectiveness for
NBP inference. However, such approximations used within the traditional "push"
message update procedures quickly become computationally prohibitive for
multi-modal distributions over high-dimensional variables. In contrast, we
propose a "pull" method, as the Pull Message Passing for Nonparametric Belief
propagation (PMPNBP) algorithm, and demonstrate its viability for efficient
inference. We report results using an experiment from an existing NBP method,
PAMPAS, for inferring the pose of an articulated structure in clutter. Results
from this illustrative problem found PMPNBP has a greater ability to
efficiently scale the number of components in its mixtures and, consequently,
improve inference accuracy.
