  Bayesian feature allocation models are a popular tool for modelling data with
a combinatorial latent structure. Exact inference in these models is generally
intractable and so practitioners typically apply Markov Chain Monte Carlo
(MCMC) methods for posterior inference. The most widely used MCMC strategies
rely on an element wise Gibbs update of the feature allocation matrix. These
element wise updates can be inefficient as features are typically strongly
correlated. To overcome this problem we have developed a Gibbs sampler that can
update an entire row of the feature allocation matrix in a single move.
However, this sampler is impractical for models with a large number of features
as the computational complexity scales exponentially in the number of features.
We develop a Particle Gibbs sampler that targets the same distribution as the
row wise Gibbs updates, but has computational complexity that only grows
linearly in the number of features. We compare the performance of our proposed
methods to the standard Gibbs sampler using synthetic data from a range of
feature allocation models. Our results suggest that row wise updates using the
PG methodology can significantly improve the performance of samplers for
feature allocation models.
