  Analyzing the underlying structure of multiple time-sequences provides
insights into the understanding of social networks and human activities. In
this work, we present the \emph{Bayesian nonparametric Poisson process
allocation} (BaNPPA), a latent-function model for time-sequences, which
automatically infers the number of latent functions. We model the intensity of
each sequence as an infinite mixture of latent functions, each of which is
obtained using a function drawn from a Gaussian process. We show that a
technical challenge for the inference of such mixture models is the
unidentifiability of the weights of the latent functions. We propose to cope
with the issue by regulating the volume of each latent function within a
variational inference algorithm. Our algorithm is computationally efficient and
scales well to large data sets. We demonstrate the usefulness of our proposed
model through experiments on both synthetic and real-world data sets.

Machine Learning