  In population synthesis applications, when considering populations with many
attributes, a fundamental problem is the estimation of rare combinations of
feature attributes. Unsurprisingly, it is notably more difficult to reliably
representthe sparser regions of such multivariate distributions and in
particular combinations of attributes which are absent from the original
sample. In the literature this is commonly known as sampling zeros for which no
systematic solution has been proposed so far. In this paper, two machine
learning algorithms, from the family of deep generative models,are proposed for
the problem of population synthesis and with particular attention to the
problem of sampling zeros. Specifically, we introduce the Wasserstein
Generative Adversarial Network (WGAN) and the Variational Autoencoder(VAE), and
adapt these algorithms for a large-scale population synthesis application. The
models are implemented on a Danish travel survey with a feature-space of more
than 60 variables. The models are validated in a cross-validation scheme and a
set of new metrics for the evaluation of the sampling-zero problem is proposed.
Results show how these models are able to recover sampling zeros while keeping
the estimation of truly impossible combinations, the structural zeros, at a
comparatively low level. Particularly, for a low dimensional experiment, the
VAE, the marginal sampler and the fully random sampler generate 5%, 21% and
26%, respectively, more structural zeros per sampling zero generated by the
WGAN, while for a high dimensional case, these figures escalate to 44%, 2217%
and 170440%, respectively. This research directly supports the development of
agent-based systems and in particular cases where detailed socio-economic or
geographical representations are required.
