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.
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