  A key problem in computational sustainability is to understand the
distribution of species across landscapes over time. This question gives rise
to challenging large-scale prediction problems since (i) hundreds of species
have to be simultaneously modeled and (ii) the survey data are usually inflated
with zeros due to the absence of species for a large number of sites. The
problem of tackling both issues simultaneously, which we refer to as the
zero-inflated multi-target regression problem, has not been addressed by
previous methods in statistics and machine learning. In this paper, we propose
a novel deep model for the zero-inflated multi-target regression problem. To
this end, we first model the joint distribution of multiple response variables
as a multivariate probit model and then couple the positive outcomes with a
multivariate log-normal distribution. By penalizing the difference between the
two distributions' covariance matrices, a link between both distributions is
established. The whole model is cast as an end-to-end learning framework and we
provide an efficient learning algorithm for our model that can be fully
implemented on GPUs. We show that our model outperforms the existing
state-of-the-art baselines on two challenging real-world species distribution
datasets concerning bird and fish populations.
