  Learning from implicit feedback is challenging because of the difficult
nature of the one-class problem: we can observe only positive examples. Most
conventional methods use a pairwise ranking approach and negative samplers to
cope with the one-class problem. However, such methods have two main drawbacks
particularly in large-scale applications; (1) the pairwise approach is severely
inefficient due to the quadratic computational cost; and (2) even recent
model-based samplers (e.g. IRGAN) cannot achieve practical efficiency due to
the training of an extra model.
  In this paper, we propose a learning-to-rank approach, which achieves
convergence speed comparable to the pointwise counterpart while performing
similarly to the pairwise counterpart in terms of ranking effectiveness. Our
approach estimates the probability densities of positive items for each user
within a rich class of distributions, viz. \emph{exponential family}. In our
formulation, we derive a loss function and the appropriate negative sampling
distribution based on maximum likelihood estimation. We also develop a
practical technique for risk approximation and a regularisation scheme. We then
discuss that our single-model approach is equivalent to an IRGAN variant under
a certain condition. Through experiments on real-world datasets, our approach
outperforms the pointwise and pairwise counterparts in terms of effectiveness
and efficiency.
