The paper derives a new estimation method for multi-variate point processes that is based on the'ranking'-variant of NCE. The paper is borderline: two reviewers think that the difference to previous work by Gao (who use NCE to estimate point-processes) and the empirical comparison is not sufficient. Two other reviewers disagree, with one in particular arguing that the paper should be accepted. The meta-reviewer thinks that the theory in the paper is sufficiently different from Gao's work, and that the theoretical aspects of the paper are deeper and more rigorous. The results do not follow directly from previous work by Gutmann & Hyvarinen (2012) or Ma & Collins (2018). The empirical results are good and the method should be useful in practice.

The log-likelihood of a generative model often involves both positive and negative terms. As a result, maximum likelihood estimation is expensive. We show how to instead apply a version of noise-contrastive estimation---a general parameter estimation method with a less expensive stochastic objective. Our specific instantiation of this general idea works out in an interestingly non-trivial way and has provable guarantees for its optimality, consistency and efficiency. On several synthetic and real-world datasets, our method shows benefits: for the model to achieve the same level of log-likelihood on held-out data, our method needs considerably fewer function evaluations and less wall-clock time.