Noise-Contrastive Estimation for Multivariate Point Processes
This work addresses efficiency issues in parameter estimation for temporal multivariate point processes, which is an incremental improvement for researchers and practitioners in fields like event modeling.
The paper tackles the computational expense of maximum likelihood estimation for multivariate point processes by applying noise-contrastive estimation, resulting in a method that requires fewer function evaluations and less wall-clock time to achieve the same log-likelihood on held-out data.
The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the possible times. 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.