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arXiv · 2011.00717

Noise-Contrastive Estimation for Multivariate Point Processes

Hongyuan Mei·Tom Wan·Jason Eisner
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Abstract

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.

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Hongyuan Mei, Tom Wan, Jason Eisner. 2020-11-02. Noise-Contrastive Estimation for Multivariate Point Processes. https://arxiv.org/abs/2011.00717

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