# Noise-Contrastive Estimation for Multivariate Point Processes

arXiv: https://arxiv.org/abs/2011.00717 · HTML: https://mlsanity.com/paper/2011.00717/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2020.

## Built on by (most cited first, 20 of 20)

- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [On the Predictive Accuracy of Neural Temporal Point Process Models for Continuous-time Event Data](https://mlsanity.com/paper/2306.17066/) (2023)
- [An Empirical Study: Extensive Deep Temporal Point Process](https://mlsanity.com/paper/2110.09823/) (2021)
- [Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes](https://mlsanity.com/paper/2210.15294/) (2022)
- [SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process](https://mlsanity.com/paper/2310.16336/) (2023)
- [Non-Autoregressive Diffusion-based Temporal Point Processes for Continuous-Time Long-Term Event Prediction](https://mlsanity.com/paper/2311.01033/) (2023)
- [Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2401.04612/) (2024)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG Signals](https://mlsanity.com/paper/2112.06652/) (2021)
- [Self-Supervised Contrastive Pre-Training for Multivariate Point Processes](https://mlsanity.com/paper/2402.00987/) (2024)
- [Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantification](https://mlsanity.com/paper/2310.16310/) (2023)
- [Hawkes Processes on Graphons](https://mlsanity.com/paper/2102.02741/) (2021)
- [Intensity-free Integral-based Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/2308.02360/) (2023)
- [Towards Unified Approaches in Self-Supervised Event Stream Modeling: Progress and Prospects](https://mlsanity.com/paper/2502.04899/) (2025)
- [Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2510.20414/) (2025)

## Abstract (arXiv)

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.