# Differentially Private Learning of Hawkes Processes

arXiv: https://arxiv.org/abs/2207.13741 · HTML: https://mlsanity.com/paper/2207.13741/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 18 of 18)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Tick: a Python library for statistical learning, with a particular emphasis on time-dependent modelling](https://mlsanity.com/paper/1707.03003/) (2017)
- [Differential Privacy Techniques for Cyber Physical Systems: A Survey](https://mlsanity.com/paper/1812.02282/) (2018)
- [On the Privacy Properties of GAN-generated Samples](https://mlsanity.com/paper/2206.01349/) (2022)
- [Pufferfish Privacy Mechanisms for Correlated Data](https://mlsanity.com/paper/1603.03977/) (2016)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Contact Tracing Mobile Apps for COVID-19: Privacy Considerations and Related Trade-offs](https://mlsanity.com/paper/2003.11511/) (2020)
- [Correlated Data in Differential Privacy: Definition and Analysis](https://mlsanity.com/paper/2008.00180/) (2020)
- [Quantifying Differential Privacy in Continuous Data Release under Temporal Correlations](https://mlsanity.com/paper/1711.11436/) (2017)
- [Algebraic and Analytic Approaches for Parameter Learning in Mixture Models](https://mlsanity.com/paper/2001.06776/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fast Learning of Multidimensional Hawkes Processes via Frank-Wolfe](https://mlsanity.com/paper/2212.06081/) (2022)

## Abstract (arXiv)

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as sample complexity for learning the parameters and releasing differentially private versions, are yet to be thoroughly analyzed. In this work, we study standard Hawkes processes with background intensity μ and excitation function α e-β t. We provide both non-private and differentially private estimators of μ and α, and obtain sample complexity results in both settings to quantify the cost of privacy. Our analysis exploits the strong mixing property of Hawkes processes and classical central limit theorem results for weakly dependent random variables. We validate our theoretical findings on both synthetic and real datasets.