# Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes

arXiv: https://arxiv.org/abs/2109.11634 · HTML: https://mlsanity.com/paper/2109.11634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 23 Sep 2021.

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

- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Connectivity Inference from Neural Recording Data: Challenges, Mathematical Bases and Research Directions](https://mlsanity.com/paper/1708.01888/) (2017)
- [High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models](https://mlsanity.com/paper/1804.00778/) (2018)
- [Latent Network Structure Learning from High Dimensional Multivariate Point Processes](https://mlsanity.com/paper/2004.03569/) (2020)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation](https://mlsanity.com/paper/1707.04928/) (2017)
- [Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models](https://mlsanity.com/paper/1711.07357/) (2017)
- [Estimating Time-Varying Graphical Models](https://mlsanity.com/paper/1804.03811/) (2018)
- [Joint Estimation of Multiple Graphical Models from High Dimensional Time Series](https://mlsanity.com/paper/1311.0219/) (2013)
- [Differential Network Analysis: A Statistical Perspective](https://mlsanity.com/paper/2003.04235/) (2020)
- [Joint Estimation of Precision Matrices in Heterogeneous Populations](https://mlsanity.com/paper/1601.00142/) (2016)
- [Statistical Inference for Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2007.07448/) (2020)
- [On model selection consistency of regularized M-estimators](https://mlsanity.com/paper/1305.7477/) (2013)
- [On Joint Estimation of Gaussian Graphical Models for Spatial and Temporal Data](https://mlsanity.com/paper/1507.01933/) (2015)
- [On Procedures Controlling the FDR for Testing Hierarchically Ordered Hypotheses](https://mlsanity.com/paper/1612.04467/) (2016)

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

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)

## Abstract (arXiv)

Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to share many edges, but also exhibit unique, condition-specific ones. However, the degree of similarity among the networks from different conditions is generally unknown. Existing approaches for multivariate point processes do not take these structures into account and do not provide inference for jointly estimated networks. To address these needs, we propose a joint estimation procedure for networks of high-dimensional point processes that incorporates easy-to-compute weights in order to data-adaptively encourage similarity between the estimated networks. We also propose a powerful hierarchical multiple testing procedure for edges of all estimated networks, which takes into account the data-driven similarity structure of the multi-experiment networks. Compared to conventional multiple testing procedures, our proposed procedure greatly reduces the number of tests and results in improved power, while tightly controlling the family-wise error rate. Unlike existing procedures, our method is also free of assumptions on dependency between tests, offers flexibility on p-values calculated along the hierarchy, and is robust to misspecification of the hierarchical structure. We verify our theoretical results via simulation studies and demonstrate the application of the proposed procedure using neuronal spike train data.