# Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes

arXiv: https://arxiv.org/abs/2109.10947 · HTML: https://mlsanity.com/paper/2109.10947/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 61 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 16 of 16)

- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Heteroskedastic PCA: Algorithm, Optimality, and Applications](https://mlsanity.com/paper/1810.08316/) (2018)
- [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)
- [Spectral Deconfounding via Perturbed Sparse Linear Models](https://mlsanity.com/paper/1811.05352/) (2018)
- [Connectivity Inference from Neural Recording Data: Challenges, Mathematical Bases and Research Directions](https://mlsanity.com/paper/1708.01888/) (2017)
- [Latent Network Structure Learning from High Dimensional Multivariate Point Processes](https://mlsanity.com/paper/2004.03569/) (2020)
- [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)
- [Simultaneous whole-animal 3D-imaging of neuronal activity using light field microscopy](https://mlsanity.com/paper/1401.5333/) (2014)
- [Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series](https://mlsanity.com/paper/1704.02519/) (2017)
- [Causal Structural Learning Via Local Graphs](https://mlsanity.com/paper/2107.03597/) (2021)
- [Statistical Inference for Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2007.07448/) (2020)
- [A shotgun sampling solution for the common input problem in neural connectivity inference](https://mlsanity.com/paper/1309.3724/) (2013)
- [Adaptive Estimation in Multivariate Response Regression with Hidden Variables](https://mlsanity.com/paper/2003.13844/) (2020)

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

- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)

## Abstract (arXiv)

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naive estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.