Regularised Spectral Estimation for High-Dimensional Point Processes

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ID: 329937
2026
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Abstract
Summary Advances in modern technology have enabled the simultaneous recording of neural spiking activity across large numbers of neurons, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the spectral density matrix, a frequency domain equivalent of the covariance matrix. In the context of neuronal analysis, statistics based on the spectral density matrix can be used to infer connectivity in the brain network between individual neurons. However, the high-dimensional nature of spike train data mean that it is often difficult, or at times impossible, to compute these statistics. To improve the efficiency of spectral estimation for point processes, we propose methodology that combines a Whittle pseudo-likelihood with ridge or Lasso style penalties. We establish asymptotic and large sample properties for our proposed estimators and evaluate their performance on synthetic data simulated from multivariate Hawkes processes. Finally, we apply our methodology to neuroscience spike train data in order to illustrate its ability to infer brain connectivity.
Reference Key
openalex_W4393027737 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Carla Pinkney, Carolina Euán, Alex Gibberd, Ali Shojaie
Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag059
URL
https://doi.org/10.1093/biomet/asag059
Keywords Keywords not found

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