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Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling

Abstract: 

We consider the problem of estimating discrete self- exciting point process models from limited binary observations, where the history of the process serves as the covariate. We analyze the performance of two classes of estimators: l1-regularized maximum likelihood and greedy estimation for a discrete version of the Hawkes process and characterize the sampling tradeoffs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear and generalized linear models with i.i.d. covariates to point processes with highly inter-dependent covariates. We further provide simulation studies as well as application to real spiking data from mouse’s lateral geniculate nucleus and ferret’s retinal ganglion cells which agree with our theoretical predictions.

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Paper Details

Authors:
Abbas Kazemipour, Min Wu and Behtash Babadi
Submitted On:
12 December 2016 - 9:35am
Short Link:
Type:
Research Manuscript
Document Year:
2016
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Robust_SEPP_TSP.pdf

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[1] Abbas Kazemipour, Min Wu and Behtash Babadi, "Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1261. Accessed: Dec. 15, 2017.
@article{1261-16,
url = {http://sigport.org/1261},
author = {Abbas Kazemipour; Min Wu and Behtash Babadi },
publisher = {IEEE SigPort},
title = {Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling},
year = {2016} }
TY - EJOUR
T1 - Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling
AU - Abbas Kazemipour; Min Wu and Behtash Babadi
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1261
ER -
Abbas Kazemipour, Min Wu and Behtash Babadi. (2016). Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling. IEEE SigPort. http://sigport.org/1261
Abbas Kazemipour, Min Wu and Behtash Babadi, 2016. Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling. Available at: http://sigport.org/1261.
Abbas Kazemipour, Min Wu and Behtash Babadi. (2016). "Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling." Web.
1. Abbas Kazemipour, Min Wu and Behtash Babadi. Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1261