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A novel family of non-parametric cumulative based divergences for point processes
Sohan Seth · Il Memming Park · Austin J Brockmeier · Mulugeta Semework · John S Choi · Joseph T Francis · Jose C Principe

Wed Dec 08 12:00 AM -- 12:00 AM (PST) @

Hypothesis testing on point processes has several applications such as model fitting, plasticity detection, and non-stationarity detection. Standard tools for hypothesis testing include tests on mean firing rate and time varying rate function. However, these statistics do not fully describe a point process and thus the tests can be misleading. In this paper, we introduce a family of non-parametric divergence measures for hypothesis testing. We extend the traditional Kolmogorov--Smirnov and Cramer--von-Mises tests for point process via stratification. The proposed divergence measures compare the underlying probability structure and, thus, is zero if and only if the point processes are the same. This leads to a more robust test of hypothesis. We prove consistency and show that these measures can be efficiently estimated from data. We demonstrate an application of using the proposed divergence as a cost function to find optimally matched spike trains.

Author Information

Sohan Seth (University of Florida)
Il Memming Park (Stony Brook University)
Austin J Brockmeier (University of Florida)
Mulugeta Semework (SUNY Downstate Medical Center)
John S Choi (SUNY Downstate Medical Center and NYU-Poly)
Joseph T Francis (SUNY Downstate and NYU-Poly)
Jose C Principe (University of Florida at Gainesville)

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