Quantifying Statistical Interdependence by Message Passing on Graphs-Part I: One-Dimensional Point Processes
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Dauwels-2009-Quantifying Statistical Interdependence by Message Passing on Graphs-Part I.pdf
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Author(s)
Dauwels, Justin H. G.
Vialatte, F.
Cichocki, Andrzej
Weber, Theophane G.
Date Issued
August 2009
Journal
Neural Computation
Publisher
MIT Press
Citation
Dauwels, J. et al. “Quantifying Statistical Interdependence by Message Passing on Graphs—Part II: Multidimensional Point Processes.” Neural Computation 21.8 (2009): 2203-2268. ©2009 Massachusetts Institute of Technology.
Version
Final published version
Abstract
We present a novel approach to quantify the statistical interdependence
of two time series, referred to as stochastic event synchrony (SES). The
first step is to extract “events” from the two given time series. The next
step is to try to align events from one time series with events from the
other. The better the alignment, the more similar the two time series
are considered to be. More precisely, the similarity is quantified by the
following parameters: time delay, variance of the timing jitter, fraction of
noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical
inference. In particular, the SES parameters are computed by
maximum a posteriori (MAP) estimation, and the pairwise alignment
is obtained by applying the max-product algorithm. This letter deals
with one-dimensional point processes; the extension to multidimensional
point processes is considered in a companion letter in this issue.
By analyzing surrogate data, we demonstrate that SES is able to
quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated
by the Morris-Lecar neuron model are considered.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Operations Research Center
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