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In this work, we introduce a new methodology for inferring the interactionstructure of discrete valued time series which are Poisson distributed. Whilemost related methods are premised on continuous state stochastic processes, infact, discrete and counting event oriented stochastic process are natural andcommon, so called time-point processes (TPP). An important application that wefocus on here is gene expression. Nonparameteric methods such as the populark-nearest neighbors (KNN) are slow converging for discrete processes, and thusdata hungry. Now, with the new multi-variate Poisson estimator developed hereas the core computational engine, the causation entropy (CSE) principle,together with the associated greedy search algorithm optimal CSE (oCSE) allowsus to efficiently infer the true network structure for this class of stochasticprocesses that were previously not practical. We illustrate the power of ourmethod, first in benchmarking with synthetic datum, and then by inferring thegenetic factors network from a breast cancer micro-RNA (miRNA) sequence countdata set. We show the Poisson oCSE gives the best performance among the testedmethods anfmatlabd discovers previously known interactions on the breast cancerdata set.

Interaction Networks from Discrete Event Data by Poisson Multivariate  Mutual Information Estimation and Information Flow with Applications from  Gene Expression Data