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Register a new userInteraction Networks from Discrete Event Data by Poisson Multivariate Mutual Information Estimation and Information Flow with Applications from Gene Expression Data
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In this work, we introduce a new methodology for inferring the interaction structure of discrete valued time series which are Poisson distributed. While most related methods are premised on continuous state stochastic processes, in fact, discrete and counting event oriented stochastic process are natural and common, so called time-point processes (TPP). An important application that we focus on here is gene expression. Nonparameteric methods such as the popular k-nearest neighbors (KNN) are slow converging for discrete processes, and thus data hungry. Now, with the new multi-variate Poisson estimator developed here as the core computational engine, the causation entropy (CSE) principle, together with the associated greedy search algorithm optimal CSE (oCSE) allows us to efficiently infer the true network structure for this class of stochastic processes that were previously not practical. We illustrate the power of our method, first in benchmarking with synthetic datum, and then by inferring the genetic factors network from a breast cancer micro-RNA (miRNA) sequence count data set. We show the Poisson oCSE gives the best performance among the tested methods anfmatlabd discovers previously known interactions on the breast cancer data set.
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Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data.
Manual interpretation of data collected from drill holes for mineral or oil and gas exploration is time-consuming and subjective. Identification of geological boundaries and distinctive rock physical property domains is the first step of interpretation. We introduce a multivariate technique, that can identify geological boundaries from petrophysical or geochemical data. The method is based on time-series techniques that have been adapted to be applicable for detecting transitions in geological spatial data. This method allows for the use of multiple variables in detecting different lithological layers. Additionally, it reconstructs the phase space of a single drill-hole or well to be applicable for further investigations across other holes or wells. The computationally cheap method shows efficiency and accuracy in detecting boundaries between lithological layers, which we demonstrate using examples from mineral exploration boreholes and an offshore gas exploration well.
We train a neural network to predict chemical toxicity based on gene expression data. The input to the network is a full expression profile collected either in vitro from cultured cells or in vivo from live animals. The output is a set of fine grained predictions for the presence of a variety of pathological effects in treated animals. When trained on the Open TG-GATEs database it produces good results, outperforming classical models trained on the same data. This is a promising approach for efficiently screening chemicals for toxic effects, and for more accurately evaluating drug candidates based on preclinical data.
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good estimators provably do not exist. Kraskov et al. (PRE, 2004) introduced a successful mutual information estimation approach based on the statistics of distances between neighboring data points, which empirically works for a wide class of underlying probability distributions. Here we improve this estimator by (i) expanding its range of applicability, and by providing (ii) a self-consistent way of verifying the absence of bias, (iii) a method for estimation of its variance, and (iv) a criterion for choosing the values of the free parameter of the estimator. We demonstrate the performance of our estimator on synthetic data sets, as well as on neurophysiological and systems biology data sets.
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