Abordagens da teoria da informação para análise de causalidade e conectividade em processos contínuos.

Abstract

Information theory consolidates a mathematical approach to measure the causal influ- ence among multivariate time series. Although the concepts in information theory are relatively simple and mathematical formulations are objective, in practice, their estima- tion can be a complex process, since the estimators have few or none knowledge about the statistical properties of the stochastic processes. Currently, some of the areas with application of information measures are: economics, neuroscience, biomedical diagnosis, connectivity detection in industrial process. In this dissertation, a method is proposed for characterization of effective support for the applicability of the supervised learning method, Support Vector Machine (SVM), in estimation of entropy of continuous random variables. This method provides asymptotically good results when compared to analytical values and values estimated from histogram techniques, kernel smoothing and distances of nearest neighbors. In addition, we discuss the use of transfer entropy, estimated from the estimator based on distances between nearest neighbors, as an assist in the biomedical diagnosis in cases of brain lesions and in the detection of connectivity in a system with four tanks.