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"Assessing Granger non-causality using nonparametric measures of conditional independence" by Seth and Principe

In recent years, Granger causality has become a popular method in a variety of research areas including engineering, neuroscience, and economics. However, despite its simplicity and wide applicability the linear Granger causality is an insufficient tool for analyzing exotic stochastic processes such as process involving non-linear dynamics or process involving causality in higher order statistics. In order to analyze such processes more reliably, a different approach toward Granger causality has become increasingly popular. This new approach employs conditional independence as a tool to discover Granger non-causality without any assumption on the underlying stochastic process. This paper discusses the concept of discovering Granger non-causality using measures of conditional independence, and proposes a novel measure of conditional independence. In brief, the proposed approach estimates the conditional distribution function through a kernel based least square regression approach. The paper also explores the strengths and weaknesses of the proposed method compared to other available methods, and provides a detailed comparison of these methods using a variety of synthetic data sets.

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Matlab code

demo.m Run this file first
test.m Compare several methods
surrtest.m Surrogate test to detect causal connections
cm.m Cramer-von Mises statistic
hd.m Weighted Hellinger distance statistic
hsncic.m Hilbert-Schmidt normalized conditional independence criterion
mci.m Asymmetric quadratic measure of conditional independence
grammat.m Supporting file for generating Gram matrix with arbitrary kernel
dgp7700.m DGP for Experiment B
dgp7701.m DGP for Experiment E 
dgp7703.m DGP for Experiment F
dgp7704.m DGP for Experiment G
dgp7705.m DGP for Experiment H
dgp7706.m DGP for Experiment C
dgp7708.m DGP for Experiment D
dgp7709.m DGP for Experiment A

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"A test of Granger non-causality based on nonparametric conditional independence" by Seth and Principe

In this paper we describe a test of Granger noncausality from the perspective of a new measure of nonparametric conditional independence. We apply the proposed test on two synthetic nonlinear problems where linear Granger causality fails and show that the proposed method is able to derive the true causal connectivity effectively.

"A conditional distribution function based approach to design nonparametric tests of independence and conditional independence" by Seth and Principe

Measures of independence and conditional independence are two important statistical concepts that have found profound applications in engineering such as in feature selection and causality detection, respectively. Therefore, designing efficient ways, typically nonparametric, to estimate these measures has been an active research area in the last decade. In this paper, we propose a novel framework to test (conditional) independence, using the concept of conditional distribution function. Although, estimating conditional distribution function is a difficult task on its own, we show that the proposed measures can be estimated efficiently and actually can be expressed as the Frobenius norm of a matrix. We compare the proposed methods with other state-of-the-art techniques and show that they yield very promising results.

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