Non-Uniform Embedding Scheme and Low-Dimensional Approximation Methods for Causality Detection.

Angeliki Papana

doi:10.3390/e22070745

Abstract

Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the “curse of dimensionality”, since the estimation relies on high-dimensional conditional mutual information (CMI) terms. Although the NUE scheme is a dimension reduction technique, the estimation of high-dimensional CMIs is still required. A possible solution is the utilization of low-dimensional approximation (LA) methods for the computation of CMIs. In this study, we aim to provide useful insights regarding the effectiveness of causality measures that rely on NUE and/or on LA methods. In a comparative study, three causality detection methods are evaluated, namely partial transfer entropy (PTE) defined using uniform embedding, PTE using the NUE scheme (PTENUE), and PTE utilizing both NUE and an LA method (LATE). Results from simulations on well known coupled systems suggest the superiority of PTENUE over the other two measures in identifying the true causal effects, having also the least computational cost. The effectiveness of PTENUE is also demonstrated in a real application, where insights are presented regarding the leading forces in financial data.

Highlights

Causality is the relationship between cause and effect
Reichenbach [2] postulated the principle of common cause, i.e., the dependence of two variables can be explained by at least one of the following cases: there is a unidirectional or bidirectional causation between the variables, or there exists a common cause of the two variables
In order to evaluate the effectiveness of the three causality measures in the case of weak couplings, we considered the chaotic system in K = 9 variables, while the coupling strength was fixed to c = 0.1

Summary

Introduction

Causality is the relationship between cause and effect. There is a causal relationship between two situations when it is certain that the second one arose due to the first one. The causal link is not mentioned exclusively in the relationship between two events or situations alone, but a causal chain may exist between causes and effects. The key component of causality is the succession of cause and effect. Reinchenbach [1] was the first to point out that the hypothesis of causality in real phenomena should be questioned and not taken a priori as granted. Reichenbach [2] postulated the principle of common cause, i.e., the dependence of two variables can be explained by at least one of the following cases: there is a unidirectional or bidirectional causation between the variables, or there exists a common cause of the two variables

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Conclusion