Differentiating Granger Causal Influence and Stimulus-Related Information Flow
Information flow is becoming an increasingly popular term in the context of understanding neural circuitry, both in neuroscience and in Artificial Neural Networks. Granger causality has long been the tool of choice in the neuroscience literature for identifying functional connectivity in the brain, i.e., pathways along which information flows. However, there has been relatively little work on providing a fundamental theory for information flow, and as part of that, understanding whether Granger causality captures the intuitive direction of information flow in a computational circuit. Recently, Venkatesh et al. [2019] proposed a theoretical framework for identifying stimulus-related information paths in a computational graph. They also provided a counterexample showing that the direction of greater Granger causal influence can be opposite to that of information flow [Venkatesh and Grover, 2015]. Here, we reexamine and expand on this counterexample. In particular, we find that Granger Causal influence can be statistically insignificant in the direction of information flow, while being significant in the opposite direction. By examining the mutual- (and conditional-mutual-) information that each signal shares with the stimulus, we are able to gain a more nuanced understanding of the actual information flows in this system.
Code (0)
등록된 구현이 없습니다.
Tasks
Functional ConnectivitySimilar Papers 제목 키워드 기반
Collective behavior of stock prices in the time of crisis as a response to the external stimulus
We analyze the interaction between stock prices of big companies in the USA and Germany using Granger Causality. We claim that the increase in pair-wise Granger causality interaction between prices in the times of crisis…
Variable-lag Granger Causality for Time Series Analysis
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that e…
Causal InferenceLeadership InferenceTime SeriesTime Series AnalysisVariable-lag Granger Causality and Transfer Entropy for Time Series Analysis
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that e…
Causal InferenceDynamic Time WarpingLeadership InferenceTime Series+1Local Granger Causality
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed …
Gaussian ProcessesMulti-Band Variable-Lag Granger Causality: A Unified Framework for Causal Time Series Inference across Frequencies
Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality i…