On Geometry of Information Flow for Causal Inference history

Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine learning experts, and scientists from many other fields. This video takes the perspective of information flow, which includes the Nobel prize winning work on Granger-causality, and the recently highly popular transfer entropy, these being probabilistic in nature. Authors main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy. They will describe the effective dimensionality of an underlying manifold as projected into the outcome space that summarizes information flow. Therefore, contrasting the probabilistic and geometric perspectives, authors will introduce a new measure of causal inference based on the fractal correlation dimension conditionally applied to competing explanations of future forecasts, which authors will write G e o C y x . This avoids some of the boundedness issues that they show exist for the transfer entropy, T y x . Authors will highlight our discussions with data developed from synthetic models of successively more complex nature: these include the Hénon map example, and finally a real physiological example relating breathing and heart rate function. 

This video is adapted from 10.3390/e22040396

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