Spatio-temporal causality provides data-specific optimization of information modeling

Causality, arguably, lies at the very heart of the scientific method. It not only links dependent information to one another, but does so with directionality, with a particular ordering. Commonly delineated by the arrow of time, understanding a system’s causality is often key to making the best possible predictions, whether it be how ocean dynamics affect atmospheric temperatures or how concentrations of prey drive their predators’ behavior.

From the informational perspective, authors report in Chaos how the temporal description of causality gives rise to another spatio-temporal definition that can offer more efficient ways of calculating information flow. By exploiting both the time and space nature of causality, they rigorously quantify the flow of information and its direction. They also provide a colorful dynamical visualization of how information is de facto transmitted.

The additional spatio-temporal description provides a way to break the symmetry in probability space for the possible states of some “first” and “second” causally linked variables. The causal information and its direction, quantified by the transfer entropy, are calculated from a new, simpler quantifier of the variables’ mutual information on this nonsymmetric probabilistic space.

The model clarifies that the flow and directionality of information is intrinsically connected to the predictability of past and future states of the observed variables with different spatio-temporal configurations. With higher resolution measurements in the second variable — or equivalently, a longer time series — than the first variable reveals its past states, the information flows from the first to the second variable. Conversely, measuring the first with higher resolution tests the information, if any, flowing in the opposite direction.

Co-author Murilo Baptista points out that this spatio-temporal character of causality can be useful for real-world demands like having access to only a few high resolution data points, or a long-time series of low resolution data points.

Source: “Space-time nature of causality,” by Ezequiel Bianco Martinez and Murilo S. Baptista, Chaos: An Interdisciplinary Journal of Nonlinear Science (2018). The article can be accessed at https://doi.org/10.1063/1.5019917 .