A Causal Map Without Intervention ✎

Original: "A Framework for Causal Discovery in non-intervenable systems"

· Peter Jan van Leeuwen, Michael DeCaria, Nachiketa Chakaborty, Manuel Pulido

arXiv:2010.02247 · 2020-10-05 · arXiv non-exclusive · independent analysis · 3 min

stat.ME cs.IR Information Theory Chaotic Dynamics

A new method decomposes cause-and-effect relationships in complex systems into direct and joint contributions, even when experiments are impossible.

An orchestra without a conductor plays in harmony, and you want to understand who influences whom. The violinist hears the cello, the cellist catches the rhythm of the percussion, and the flute adapts to everyone at once. In the science of complex systems, such as climate or the brain, there has long been no tool to decompose this interplay into individual contributions. The new method offers a causal map that shows both direct influences and joint effects, where several musicians together create something that would not exist alone.

Previously, causality was sought through experiments: pull one string and see what changes. But you cannot pull the atmosphere or a neural network. Graphical models linked factors in pairs, like notes in a chord, and missed that three notes together sound different from the sum of three separate sounds.

The authors of the method abandoned the usual entropy and introduced "confidence": a measure of how well we know the process when compared to a broad reference. The total mutual information between the target and all factors is decomposed into direct contributions of each factor and joint contributions of pairs, triples, and so on. To avoid counting the same thing twice, contributions of lower orders are subtracted from those of higher orders. The result is normalized by conditional confidence, which gives causal strength as a percentage and allows comparison across different studies.

Tests on the chaotic Lorenz system from 1963 revealed something unexpected: joint contributions turned out to be much stronger than direct ones. Knowing coordinates x and y together provides 9 times more information about the future of x than knowing x alone, even though the equation for x does not contain y. This means that the influence of y on x is not direct but through joint interaction with other variables. On El Niño data from 1979 to 2019, the method showed that the largest contribution to sea surface temperature comes from the heat content of the upper 300 meters, accounting for 25% of causal strength. Joint interactions amplify each factor's contribution roughly twofold compared to direct links.

The method also estimates the contribution of unknown processes. If part of the information about the target is not explained by known factors, that fraction is attributed to hidden forces, as in a concert where you hear another instrument but cannot see the musician.

This framework, for the first time, allows decomposing causal influence into all orders of interaction without interventions or additional data. It is a step from binary links to polyadic ones, where multiple causes act together. For atmospheric physics, oceanography, and other systems with strong feedback, this changes the ranking of factor importance: ignoring joint contributions can lead to incorrect conclusions. Now you can not only listen to the conductorless orchestra but also read its score.

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On the Lorenz 1963 model, the method showed that knowing coordinates x and y together gives 9 times more information about the future of x than knowing x alone, even though y does not appear in the equation for x.

Concepts

causality probabilistic model complex systems gaussian process drug discovery causal set theory probability theory pattern recognition neural network scientific discovery null hypothesis testing probabilistic forecast diagnosis classification clustering drug design network nonlinear laplacian spectral analysis granger causality bayesian evidence epidemic model

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A Causal Map Without Intervention ✎