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Who Influences Whom in the Orchestra ✎

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 · 1 min
stat.ME cs.IR Information Theory Chaotic Dynamics
Scientists have found a way to disentangle the influences of factors on each other, 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 from the percussion, and the flute adjusts to everyone at once. In the past, scientists could only pull strings in experiments, but you cannot pull strings on the atmosphere or the brain. The new method measures the influence of each factor on another, as if we had recorded the sound of each instrument separately and then summed their contributions.

The method introduces "confidence": how well we know a process. The total information about a target is decomposed into direct contributions from each factor and joint contributions from pairs, triples, and so on. To avoid double counting, smaller contributions are subtracted from larger ones.

Tests on El Niño data showed that the heat content of the upper 300 meters of the ocean contributes 25% of the causal force to surface temperature. Joint interactions amplify each factor's contribution roughly twofold. The method also estimates the contribution of unknown processes: as if another instrument were heard in the orchestra, but the musician were invisible. Now we can not only listen to the 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.

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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