Abstract
We introduce a conceptual framework and an interventional calculus to steer, manipulate, reconstruct the dynamics and generating mechanisms of dynamical systems from partial and disordered observations based on the contribution of each of the system’s by exploiting first principles from the theory of computability and algorithmic information. This calculus consists in finding and applying controlled interventions to an evolving object to estimate how its algorithmic information content is affected in terms of positive or negative shifts towards and away from randomness in connection to causation. The approach is an alternative to statistical approaches to infer causal relationships and to provide theoretical expectations from perturbation analysis. We find that the algorithmic information landscape of a system’s runs in parallel to its dynamic landscape providing a path to move systems on one plane to have controlled effects on the other plane. Based on these methods, we advance tools for reprogramming a system that do not require full knowledge or access to the system’s actual kinetic equations or to probability distributions. This new dimension provides a suite of powerful parameter-free algorithms of wide applicability ranging from causal discovery, dimension reduction, feature selection, model generation, a maximal algorithmic-randomness principle and a system’s (re)programmability index. We apply these methods to static (e.coli Transcription Factor network) and to evolving genetic regulatory networks (differentiating naïve to Th17 cell, and the CellNet database). We show the capabilities to pinpoint key elements (genes) related to cell function and cell development conforming with the biological knowledge from experimentally validated data and the literature demonstrating how the method can reshape a system’s dynamics in a controlled manner through algorithmic causal mechanisms.
Footnotes
↵* Shared-first authors
The Online Algorithmic Complexity Calculator implements the perturbation analysis method introduced in this paper: http://complexitycalculator.com/ and an online animated video explains some of the basic concepts and motivations for general understanding: https://youtu.be/ufzq2p5tVLI