An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems

Abstract

* Shared--first authorsCorresponding authors Author Contributions: HZ, NK and JT are responsible for the general design and conception. HZ and NK are responsible for data acquisition. HZ, NK, YD, FM, SE and AS contributed to data analysis. HZ developed the methodology, with key contributions from NK and JT. HZ undertook most of the numerical experiments, with YD and FM contributing. HZ, AS, GB and SE contributed the literature--based Th17 enrichment analysis. HZ and JT wrote the article, with key contributions from NK. Correspondence should be addressed to HZ: hector.zenil@algorithmicnaturelab.org and JT jesper.tegner@kaust.edu.saThe 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 to a general audience: https://youtu.be/ufzq2p5tVLI Abstract:We introduce a conceptual framework and an interventional calculus to steer, manipulate, and reconstruct the dynamics and generating mechanisms of non--linear dynamical systems from partial and disordered observations based on the contributions of each of the systems, by exploiting first principles from the theory of computability and algorithmic information. This calculus entails 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 for inferring causal relationships and formulating theoretical expectations from perturbation analysis. We find that the algorithmic information landscape of a system runs parallel to its dynamic attractor landscape, affording an avenue for moving systems on one plane so they can be controlled 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 approach yields a suite of universal parameter--free algorithms of wide applicability, ranging from the discovery of causality, 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 from Th17 cells, and the CellNet database). We highlight their ability to pinpoint key elements (genes) related to cell function and cell development, conforming to biological knowledge from experimentally validated data and the literature, and demonstrate how the method can reshape a system's dynamics in a controlled manner through algorithmic causal mechanisms.

Compression is Comprehension and the Unreasonable Effectiveness of Digital Computation in the Natural World

“…Equipped with the measures that we have developed, my team and I aim to tackle a fundamental challenge in science: that of developing tools for causal discovery [14,35]. This in order to unveil the design principles and generating mechanisms of arbitrary dynamic systems.…”

“…Determinism from classical mechanics implies that everything can be seen as a computer program and that the complexity of systems led purely by causal elements included in their description are dominated by their evolving time. This allows us to find clues to move systems between different functions, thereby effectively reprogramming them [35].…”

“…One could then discern the variation among the compressed outcomes for answers of varying complexity and assess the system's capabilities. The idea has evolved into a perturbation algorithmic calculus able to characterize artificial and biological systems [35,14].…”

Algorithmic Complexity and Reprogrammability of Chemical Structure Networks

“…For this approach we will use the techniques and methods developed in [33,31]. The basic idea is to estimate the likelihood of similarity between compounds based on an induced partition of possible common underlying mechanisms (models are found by an exhaustive algorithm that explains small pieces of the data).…”

“…In this sense, a causal path is a path where the changes between one state and another is merely the product of an underlying dynamical system following its normal course, sans external intervention [31].…”