This repository provides an implementation for examining whether complex dynamical systems host macroscopic processes that exhibit information closure, via assessing the lumpability of their causal states.
lump_library.pyis a library of functions to generate epsilon-machines, lump them, evaluate their information-theoretic properties, and generate null models.
lump_synthetic.ipynbshows application to toy systems.lump_empirical.ipynbshows application to fMRI data from 100 unrelated subjects from the Human Connectome Project, using thee_lump.pyscript.
Note: This package contains a lightly edited copy of the CoMaC library for Markov aggregation.
If you use this code in your research, kindly cite:
- Rosas et al (2024) Software in the natural world: A computational approach to hierarchical emergence. arXiv.
- Steger et al (2022) Semi-Supervised Clustering via Information-Theoretic Markov Chain Aggregation. arXiv.
- Crutchfield & Young (1989) Inferring statistical complexity. PRL.