Symbolic Regression of Dynamic Network Models
Govind Gandhi
Growing interest in modelling complex systems from brains to societies to
cities using networks has led to increased efforts to describe generative
processes that explain those networks. Recent successes in machine learning
have prompted the usage of evolutionary computation, especially genetic
programming to evolve computer programs that effectively forage a
multidimensional search space to iteratively find better solutions that explain
network structure. Symbolic regression contributes to these approaches by
replicating network morphologies using both structure and processes, all while
not relying on the scientists intuition or expertise. It distinguishes itself
by introducing a novel formulation of a network generator and a parameter-free
fitness function to evaluate the generated network and is found to consistently
retrieve synthetically generated growth processes as well as simple,
interpretable rules for a range of empirical networks. We extend this approach
by modifying generator semantics to create and retrieve rules for time-varying
networks. Lexicon to study networks created dynamically in multiple stages is
introduced. The framework was improved using methods from the genetic
programming toolkit (recombination) and computational improvements (using
heuristic distance measures) and used to test the consistency and robustness of
the upgrades to the semantics using synthetically generated networks. Using
recombination was found to improve retrieval rate and fitness of the solutions.
The framework was then used on three empirical datasets - subway networks of
major cities, regions of street networks and semantic co-occurrence networks of
literature in Artificial Intelligence to illustrate the possibility of
obtaining interpretable, decentralised growth processes from complex networks.