We propose a new evolutionary approach for discovering causal rules in complex classification problems from batch data. Key aspects include (a) the use of a hypergeometric probability mass function as a principled statistic for assessing fitness that quantifies the probability that the observed association between a given clause and target class is due to chance, taking into account the size of the dataset, the amount of missing data, and the distribution of outcome categories, (b) tandem age-layered evolutionary algorithms for evolving parsimonious archives of conjunctive clauses, and disjunctions of these conjunctions, each of which have probabilistically significant associations with outcome classes, and (c) separate archive bins for clauses of different orders, with dynamically adjusted order-specific thresholds. The method is validated on majority-on and multiplexer benchmark problems exhibiting various combinations of heterogeneity, epistasis, overlap, noise in class associations, missing data, extraneous features, and imbalanced classes. We also validate on a more realistic synthetic genome dataset with heterogeneity, epistasis, extraneous features, and noise. In all synthetic epistatic benchmarks, we consistently recover the true causal rule sets used to generate the data. Finally, we discuss an application to a complex real-world survey dataset designed to inform possible ecohealth interventions for Chagas disease.

In complex adaptive systems, the topological properties of the interaction network are strong governing influences on the rate of flow of information throughout the system. For example, in epidemiological models, the structure of the underlying contact network has a pronounced impact on the rate of spread of infectious disease throughout a population. Similarly, in evolutionary systems, the topology of potential mating interactions (i.e., population structure) affects the rate of flow of genetic information and therefore affects selective pressure. One commonly employed method for quantifying selective pressure in evolutionary algorithms is through the analysis of the dynamics with which a single favorable mutation spreads throughout the population (a.k.a. takeover time analysis). While models of takeover dynamics have been previously derived for several specific regular population structures, these models lack generality. In contrast, so-called pair approximations have been touted as a general technique for rapidly approximating the flow of information in spatially structured populations with a constant (or nearly constant) degree of nodal connectivities, such as in epidemiological and ecological studies. In this work, we reformulate takeover time analysis in terms of the well-known Susceptible-Infectious-Susceptible model of disease spread and adapt the pair approximation for takeover dynamics. Our results show that the pair approximation, as originally formulated, is insufficient for approximating pre-equibilibrium dynamics, since it does not properly account for the interaction between the size and shape of the local neighborhood and the population size. After parameterizing the pair approximation to account for these influences, we demonstrate that the resulting pair approximation can serve as a general and rapid approximator for takeover dynamics on a variety of spatially-explicit regular interaction topologies with varying population sizes and varying uptake and reversion probabilities. Strengths, limitations, and potential applications of the pair approximation to evolutionary computation are discussed.