Michigan-style learning classifier systems (M-LCSs) represent an adaptive and powerful class of evolutionary algorithms which distribute the learned solution over a sizable population of rules. However their application to complex real world data mining problems, such as genetic association studies, has been limited. Traditional knowledge discovery strategies for M-LCS rule populations involve sorting and manual rule inspection. While this approach may be sufficient for simpler problems, the confounding influence of noise and the need to discriminate between predictive and non-predictive attributes calls for additional strategies. Additionally, tests of significance must be adapted to M-LCS analyses in order to make them a viable option within fields that require such analyses to assess confidence. In this work we introduce an M-LCS analysis pipeline that combines uniquely applied visualizations with objective statistical evaluation for the identification of predictive attributes, and reliable rule generalizations in noisy single-step data mining problems. This work considers an alternative paradigm for knowledge discovery in M-LCSs, shifting the focus from individual rules to a global, population-wide perspective. We demonstrate the efficacy of this pipeline applied to the identification of epistasis (i.e., attribute interaction) and heterogeneity in noisy simulated genetic association data.

No abstract

Background:The statistical genetics phenomenon of epistasis is widely acknowledged to confound disease etiology. In order to evaluate strategies for detecting these complex multi-locus disease associations, simulation studies are required. The development of the GAMETES software for the generation of complex genetic models, has provided the means to randomly generate an architecturally diverse population of epistatic models that are both pure and strict, i.e. all n loci, but no fewer, are predictive of phenotype. Previous theoretical work characterizing complex genetic models has yet to examine pure, strict, epistasis which should be the most challenging to detect. This study addresses three goals: (1) Classify and characterize pure, strict, two-locus epistatic models, (2) Investigate the effect of model 'architecture' on detection difficulty, and (3) Explore how adjusting GAMETES constraints influences diversity in the generated models.Results: In this study we utilized a geometric approach to classify pure, strict, two-locus epistatic models by "shape". In total, 33 unique shape symmetry classes were identified. Using a detection difficulty metric, we found that model shape was consistently a significant predictor of model detection difficulty. Additionally, after categorizing shape classes by the number of edges in their shape projections, we found that this edge number was also significantly predictive of detection difficulty. Analysis of constraints within GAMETES indicated that increasing model population size can expand model class coverage but does little to change the range of observed difficulty metric scores. A variable population prevalence significantly increased the range of observed difficulty metric scores and, for certain constraints, also improved model class coverage. Conclusions:These analyses further our theoretical understanding of epistatic relationships and uncover guidelines for the effective generation of complex models using GAMETES. Specifically, (1) we have characterized 33 shape classes by edge number, detection difficulty, and observed frequency (2) our results support the claim that model architecture directly influences detection difficulty, and (3) we found that GAMETES will generate a maximally diverse set of models with a variable population prevalence and a larger model population size. However, a model population size as small as 1,000 is likely to be sufficient.