  Data complexity analysis quantifies the hardness of constructing a predictive
model on a given dataset. However, the effectiveness of existing data
complexity measures can be challenged by the existence of irrelevant features
and feature interactions in biological micro-array data. We propose a novel
data complexity measure, depth, that leverages an evolutionary inspired feature
selection algorithm to quantify the complexity of micro-array data. By
examining feature subsets of varying sizes, the approach offers a novel
perspective on data complexity analysis. Unlike traditional metrics, depth is
robust to irrelevant features and effectively captures complexity stemming from
feature interactions. On synthetic micro-array data, depth outperforms existing
methods in robustness to irrelevant features and identifying complexity from
feature interactions. Applied to case-control genotype and gene-expression
micro-array datasets, the results reveal that a single feature of
gene-expression data can account for over 90% of the performance of
multi-feature model, confirming the adequacy of the commonly used
differentially expressed gene (DEG) feature selection method for the gene
expression data. Our study also demonstrates that constructing predictive
models for genotype data is harder than gene expression data. The results in
this paper provide evidence for the use of interpretable machine learning
algorithms on microarray data.
