Algebraic model selection and experimental design in biological data science (Q2665755)

The authors of the paper under review propose a computational framework as a data-driven approach for systematic and efficient experimental design and model selection as one process rather than independent steps in the data science pipeline. Contrary to the approaches using Groebner bases for handling data from unspecified distributions and nonlinear models developed so far, the authors propose a method for deleting redundant information (and thus reducing the model space) which relies on an equivalence relation on data sets based on affine transformation called linear shifts. To facilitate linking design of experiments and model selection, they built a database of all annotated equivalence classes of input data sets consisting of \(m\) points in \(\mathbb{F}_p^n\) (\(p\) a prime number) for the cases \(p=2\), \(2 \leq n \leq 4\), and \(1 \leq m \leq p^n\); and for the cases \(p=3\), \( n =2\), and \(1 \leq m \leq p^n\). As application, the authors give examples illustrating their two guiding questions, namely, given a known interaction, knowing which experiments/data identify the interaction, and, given a set of data corresponding to experimental conditions, knowing what interactions are identifiable.