He Q, Dimitrova ES, Stigler B, Zhang A. Geometric Characterization of Data Sets with Unique Reduced Gröbner Bases.
Bull Math Biol 2019;
81:2691-2705. [PMID:
31256302 DOI:
10.1007/s11538-019-00624-x]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2018] [Accepted: 05/27/2019] [Indexed: 11/24/2022]
Abstract
Model selection based on experimental data is an important challenge in biological data science. Particularly when collecting data is expensive or time-consuming, as it is often the case with clinical trial and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models. We identify geometric properties of input data that result in an unique algebraic model, and we show that if the data form a staircase, or a so-called linear shift of a staircase, the ideal of the points has a unique reduced Gröbner basis and thus corresponds to a unique model. We use linear shifts to partition data into equivalence classes with the same basis. We demonstrate the utility of the results by applying them to a Boolean model of the well-studied lac operon in E. coli.
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