Discovery of statistical equivalence classes using computer algebra
Christiane Görgen, Anna Bigatti, Eva Riccomagno, and Jim Q. Smith
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Submission date: 26. May. 2017
published in: International journal of approximate reasoning, 95 (2018), p. 167-184
DOI number (of the published article): 10.1016/j.ijar.2018.01.003
Keywords and phrases: graphical models, staged tree models, computer algebra, ideal decomposition, algebraic statistics
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Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the primary decom- position of monomial ideals associated with an interpolating polynomial to quickly compute all nested representations of that polynomial. It hereby determines an im- portant subclass of all trees representing the same statistical model. To illustrate this method we analyze the full polynomial equivalence class of a staged tree repre- senting the best fitting model inferred from a real-world dataset.