# Discovery of statistical equivalence classes using computer algebra

## TL;DR

This paper introduces a novel algorithm leveraging computer algebra to identify all nested representations of interpolating polynomials in discrete statistical models, enabling efficient discovery of equivalence classes of event trees.

## Contribution

It presents a new method using primary decomposition of monomial ideals to compute all nested representations of interpolating polynomials in statistical models.

## Key findings

- Identifies all nested representations of a polynomial in polynomial time.
- Analyzes the equivalence class of a real-world staged tree model.
- Demonstrates the method on a dataset fitting scenario.

## Abstract

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 decomposition of monomial ideals associated with an interpolating polynomial to quickly compute all nested representations of that polynomial. It hereby determines an important subclass of all trees representing the same statistical model. To illustrate this method we analyze the full polynomial equivalence class of a staged tree representing the best fitting model inferred from a real-world dataset.