Staged tree models with toric structure
arXiv:2107.04516 · doi:10.1016/j.jsc.2022.04.006
Abstract
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety. For certain trees, called balanced, the model is in fact the intersection of the toric variety and the probability simplex. This gives the model a straightforward description, and has computational advantages. In this paper we show that the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. It is an open problem whether all staged tree models have toric structure.
References in corpus (9)
- On the toric algebra of graphical models
- Maximum likelihood estimation in log-linear models
- Equations defining probability tree models
- Algorithms for Causal Reasoning in Probability Trees
- Gröbner bases for staged trees
- Representation of Context-Specific Causal Models with Observational and Interventional Data
- The R Package stagedtrees for Structural Learning of Stratified Staged Trees
- Context-Specific Causal Discovery for Categorical Data Using Staged Trees
- The curved exponential family of a staged tree