[Paper Review] The R Package stagedtrees for Structural Learning of Stratified Staged Trees

Federico Carli, Manuele Leonelli+2 more|arXiv (Cornell University)|Apr 14, 2020

Bayesian Modeling and Causal Inference4 citations

TL;DR

The paper introduces the R package stagedtrees, which implements score-based and clustering-based algorithms for structural learning of stratified staged trees and chain event graphs from data. It enables model visualization, inference, and comparison, with empirical validation on the Titanic dataset showing that hill-climbing-based learning outperforms distance-based clustering in model fit according to AIC and BIC criteria.

ABSTRACT

stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets both included in the package or bundled in R.

Motivation & Objective

• To develop a comprehensive R package for learning the structure of staged trees and chain event graphs from data.
• To provide researchers with tools for visualizing, inferring, and comparing staged tree models.
• To support structural learning using both score-based (e.g., hill-climbing) and clustering-based (e.g., agglomerative hierarchical) algorithms.
• To enable integration with existing Bayesian network tools, such as bnlearn, by translating BNs into staged trees.
• To offer model selection criteria (AIC, BIC) for evaluating and comparing learned models.

Proposed method

• Implement score-based structural learning via hill-climbing (stages_hc) and backward selection (stages_bj) algorithms to optimize model fit.
• Integrate clustering-based learning using agglomerative hierarchical clustering (stages_ahc) to group vertices into stages based on edge label similarity.
• Provide functions to convert Bayesian networks (from bnlearn) into staged trees using the as_sevt function.
• Support model visualization through plotting functions with options to display stage labels, node sizes, and path probabilities.
• Enable model comparison using the compare_stages function, which identifies discrepancies in stage structures between two models.
• Implement model evaluation using AIC and BIC criteria to select the best-fitting model among competing structures.

Experimental results

Research questions

• RQ1 How can staged trees and chain event graphs be effectively learned from discrete data using score-based and clustering-based algorithms?
• RQ2 What is the performance difference between hill-climbing and distance-based clustering algorithms in learning staged tree structures?
• RQ3 How can Bayesian networks be systematically translated into staged tree representations for enhanced modeling of context-specific conditional independence?
• RQ4 To what extent do model selection criteria like AIC and BIC help identify the optimal staged tree structure?
• RQ5 Can the stagedtrees package support iterative refinement of learned models through re-staging and re-estimation?

Key findings

• The stagedtrees package successfully implements structural learning algorithms for staged trees and chain event graphs, with support for model visualization and inference.
• The hill-climbing algorithm (stages_hc) produced the best model fit among tested methods, as indicated by the lowest AIC (10364.49) and BIC (10449.94) values on the Titanic dataset.
• The clustering-based algorithm (stages_bj) yielded the worst BIC score (10475.82), confirming that it is less optimal for model selection despite being computationally efficient.
• Model comparison using compare_stages revealed that mod1 and mod3 differ significantly in stage structure over the Age variable, despite similar staging for Sex and Survived.
• The package enables seamless conversion of bnlearn Bayesian networks into staged trees, allowing for richer modeling of context-specific independence.
• The stagedtrees package is freely available on CRAN and includes two built-in datasets for demonstration and validation.