Learning Staged Trees from Incomplete Data

TL;DR

This paper introduces novel algorithms for learning staged trees directly from incomplete data, effectively handling missingness patterns without prior data imputation, and demonstrates their practical feasibility.

Contribution

It presents the first algorithms for staged tree learning that incorporate missing data directly into the model estimation process.

Findings

Algorithms effectively handle various missing data patterns.

The expectation-maximization approach estimates models from incomplete data.

Computational experiments confirm the feasibility of the proposed methods.

Abstract

Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees from data, under the frequentist or Bayesian paradigm. They assume a data set has been observed fully and, in practice, observations with missing entries are either dropped or imputed before learning the model. Here, we introduce the first algorithms for staged trees that handle missingness within the learning of the model. To this end, we characterize the likelihood of staged tree models in the presence of missing data and discuss pseudo-likelihoods that approximate it. A structural expectation-maximization algorithm estimating the model directly from the full likelihood is also implemented and evaluated. A computational experiment showcases the performance of the novel learning algorithms, demonstrating that it is feasible to account for different missingness patterns when learning staged trees.