Context-specific independencies in stratified chain regression graphical models

Abstract

Graphical models are a useful tool with increasing diffusion. In the categorical variable framework, they provide important visual support to understand the relationships among the considered variables. Besides, particular chain graphical models are suitable to represent multivariate regression models. However, the associated parameterization, such as marginal log-linear models, is often difficult to interpret when the number of variables increases because of a large number of parameters involved. On the contrary, conditional and marginal independencies reduce the number of parameters needed to represent the joint probability distribution of the variables. In compliance with the parsimonious principle, it is worthwhile to consider also the so-called context-specific independencies, which are conditional independencies holding for particular values of the variables in the conditioning set. In this work, we propose a particular chain graphical model able to represent these context-specific independencies through labeled arcs. We provide also the Markov properties able to describe marginal, conditional, and context-specific independencies from this new chain graph. Finally, we show the results in an application to a real data set.

Structural Learning of Simple Staged Trees

“…For this reason, extensions of BNs which formally account for non-symmetric conditional independences have been proposed (Boutilier et al, 1996;Cano et al, 2012;Chickering et al, 1997;DesJardins et al, 2008;Friedman and Goldszmidt, 1996;Geiger and Heckerman, 1996;Jaeger et al, 2006;Hyttinen et al, 2018;Pensar et al, 2015Pensar et al, , 2016Poole and Zhang, 2003;Salmerón et al, 2000) and there has been an increasing interest in formalizing the notion of non-symmetric independence (Corander et al, 2019;Nicolussi and Cazzaro, 2021;Shen et al, 2020;Tikka et al, 2019). With the exception of Jaeger et al (2006) and Pensar et al (2015), all the above-cited models somehow lose the intuitiveness of BNs since they cannot represent all the models' information into a unique graph.…”