Graphical models for circular variables

TL;DR

This paper explores graphical models tailored for circular variables, analyzing three distributions and demonstrating their application in modeling protein dihedral angles to understand their conditional independence structures.

Contribution

It introduces graphical models for circular variables based on von Mises, Wrapped Normal, and Inverse Stereographic distributions, addressing a gap in existing probabilistic models.

Findings

Analyzed properties of three circular distributions regarding conditional independence.

Proposed suitable classes of graphical models for each distribution.

Applied models to protein structure data to illustrate usefulness.

Abstract

Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts and fields. However, models for studying the dependence/independence structure of circular variables are under-explored. This paper analyses three multivariate circular distributions, the von Mises, the Wrapped Normal and the Inverse Stereographic distributions, focusing on their properties concerning conditional independence. For each one of these distributions, we discuss the main properties related to conditional independence and introduce suitable classes of graphical models. The usefulness of the proposed models is shown by modelling the conditional independence among dihedral angles characterizing the three-dimensional structure of some proteins.