The Topology of a Family Tree Graph and Its Members' Satisfaction with One Another: A Machine Learning Approach

TL;DR

The paper addresses whether the topology of a family tree can predict how members rate each other’s satisfaction. It introduces a two-stage pipeline that encodes topology via a Variational Graph AutoEncoder into a $16$-dimensional vector and then uses a TPOT-driven regression to predict $EFS$ and $NFS$, demonstrating strong predictive performance on $N=486$ families. Key contributions include formalizing topology-based prediction for $EFS$ and $NFS$, showing substantial gains over traditional feature-based baselines, and providing a reproducible framework for topology-centric analysis in family studies. The findings suggest that graph topology alone carries significant information about family satisfaction, with practical implications for targeted interventions and future explainability research.

Abstract

Family members' satisfaction with one another is central to creating healthy and supportive family environments. In this work, we propose and implement a novel computational technique aimed at exploring the possible relationship between the topology of a given family tree graph and its members' satisfaction with one another. Through an extensive empirical evaluation ($N=486$ families), we show that the proposed technique brings about highly accurate results in predicting family members' satisfaction with one another based solely on the family graph's topology. Furthermore, the results indicate that our technique favorably compares to baseline regression models which rely on established features associated with family members' satisfaction with one another in prior literature.

Figures (3)

• Figure 1: A schematic view of the proposed technique. The family tree graph is first converted by the VGAE model into a representative feature vector. In parallel, the satisfaction matrix is used for computing the family satisfaction measures of interest (e.g., the EFS and NFS measures). The extended feature vectors, now including the target variables, are then used as input to an optimization tool aimed at finding an optional regression model $R$.
• Figure 2: A schematic view of the empirical study's workflow.
• Figure 3: A comparison of the four models in question: $R_{l},R_{nl},B_{l}$ and $B_{nl}$ using scatter plots. The x-axis represents the actual values, and the y-axis represents the predicted values. Ideally, if the predictions are perfect, the points will lie along a straight solid black line with a slope of 1. Each sub-figure denotes the prediction made by one specific model captioned by its name, Mean Average Error (MEA, the lower - the better), and its determination of coefficients ($R^2$, the higher - the better), respectively. The top row presents the results using the EFS measure and the bottom row represents the results using the NFS measure. The gray dashed line indicates the linear regression fitting on the scatter points.