Advances in Statistical Modelling for Complex Data: Two Perspectives

Dott. Matteo FONTANA (Assistant Professor of Statistics)

Dott. Matteo VENTURA  (Research Associate of Statistics)

Department of Statistical sciences, Università Cattolica del Sacro Cuore

Abstract

Part I – Matteo Fontana  (A Conformal Prediction Approach to Predict Populations of Graphs)
Uncertainty quantification for populations of graph-valued data remains largely unexplored. Although many methods exist for predicting graphs, techniques for assessing the uncertainty of such predictions are scarce. We propose a conformal prediction framework that constructs prediction regions for both labelled graphs, in which nodes correspond across observations, and unlabelled graphs, in which no such correspondence exists.
For unlabelled graphs, the prediction regions are defined in a discrete quotient metric space, referred to as graph space. The approach is model-free and requires no distributional assumptions. It attains finite-sample validity and yields component-wise interpretable prediction regions shaped as parallelotopes. In addition, a length modulation mechanism accounts for the local variability of individual edge or node attributes.
The theoretical properties and empirical performance of the framework are assessed through two simulation studies, covering labelled and unlabelled graphs respectively. The practical utility of the method is then demonstrated on a real-world dataset of player passing networks from the 2018 FIFA World Cup. This application shows how the framework can be used to analyze network topology and to quantify the uncertainty of predictions for football teams.

Part II – Matteo Ventura (Model-based clustering for rating data: Accounting for dependence and response styles)
Survey rating data are central to many scientific fields, yet their effective analysis requires accounting for complex latent mechanisms, such as respondent preferences, uncertainty, and systematic response styles. We present a model-based clustering framework for rating data, showing how latent class structures can be used to group respondents according to their underlying profiles and how the framework can be extended to accommodate real-world complexities. Specifically, we discuss how copula functions can relax the assumption of local independence, how suitable distributional assumptions can account for response styles, and how pairwise likelihood methods make copula estimation computationally feasible.