arXiv subjects

Laura Ferrini

Publications and source records attributed to Laura Ferrini.

2 recordsLinked to original sources

arXiv2026

Graphical model-based clustering of categorical data

Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel of a distribution characterizing a latent sub-group. Current methods developed within this framework employ multivariate distributions built under the assumption of independence among variables given the cluster allocation. Accordingly, possible dependence structures characterizing differences across groups are not directly accounted for during the clustering process. In this paper we consider multivariate categorical data, and introduce a model-based clustering method which employs graphical models as a tool to encode dependencies between variables. Specifically, we consider a Dirichlet Process mixture of categorical graphical models, which clusters individuals into groups that are homogeneous in terms of dependence (graphical) structure and allied parameters. We provide full Bayesian inference for the model and develop a Markov chain Monte Carlo scheme for posterior analysis. Our method is evaluated through simulations and applied to real case studies, including the analysis of genomic data and voting records. Results reveal the merits of a graphical model-based clustering, in comparison with approaches that do not explicitly account for dependencies in the multivariate distribution of variables.

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arXiv2024

Bayesian nonparametric mixtures of categorical directed graphs for heterogeneous causal inference

Quantifying causal effects of exposures on outcomes, such as a treatment and a disease respectively, is a crucial issue in medical science for the administration of effective therapies. Importantly, any related causal analysis should account for all those variables, e.g. clinical features, that can act as risk factors involved in the occurrence of a disease. In addition, the selection of targeted strategies for therapy administration requires to quantify such treatment effects at personalized level rather than at population level. We address these issues by proposing a methodology based on categorical Directed Acyclic Graphs (DAGs) which provide an effective tool to infer causal relationships and causal effects between variables. In addition, we account for population heterogeneity by considering a Dirichlet Process mixture of categorical DAGs, which clusters individuals into homogeneous groups characterized by common causal structures, dependence parameters and causal effects. We develop computational strategies for Bayesian posterior inference, from which a battery of causal effects at subject-specific level is recovered. Our methodology is evaluated through simulations and applied to a dataset of breast cancer patients to investigate cardiotoxic side effects that can be induced by the administrated anticancer therapies.

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