arXiv subjects

Maria De Iorio

Publications and source records attributed to Maria De Iorio.

At least 19 recordsLinked to original sources

arXiv2026

Similarity-Driven Proposals for MCMC Algorithms on Discrete Spaces

Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC methodology based upon similarity-driven proposals. Such proposals sway transitions towards states favored by the posterior via use of a data-driven measure of discrepancy between observations and the proposed model. Our approach can naturally cover classes of hierarchical models that involve both discrete variables and additional latent ones, without a requirement of integrating our the latter, in contrast to previous works in this field. The new algorithms are illustrated in simulation settings and in a involved real data scenario with a Dirichlet-Multinomial regression model.

stat.ME↗

arXiv2025

Latent Modularity in Multi-View Data

In this article, we consider the problem of clustering multi-view data, that is, information associated to individuals that form heterogeneous data sources (the views). We adopt a Bayesian model and in the prior structure we assume that each individual belongs to a baseline cluster and conditionally allow each individual in each view to potentially belong to different clusters than the baseline. We call such a structure ''latent modularity''. Then for each cluster, in each view we have a specific statistical model with an associated prior. We derive expressions for the marginal priors on the view-specific cluster labels and the associated partitions, giving several insights into our chosen prior structure. Using simple Markov chain Monte Carlo algorithms, we consider our model in a simulation study, along with a more detailed case study that requires several modeling innovations.

stat.ME↗

arXiv2025

Repulsive mixtures via the sparsity-inducing partition prior

We introduce a novel prior distribution for modelling the weights in mixture models based on a generalisation of the Dirichlet distribution, the Selberg Dirichlet distribution. This distribution contains a repulsive term, which naturally penalises values that lie close to each other on the simplex, thus encouraging few dominating clusters. The repulsive behaviour induces additional sparsity on the number of components. We refer to this construction as sparsity-inducing partition (SIP) prior. By highlighting differences with the conventional Dirichlet distribution, we present relevant properties of the SIP prior and demonstrate their implications across a variety of mixture models, including finite mixtures with a fixed or random number of components, as well as repulsive mixtures. We propose an efficient posterior sampling algorithm and validate our model through an extensive simulation study as well as an application to a biomedical dataset describing children's Body Mass Index and eating behaviour.

stat.ME↗

arXiv2025

Conditional partial exchangeability: a probabilistic framework for multi-view clustering

Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to accurately capture dependence structures and heterogeneity. In this setting, classical model-based clustering fails to account for within-subject dependence across domains. We introduce conditional partial exchangeability, a novel probabilistic paradigm for dependent random partitions of the same objects across distinct domains. Additionally, we study a wide class of Bayesian clustering models based on conditional partial exchangeability, which allows for flexible dependent clustering of individuals across features, capturing the specific contribution of each feature and the within-subject dependence, while ensuring computational feasibility.

stat.ME↗

arXiv2025

A Bayesian semi-parametric model for longitudinal growth and appetite phenotypes in children

This study develops a Bayesian semi-parametric model to examine the longitudinal growth and appetite phenotypes in children from the GUSTO cohort, with a focus on understanding the relationship between eating behaviours and growth outcomes over time. While eating behaviours, such as picky eating, have been shown to influence future weight and obesity risk, their developmental patterns and associations with growth trajectories remain under-explored. This work addresses these gaps by modelling longitudinal data, including both growth metrics (e.g., BMI) and eating behaviours (e.g., Child Eating Behaviour Questionnaire, CEBQ), across multiple time points. We extend the Partial Credit Model, commonly used for questionnaire data analysis, to accommodate repeated measurements and incorporate covariates. The growth outcomes are modelled using flexible splines regression. The two components of the model are linked through a shared Bayesian nonparametric prior distribution, specifically a Normalized Generalized Gamma process, allowing to identify clinically relevant subgroups. This joint modelling approach offers a more nuanced understanding of how early eating behaviours relate to growth patterns and developmental outcomes, providing insights into childhood obesity risk.

stat.ME↗

arXiv2025

Singularities in Bayesian Inference: Crucial or Overstated?

Over the past two decades, shrinkage priors have become increasingly popular, and many proposals can be found in the literature. These priors aim to shrink small effects to zero while maintaining true large effects. Horseshoe-type priors have been particularly successful in various applications, mainly due to their computational advantages. However, there is no clear guidance on choosing the most appropriate prior for a specific setting. In this work, we propose a framework that encompasses a large class of shrinkage distributions, including priors with and without a singularity at zero. By reframing such priors in the context of reliability theory and wealth distributions, we provide insights into the prior parameters and shrinkage properties. The paper's key contributions are based on studying the folded version of such distributions, which we refer to as the Gambel distribution. The Gambel can be rewritten as the ratio between a Generalised Gamma and a Generalised Beta of the second kind. This representation allows us to gain insights into the behaviours near the origin and along the tails, compute measures to compare their distributional properties, derive consistency results, devise MCMC schemes for posterior inference and ultimately provide guidance on the choice of the hyperparameters.

math.ST↗

arXiv2024

From Coin to Data: The Impact of Object Detection on Digital Numismatics

In this work we investigate the application of advanced object detection techniques to digital numismatics, focussing on the analysis of historical coins. Leveraging models such as Contrastive Language-Image Pre-training (CLIP), we develop a flexible framework for identifying and classifying specific coin features using both image and textual descriptions. By examining two distinct datasets, modern Russian coins featuring intricate "Saint George and the Dragon" designs and degraded 1st millennium AD Southeast Asian coins bearing Hindu-Buddhist symbols, we evaluate the efficacy of different detection algorithms in search and classification tasks. Our results demonstrate the superior performance of larger CLIP models in detecting complex imagery, while traditional methods excel in identifying simple geometric patterns. Additionally, we propose a statistical calibration mechanism to enhance the reliability of similarity scores in low-quality datasets. This work highlights the transformative potential of integrating state-of-the-art object detection into digital numismatics, enabling more scalable, precise, and efficient analysis of historical artifacts. These advancements pave the way for new methodologies in cultural heritage research, artefact provenance studies, and the detection of forgeries.

cs.CV↗

arXiv2024

Graph of Graphs: From Nodes to Supernodes in Graphical Models

High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data by representing variables as nodes and dependencies as edges. Inference is often focused on individual edges in the latent graph. Nonetheless, there is increasing interest in determining more complex structures, such as communities of nodes, for multiple reasons, including more effective information retrieval and better interpretability. In this work, we propose a hierarchical graphical model where we first cluster nodes and then, at the higher level, investigate the relationships among groups of nodes. Specifically, nodes are partitioned into supernodes with a data-coherent size-biased tessellation prior which combines ideas from Bayesian nonparametrics and Voronoi tessellations. This construct also allows accounting for the dependence of nodes within supernodes. At the higher level, dependence structure among supernodes is modeled through a Gaussian graphical model, where the focus of inference is on superedges. We provide theoretical justification for our modeling choices. We design tailored Markov chain Monte Carlo schemes, which also enable parallel computations. We demonstrate the effectiveness of our approach for large-scale structure learning in simulations and a transcriptomics application.

stat.ME↗

arXiv2024

The Multivariate Bernoulli detector: Change point estimation in discrete survival analysis

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffer from biased estimation. Therefore, we propose the Multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a Multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from non-conjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

stat.ME↗

arXiv2023

From Past to Future: Digital Methods Towards Artefact Analysis

Over the past two decades, Digital Humanities has transformed the landscape of humanities and social sciences, enabling advanced computational analysis and interpretation of extensive datasets. Notably, recent initiatives in Southeast Asia, particularly in Singapore, focus on categorising and archiving historical data such as artwork, literature and, most notably archaeological artefacts. This study illustrates the profound potential of Digital Humanities through the application of statistical methods on two distinct artefact datasets. Specifically, we present the results of an automated die study on mid-1st millennium AD "Rising Sun" coinage from mainland Southeast Asia, while subsequently utilising unsupervised statistical methods on 2D images of 13th-14th century earthenware ceramics excavated from the precolonial St. Andrew's Cathedral site in central Singapore. This research offers a comparative assessment showcasing the transformative impact of statistics-based approaches on the interpretation and analysis of diverse archaeological materials and within Digital Humanities overall.

stat.AP↗

arXiv2023

On a wider class of prior distributions for graphical models

Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of $\mathcal{G}_n$, the set of all graphs in $n$ vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of $\mathcal{G}_n$. In this paper, we study subsets that are vector subspaces with the cycle space $\mathcal{C}_n$ as main example. We propose a novel prior on $\mathcal{C}_n$ based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implement a Markov chain Monte Carlo algorithm, and show that (i) posterior edge inclusion estimates computed with our technique are comparable to estimates from the standard technique despite searching a smaller graph space, and (ii) the vector space perspective enables straightforward implementation of MCMC algorithms.

stat.ME↗

arXiv2023

Bayesian modelling of response to therapy and drug-sensitivity in acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a heterogeneous hematologic malignancy involving the abnormal proliferation of immature lymphocytes, accounting for most pediatric cancer cases. ALL management in children has seen great improvement in the last decades thanks to better understanding of the disease leading to improved treatment strategies evidenced through clinical trials. Commonly a first course of chemotherapy (induction phase) is administered, followed by treatment with a combination of anti-leukemia drugs. A measure of the efficacy early in the course of therapy is minimal residual disease (MRD). MRD quantifies residual tumor cells and indicates the effectiveness of the treatment over the course of therapy. MRD positivity is defined for values of MRD greater than 0.01%, yielding left-censored observations. We propose a Bayesian model to study the relationship between patient features and MRD observed at two time points during the induction phase. Specifically, we model the observed MRD values via an auto-regressive model, accounting for left-censoring of the data and for the fact that some patients are already in remission after the induction phase. Patient characteristics are included in the model via linear regression terms. In particular, patient-specific drug sensitivity based on ex-vivo assays of patient samples is exploited to identify groups of subjects with similar profiles. We include this information as a covariate in the model for MRD. We adopt horseshoe priors for the regression coefficients to perform variable selection to identify important covariates. We fit the proposed approach to data from three prospective pediatric ALL clinical trials carried out at the St. Jude Children's Research Hospital. Our results highlight that drug sensitivity profiles and leukemic subtypes play an important role in the response to induction therapy as measured by serial MRD measures.

stat.AP↗

arXiv2023

Repulsion, Chaos and Equilibrium in Mixture Models

Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior distributions for the weights and location parameters of the mixture. Widely used are Bayesian semi-parametric models based on mixtures with infinite or random number of components, such as Dirichlet process mixtures or mixtures with random number of components. Key in this context is the choice of the kernel for cluster identification. Despite their popularity, the flexibility of these models and prior distributions often does not translate into interpretability of the identified clusters. To overcome this issue, clustering methods based on repulsive mixtures have been recently proposed. The basic idea is to include a repulsive term in the prior distribution of the atoms of the mixture, which favours mixture locations far apart. This approach is increasingly popular and allows one to produce well-separated clusters, thus facilitating the interpretation of the results. However, the resulting models are usually not easy to handle due to the introduction of unknown normalising constants. Exploiting results from statistical mechanics, we propose in this work a novel class of repulsive prior distributions based on Gibbs measures. Specifically, we use Gibbs measures associated to joint distributions of eigenvalues of random matrices, which naturally possess a repulsive property. The proposed framework greatly simplifies the computations needed for the use of repulsive mixtures due to the availability of the normalising constant in closed form. We investigate theoretical properties of such class of prior distributions, and illustrate the novel class of priors and their properties, as well as their clustering performance, on benchmark datasets.

stat.ME↗

arXiv2023

Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud environments. Another concern is the identification of the bias and Monte Carlo error of produced averages. The above have prompted the recent development of fully ('embarrassingly') parallel unbiased Monte Carlo methodology based on coupling of MCMC algorithms. A caveat is that formulation of effective coupling is typically not trivial and requires model-specific technical effort. We propose coupling of MCMC chains deriving from sequential Monte Carlo (SMC) by considering adaptive SMC methods in combination with recent advances in unbiased estimation for state-space models. Coupling is then achieved at the SMC level and is, in principle, not problem-specific. The resulting methodology enjoys desirable theoretical properties. A central motivation is to extend unbiased MCMC to more challenging targets compared to the ones typically considered in the relevant literature. We illustrate the effectiveness of the algorithm via application to two complex statistical models: (i) horseshoe regression; (ii) Gaussian graphical models.

stat.CO↗

arXiv2023

The G-Wishart Weighted Proposal Algorithm: Efficient Posterior Computation for Gaussian Graphical Models

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the posterior distribution. However, posterior computation under the conjugate G-Wishart prior distribution on the precision matrix is expensive for general non-decomposable graphs. We therefore propose a new Markov chain Monte Carlo (MCMC) method named the G-Wishart weighted proposal algorithm (WWA). WWA's distinctive features include delayed acceptance MCMC, Gibbs updates for the precision matrix and an informed proposal distribution on the graph space that enables embarrassingly parallel computations. Compared to existing approaches, WWA reduces the frequency of the relatively expensive sampling from the G-Wishart distribution. This results in faster MCMC convergence, improved MCMC mixing and reduced computing time. Numerical studies on simulated and real data show that WWA provides a more efficient tool for posterior inference than competing state-of-the-art MCMC algorithms.

stat.CO↗

arXiv2023

Cohesion and Repulsion in Bayesian Distance Clustering

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of clusters. On the other hand, probabilistic model-based clustering techniques often fail to scale and devising algorithms that are able to effectively explore the posterior space is an open problem. Based on recent developments in Bayesian distance-based clustering, we propose a hybrid solution that entails defining a likelihood on pairwise distances between observations. The novelty of the approach consists in including both cohesion and repulsion terms in the likelihood, which allows for cluster identifiability. This implies that clusters are composed of objects which have small "dissimilarities" among themselves (cohesion) and similar dissimilarities to observations in other clusters (repulsion). We show how this modelling strategy has interesting connection with existing proposals in the literature as well as a decision-theoretic interpretation. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in a simulation study and an application in digital numismatics.

stat.ME↗

arXiv2023

Annealing Double-Head: An Architecture for Online Calibration of Deep Neural Networks

Model calibration, which is concerned with how frequently the model predicts correctly, not only plays a vital part in statistical model design, but also has substantial practical applications, such as optimal decision-making in the real world. However, it has been discovered that modern deep neural networks are generally poorly calibrated due to the overestimation (or underestimation) of predictive confidence, which is closely related to overfitting. In this paper, we propose Annealing Double-Head, a simple-to-implement but highly effective architecture for calibrating the DNN during training. To be precise, we construct an additional calibration head-a shallow neural network that typically has one latent layer-on top of the last latent layer in the normal model to map the logits to the aligned confidence. Furthermore, a simple Annealing technique that dynamically scales the logits by calibration head in training procedure is developed to improve its performance. Under both the in-distribution and distributional shift circumstances, we exhaustively evaluate our Annealing Double-Head architecture on multiple pairs of contemporary DNN architectures and vision and speech datasets. We demonstrate that our method achieves state-of-the-art model calibration performance without post-processing while simultaneously providing comparable predictive accuracy in comparison to other recently proposed calibration methods on a range of learning tasks.

stat.ML↗

arXiv2022

Bayesian Learning of Graph Substructures

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing interest in inferring more complex structures, such as communities, for multiple reasons, including more effective information retrieval and better interpretability. Stochastic blockmodels offer a powerful tool to detect such structure in a network. We thus propose to exploit advances in random graph theory and embed them within the graphical models framework. A consequence of this approach is the propagation of the uncertainty in graph estimation to large-scale structure learning. We consider Bayesian nonparametric stochastic blockmodels as priors on the graph. We extend such models to consider clique-based blocks and to multiple graph settings introducing a novel prior process based on a Dependent Dirichlet process. Moreover, we devise a tailored computation strategy of Bayes factors for block structure based on the Savage-Dickey ratio to test for presence of larger structure in a graph. We demonstrate our approach in simulations as well as on real data applications in finance and transcriptomics.

stat.ME↗