arXiv subjects

Beatrice Franzolini

Publications and source records attributed to Beatrice Franzolini.

14 recordsLinked to original sources

arXiv2026

Laplace and skew-Laplace approximations for Dirichlet process mixture posterior density

Posterior inference for Dirichlet process mixture models is analytically intractable and typically relies on Markov chain Monte Carlo methods, which can become computationally prohibitive at moderate to large sample sizes. In this work, we investigate the performance of Laplace and skew-Laplace posterior approximations for density estimation in this setting. Through an extensive numerical study covering four simulation scenarios with sample sizes ranging from n = 20 to n = 2,000 and four standard real datasets, we compare the standard Laplace approximation, its skew-corrected extension, and a slice sampling benchmark, assessing accuracy through total variation distance and computational efficiency through runtime. Our results show that the Gaussian Laplace approximation is more effective in this setting than might be anticipated, and that the skew-Laplace approximation consistently improves posterior recovery while remaining substantially faster than state-of-the-art Markov chain Monte Carlo samplers across all settings considered. In particular, the use of skew-Laplace in place of the standard Laplace approximation is especially beneficial in more complex density structures, where we observe error reductions typically on the order of 30%.

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arXiv2026

Complexity bounds for Dirichlet process slice samplers

Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relatively to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, superlinear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP-based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.

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arXiv2025

Multivariate Species Sampling Models

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of probabilistic invariance, making partial exchangeability a natural choice. Countless models for partially exchangeable data, collectively known as dependent nonparametric priors, have been proposed. These include hierarchical, nested and additive processes, widely used in statistics and machine learning. Still, a unifying framework is lacking and key questions about their underlying learning mechanisms remain unanswered. We fill this gap by introducing multivariate species sampling models, a new general class of nonparametric priors that encompasses most existing finite- and infinite-dimensional dependent processes. They are characterized by the induced partially exchangeable partition probability function encoding their multivariate clustering structure. We establish their core distributional properties and analyze their dependence structure, demonstrating that borrowing of information across groups is entirely determined by shared ties. This provides new insights into the underlying learning mechanisms, offering, for instance, a principled rationale for the previously unexplained correlation structure observed in existing models. Beyond providing a cohesive theoretical foundation, our approach serves as a constructive tool for developing new models and opens novel research directions for capturing richer dependence structures beyond the framework of multivariate species sampling processes.

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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.

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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.

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arXiv2024

Scalable expectation propagation for generalized linear models

Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution has motivated the development of deterministic approximations, which are generally more scalable than sampling techniques. Among them, expectation propagation (EP) showed extreme accuracy, usually higher than many variational Bayes solutions. However, the higher computational cost of EP posed concerns about its practical feasibility, especially in high-dimensional settings. We address these concerns by deriving a novel efficient formulation of EP for GLMs, whose cost scales linearly in the number of covariates p. This reduces the state-of-the-art O(p^2 n) per-iteration computational cost of the EP routine for GLMs to O(p n min{p,n}), with n being the sample size. We also show that, for binary models and log-linear GLMs approximate predictive means can be obtained at no additional cost. To preserve efficient moment matching for count data, we propose employing a combination of log-normal Laplace transform approximations, avoiding numerical integration. These novel results open the possibility of employing EP in settings that were believed to be practically impossible. Improvements over state-of-the-art approaches are illustrated both for simulated and real data. The efficient EP implementation is available at https://github.com/niccoloanceschi/EPglm.

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arXiv2023

Nonparametric priors with full-range borrowing of information

Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals allow only for non-negative correlations. We derive a new class of dependent nonparametric priors that can induce correlations of any sign, thus introducing a new and more flexible idea of borrowing of information. This is achieved thanks to a novel concept, which we term hyper-tie, and represents a direct and simple measure of dependence. We investigate prior and posterior distributional properties of the model and develop algorithms to perform posterior inference. Illustrative examples on simulated and real data show that our proposal outperforms alternatives in terms of prediction and clustering.

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arXiv2023

Efficient expectation propagation for posterior approximation in high-dimensional probit models

Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression under a multivariate Gaussian prior distribution. Adapting more general derivations in Anceschi et al. (2023), we show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine having a per-iteration cost that scales linearly in the number of covariates. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.

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arXiv2023

Efficient computation of predictive probabilities in probit models via expectation propagation

Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we focus on the computation of predictive probabilities in Bayesian probit models via expectation propagation (EP). Leveraging more general results in recent literature, we show that such predictive probabilities admit a closed-form expression. Improvements over state-of-the-art approaches are shown in a simulation study.

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arXiv2023

Entropy regularization in probabilistic clustering

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters and a large number of sparsely-populated ones. This feature translates into results that are often uninterpretable unless we accept to ignore a relevant number of observations and clusters. Interpreting the posterior distribution as penalized likelihood, we show how the unbalance can be explained as a direct consequence of the cost functions involved in estimating the partition. In light of our findings, we propose a novel Bayesian estimator of the clustering configuration. The proposed estimator is equivalent to a post-processing procedure that reduces the number of sparsely-populated clusters and enhances interpretability. The procedure takes the form of entropy-regularization of the Bayesian estimate. While being computationally convenient with respect to alternative strategies, it is also theoretically justified as a correction to the Bayesian loss function used for point estimation and, as such, can be applied to any posterior distribution of clusters, regardless of the specific model used.

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arXiv2023

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.

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arXiv2022

Bayesian clustering of multiple zero-inflated outcomes

Several applications involving counts present a large proportion of zeros (excess-of-zeros data). A popular model for such data is the Hurdle model, which explicitly models the probability of a zero count, while assuming a sampling distribution on the positive integers. We consider data from multiple count processes. In this context, it is of interest to study the patterns of counts and cluster the subjects accordingly. We introduce a novel Bayesian nonparametric approach to cluster multiple, possibly related, zero-inflated processes. We propose a joint model for zero-inflated counts, specifying a Hurdle model for each process with a shifted Negative Binomial sampling distribution. Conditionally on the model parameters, the different processes are assumed independent, leading to a substantial reduction in the number of parameters as compared to traditional multivariate approaches. The subject-specific probabilities of zero-inflation and the parameters of the sampling distribution are flexibly modelled via an enriched finite mixture with random number of components. This induces a two-level clustering of the subjects based on the zero/non-zero patterns (outer clustering) and on the sampling distribution (inner clustering). Posterior inference is performed through tailored MCMC schemes. We demonstrate the proposed approach on an application involving the use of the messaging service WhatsApp.

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arXiv2022

Change point detection in dynamic Gaussian graphical models: the impact of COVID-19 pandemic on the US stock market

Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US industry stock portfolios, over a time horizon that covers the COVID-19 pandemic. The selected stocks give a comprehensive picture of the US stock market. To this end, we develop a Bayesian multivariate stochastic volatility model based on a time-varying sequence of graphs capturing the evolution of the dependence structure. The model builds on the Gaussian graphical models and the random change points literature. In particular, we treat the number, the position of change points, and the graphs as object of posterior inference, allowing for sparsity in graph recovery and change point detection. The high dimension of the parameter space poses complex computational challenges. However, the model admits a hidden Markov model formulation. This leads to the development of an efficient computational strategy, based on a combination of sequential Monte-Carlo and Markov chain Monte-Carlo techniques. Model and computational development are widely applicable, beyond the scope of the application of interest in this work.

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arXiv2022

Model Selection for Maternal Hypertensive Disorders with Symmetric Hierarchical Dirichlet Processes

Hypertensive disorders of pregnancy occur in about 10% of pregnant women around the world. Though there is evidence that hypertension impacts maternal cardiac functions, the relation between hypertension and cardiac dysfunctions is only partially understood. The study of this relationship can be framed as a joint inferential problem on multiple populations, each corresponding to a different hypertensive disorder diagnosis, that combines multivariate information provided by a collection of cardiac function indexes. A Bayesian nonparametric approach seems particularly suited for this setup and we demonstrate it on a dataset consisting of transthoracic echocardiography results of a cohort of Indian pregnant women. We are able to perform model selection, provide density estimates of cardiac function indexes and a latent clustering of patients: these readily interpretable inferential outputs allow to single out modified cardiac functions in hypertensive patients compared to healthy subjects and progressively increased alterations with the severity of the disorder. The analysis is based on a Bayesian nonparametric model that relies on a novel hierarchical structure, called symmetric hierarchical Dirichlet process. This is suitably designed so that the mean parameters are identified and used for model selection across populations, a penalization for multiplicity is enforced, and the presence of unobserved relevant factors is investigated through a latent clustering of subjects. Posterior inference relies on a suitable Markov Chain Monte Carlo algorithm and the model behaviour is also showcased on simulated data.

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