arXiv subjects

Ruggero Bellio

Publications and source records attributed to Ruggero Bellio.

9 recordsLinked to original sources

arXiv2026

Model-based clustering of compositional trajectories for the analysis of mobility data

Understanding urban mobility patterns is crucial for designing efficient and sustainable transportation systems. Motivated by an application to the municipality of Padova and its surroundings, we propose a novel statistical framework for the analysis and clustering of mobility trajectories derived from telephonic data. We introduce a compositional representation of individual movements that integrates the uncertain device location with information on the surrounding road network, encoding at each time point the proportions of different road types compatible with the observed position. This formulation naturally accounts for measurement uncertainty and yields trajectories evolving in the simplex. To model these data, we develop a state-space framework for compositional time series that captures both the telephonic measurement error and the temporal dynamics of the latent mobility process. Building on this representation, we propose a model-based clustering approach based on mixtures of state-space models to identify groups of trajectories with similar evolution. This allows us to aggregate individual movements into interpretable mobility patterns at the population level. The results of the case study demonstrate the ability of the approach to uncover meaningful mobility behaviors, providing insights that are potentially relevant to policy makers.

stat.AP↗

arXiv2025

Scalable Fitting Methods for Multivariate Gaussian Additive Models with Covariate-dependent Covariance Matrices

We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the positive-definiteness of the covariance matrix, we model the elements of an unconstrained parametrisation matrix, focussing particularly on the modified Cholesky decomposition and the matrix logarithm. A key computational challenge arises from the fact that, for the model class considered here, the number of parameters increases quadratically with the dimension of the response vector. Hence, here we discuss how to achieve fast computation and low memory footprint in moderately high dimensions, by exploiting parsimonious model structures, sparse derivative systems and by employing block-oriented computational methods. Methods for building and fitting multivariate Gaussian additive models are provided by the SCM R package, available at https://github.com/VinGioia90/SCM, while the code for reproducing the results in this paper is available at https://github.com/VinGioia90/SACM.

stat.CO↗

arXiv2023

When Composite Likelihood Meets Stochastic Approximation

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of the conventional composite likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey.

stat.ME↗

arXiv2023

Consistent and Scalable Composite Likelihood Estimation of Probit Models with Crossed Random Effects

Estimation of crossed random effects models commonly requires computational costs that grow faster than linearly in the sample size $N$, often as fast as $\Omega(N^{3/2})$, making them unsuitable for large data sets. For non-Gaussian responses, integrating out the random effects to get a marginal likelihood brings significant challenges, especially for high dimensional integrals where the Laplace approximation might not be accurate. We develop a composite likelihood approach to probit models that replaces the crossed random effects model with some hierarchical models that require only one-dimensional integrals. We show how to consistently estimate the crossed effects model parameters from the hierarchical model fits. We find that the computation scales linearly in the sample size. We illustrate the method on about five million observations from Stitch Fix where the crossed effects formulation would require an integral of dimension larger than $700{,}000$.

stat.ME↗

arXiv2022

Parametric bootstrap inference for stratified models with high-dimensional nuisance specifications

Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures are known to perform poorly when the dimension of the nuisance parameter is large relative to the sample size and when the information about the parameters is limited. In many such cases, the use of asymptotic normality of analytical modifications of the signed likelihood root is known to recover inferential performance. It is proved here that parametric bootstrap of standard likelihood pivots results in as accurate inferences as analytical modifications of the signed likelihood root do in stratified models with stratum specific nuisance parameters. We focus on the challenging case where the number of strata increases as fast or faster than the stratum samples size. It is also shown that this equivalence holds regardless of whether constrained or unconstrained bootstrap is used. This is in contrast to when the number of strata is fixed or increases slower than the stratum sample size, where we show that constrained bootstrap corrects inference to a higher order than unconstrained bootstrap. Simulation experiments support the theoretical findings and demonstrate the excellent performance of bootstrap in extreme scenarios.

math.ST↗

arXiv2018

Multi-study Factor Analysis

We introduce a novel class of factor analysis methodologies for the joint analysis of multiple studies. The goal is to separately identify and estimate 1) common factors shared across multiple studies, and 2) study-specific factors. We develop a fast Expectation Conditional-Maximization algorithm for parameter estimates and we provide a procedure for choosing the common and specific factor. We present simulations evaluating the performance of the method and we illustrate it by applying it to gene expression data in ovarian cancer. In both cases, we clarify the benefits of a joint analysis compared to the standard factor analysis. We hope to have provided a valuable tool to accelerate the pace at which we can combine unsupervised analysis across multiple studies, and understand the cross-study reproducibility of signal in multivariate data.

stat.AP↗

arXiv2018

Bayesian Multi-study Factor Analysis for High-throughput Biological Data

This paper presents a new modeling strategy for joint unsupervised analysis of multiple high-throughput biological studies. As in Multi-study Factor Analysis, our goals are to identify both common factors shared across studies and study-specific factors. Our approach is motivated by the growing body of high-throughput studies in biomedical research, as exemplified by the comprehensive set of expression data on breast tumors considered in our case study. To handle high-dimensional studies, we extend Multi-study Factor Analysis using a Bayesian approach that imposes sparsity. Specifically, we generalize the sparse Bayesian infinite factor model to multiple studies. We also devise novel solutions for the identification of the loading matrices: we recover the loading matrices of interest ex-post, by adapting the orthogonal Procrustes approach. Computationally, we propose an efficient and fast Gibbs sampling approach. Through an extensive simulation analysis, we show that the proposed approach performs very well in a range of different scenarios, and outperforms standard Factor analysis in all the scenarios identifying replicable signal in unsupervised genomic applications. The results of our analysis of breast cancer gene expression across seven studies identified replicable gene patterns, clearly related to well-known breast cancer pathways. An R package is implemented and available on GitHub.

stat.AP↗

arXiv2015

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison.

cs.AI↗

arXiv2015

Beyond first-order asymptotics for Cox regression

To go beyond standard first-order asymptotics for Cox regression, we develop parametric bootstrap and second-order methods. In general, computation of $P$-values beyond first order requires more model specification than is required for the likelihood function. It is problematic to specify a censoring mechanism to be taken very seriously in detail, and it appears that conditioning on censoring is not a viable alternative to that. We circumvent this matter by employing a reference censoring model, matching the extent and timing of observed censoring. Our primary proposal is a parametric bootstrap method utilizing this reference censoring model to simulate inferential repetitions of the experiment. It is shown that the most important part of improvement on first-order methods - that pertaining to fitting nuisance parameters - is insensitive to the assumed censoring model. This is supported by numerical comparisons of our proposal to parametric bootstrap methods based on usual random censoring models, which are far more unattractive to implement. As an alternative to our primary proposal, we provide a second-order method requiring less computing effort while providing more insight into the nature of improvement on first-order methods. However, the parametric bootstrap method is more transparent, and hence is our primary proposal. Indications are that first-order partial likelihood methods are usually adequate in practice, so we are not advocating routine use of the proposed methods. It is however useful to see how best to check on first-order approximations, or improve on them, when this is expressly desired.

math.ST↗