arXiv subjects

Cristian Castiglione

Publications and source records attributed to Cristian Castiglione.

4 recordsLinked to original sources

arXiv2025

Optimal and computationally tractable lower bounds for logistic log-likelihoods

The logit transform is arguably the most widely-employed link function beyond linear settings. This transformation routinely appears in regression models for binary data and provides a central building-block in popular methods for both classification and regression. Its widespread use, combined with the lack of analytical solutions for the optimization of objective functions involving the logit transform, still motivates active research in computational statistics. Among the directions explored, a central one has focused on the design of tangent lower bounds for logistic log-likelihoods that can be tractably optimized, while providing a tight approximation of these log-likelihoods. This has led to the development of effective minorize-maximize (MM) algorithms for point estimation, and variational schemes for approximate Bayesian inference under several logit models. However, the overarching focus has been on tangent quadratic minorizers. In fact, it is still unclear whether tangent lower bounds sharper than quadratic ones can be derived without undermining the tractability of the resulting minorizer. This article addresses such a question through the design and study of a novel piece-wise quadratic lower bound that uniformly improves any tangent quadratic minorizer, including the sharpest ones, while admitting a direct interpretation in terms of the classical generalized lasso problem. As illustrated in realistic empirical studies, such a sharper bound not only improves the speed of convergence of common MM schemes for penalized maximum likelihood estimation, but also yields tractable variational Bayes (VB) approximations with higher accuracy relative to those obtained under popular quadratic bounds employed in VB.

stat.ML↗

arXiv2025

Non-conjugate variational Bayes for pseudo-likelihood mixed effect models

We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear predictor, eventually transformed using a bijective link, where the prediction misfit is measured using, possibly non-differentiable, loss functions. Examples include generalized linear models, quasi-likelihood models, and robust regression. To address the limitations of non-conjugate settings, we employ an efficient message passing optimization strategy under a Gaussian variational approximation of the posterior. The resulting algorithms automatically account for non-conjugate priors and non-smooth losses, without requiring model-specific data-augmented representations. Besides the general formulation, we provide closed-form updates for popular model specifications, including quantile regression and support vector machines. Overall, theoretical and empirical results highlight the effectiveness of the proposed method, demonstrating its computational efficiency and approximation accuracy as an alternative to existing Bayesian techniques.

stat.ME↗

arXiv2025

Stochastic gradient descent estimation of generalized matrix factorization models with application to single-cell RNA sequencing data

Single-cell RNA sequencing allows the quantification of gene expression at the individual cell level, enabling the study of cellular heterogeneity and gene expression dynamics. Dimensionality reduction is a common preprocessing step critical for the visualization, clustering, and phenotypic characterization of samples. This step, often performed using principal component analysis or closely related methods, is challenging because of the size and complexity of the data. In this work, we present a generalized matrix factorization model assuming a general exponential dispersion family distribution and we show that many of the proposed approaches in the single-cell dimensionality reduction literature can be seen as special cases of this model. Furthermore, we propose a scalable adaptive stochastic gradient descent algorithm that allows us to estimate the model efficiently, enabling the analysis of millions of cells. We benchmark the proposed algorithm through extensive numerical experiments against state-of-the-art methods and showcase its use in real-world biological applications. The proposed method systematically outperforms existing methods of both generalized and non-negative matrix factorization, demonstrating faster execution times and parsimonious memory usage, while maintaining, or even enhancing, matrix reconstruction fidelity and accuracy in biological signal extraction. On real data, we show that our method scales seamlessly to millions of cells, enabling dimensionality reduction in large single-cell datasets. Finally, all the methods discussed here are implemented in an efficient open-source R package, sgdGMF, available on CRAN.

stat.CO↗

arXiv2025

Dependent stochastic block models for age-indexed sequences of directed causes-of-death networks

Death events commonly arise from complex interactions among interrelated causes, formally classified in reporting practices as underlying and contributing. Leveraging information from death certificates, these interactions can be naturally represented through a sequence of directed networks encoding co-occurrence strengths between pairs of underlying and contributing causes across ages. Although this perspective opens the avenues to learn informative age-specific block interactions among endogenous groups of underlying and contributing causes displaying similar co-occurrence patterns, there has been limited research along this direction in mortality modeling. This is mainly due to the lack of suitable stochastic block models for age-indexed sequences of directed networks. We cover this gap through a novel Bayesian formulation which crucially learns two separate group structures for underlying and contributing causes, while allowing both structures to change smoothly across ages via dependent random partition priors. As illustrated in simulations, this formulation outperforms state-of-the-art solutions that could be adapted to our motivating application. Moreover, when applied to USA mortality data, it unveils structures in the composition, evolution, and modular interactions among causes-of-death groups that were hidden to previous studies. Such findings could have relevant policy implications and contribute to an improved understanding of the recent "death of despair" phenomena in USA.

stat.AP↗