arXiv subjects

Antonio Canale

Publications and source records attributed to Antonio Canale.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive partition Factor Analysis

Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study, neglecting the potential study-specific variations present in data from multiple studies. Multi-study factor analysis has emerged as a recent methodological advancement that addresses this gap by distinguishing between latent traits shared across studies and study-specific components arising from artifactual or population-specific sources of variation. In this paper, we extend the current methodologies by introducing novel shrinkage priors for the latent factors, thereby accommodating a broader spectrum of scenarios -- from the absence of study-specific latent factors to models in which factors pertain only to small subgroups nested within or shared between the studies. For the proposed construction we provide conditions for identifiability of factor loadings and guidelines to perform straightforward posterior computation via Gibbs sampling. Through comprehensive simulation studies, we demonstrate that our proposed method exhibits competing performance across a variety of scenarios compared to existing methods, yet providing richer insights. The practical benefits of our approach are further illustrated through applications to bird species co-occurrence data and ovarian cancer gene expression data.

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arXiv2025

Degrees of Freedom in Penalized Regression: Model Selection with Adaptive Penalties

Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by the size of the active set, this property does not extend to adaptive penalization methods, despite the widespread use of this approximation in practice. To solve this issue, in this paper we derive a novel unbiased estimator of the effective degrees of freedom for the Adaptive Lasso within Stein's unbiased risk estimation framework. Our analysis reveals additional terms induced by data-dependent penalization, reflecting the role of adaptive weights and regularization in determining model complexity. We further revisit the Group Lasso, providing an alternative derivation of its degrees of freedom, and extend these results to the Adaptive Group Lasso. Importantly, we characterize the behavior of the degrees of freedom along the regularization path beyond the orthonormal design setting commonly assumed in the literature, providing a new theoretical description of this behavior under general design matrices. By correcting the common misuse of active set size as a proxy for degrees of freedom, our results enable more reliable risk estimation and inference, offering a rigorous foundation for understanding model complexity in adaptive penalized regression.

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arXiv2025

Decoding Neuronal Ensembles from Spatially-Referenced Calcium Traces: A Bayesian Semiparametric Approach

Understanding how neurons coordinate their activity is a fundamental question in neuroscience, with implications for learning, memory, and neurological disorders. Calcium imaging has emerged as a powerful method to observe large-scale neuronal activity in freely moving animals, providing time-resolved recordings of hundreds of neurons. However, fluorescence signals are noisy and only indirectly reflect underlying spikes of neuronal activity, complicating the extraction of reliable patterns of neuronal coordination. We introduce a fully Bayesian, semiparametric model that jointly infers spiking activity and identifies functionally coherent neuronal ensembles from calcium traces. Our approach models each neuron's spiking probability through a latent Gaussian process and encourages anatomically coherent clustering using a location-dependent stick-breaking prior. A spike-and-slab Dirichlet process captures heterogeneity in spike amplitudes while filtering out negligible events. We consider calcium imaging data from the hippocampal CA1 region of a mouse as it navigates a circular arena, a setting critical for understanding spatial memory and neuronal representation of environments. Our model uncovers spatially structured co-activation patterns among neurons and can be employed to reveal how ensemble structures vary with the animal's position.

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arXiv2025

On the Posterior Computation Under the Dirichlet-Laplace Prior

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized optimization methods. Bayesian approaches provide a probabilistic framework to formally quantify uncertainty through shrinkage priors. Among these, the Dirichlet-Laplace prior has attained recognition for its theoretical guarantees and wide applicability. This article identifies a critical yet overlooked issue in the implementation of Gibbs sampling algorithms for such priors. We demonstrate that ambiguities in the presentation of key algorithmic steps, while mathematically coherent, have led to widespread implementation inaccuracies that fail to target the intended posterior distribution -- a target endowed with rigorous asymptotic guarantees. Using the normal-means problem and high-dimensional linear regressions as canonical examples, we clarify these implementation pitfalls and their practical consequences and propose corrected and more efficient sampling procedures.

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arXiv2025

Bayesian Adaptive Tucker Decompositions for Tensor Factorization

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the issue of pre-selecting the latent multi-rank, we introduce a Bayesian adaptive Tucker decomposition model that infers the multi-rank automatically via an infinite increasing shrinkage prior. The model introduces local sparsity in the core tensor, inducing rich and at the same time parsimonious dependency structures. Posterior inference proceeds via an efficient adaptive Gibbs sampler, supporting both continuous and binary data and allowing for straightforward missing data imputation when dealing with incomplete multiway data. We discuss fundamental properties of the proposed modeling framework, providing theoretical justification. Simulation studies and applications to chemometrics and complex ecological data offer compelling evidence of its advantages over existing tensor factorization methods.

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arXiv2025

Bayesian local clustering of functional data via semi-Markovian random partitions

We introduce a Bayesian framework for indirect local clustering of functional data, leveraging B-spline basis expansions and a novel dependent random partition model. By exploiting the local support properties of B-splines, our approach allows partially coincident functional behaviors, achieved when shared basis coefficients span sufficiently contiguous regions. This is accomplished through a cutting-edge dependent random partition model that enforces semi-Markovian dependence across a sequence of partitions. By matching the order of the B-spline basis with the semi-Markovian dependence structure, the proposed model serves as a highly flexible prior, enabling efficient modeling of localized features in functional data. Furthermore, we extend the utility of the dependent random partition model beyond functional data, demonstrating its applicability to a broad class of problems where sequences of dependent partitions are central, and standard Markovian assumptions prove overly restrictive. Empirical illustrations, including analyses of simulated data and tide level measurements from the Venice Lagoon, showcase the effectiveness and versatility of the proposed methodology.

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arXiv2025

A Semi-Parametric Bayesian Spatial Model for Rainfall Events in Geographically Complex Domains

Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of water processes. Motivated by the need to analyze rainfall across complex spatial locations, we propose a flexible Bayesian semi-parametric model for spatially distributed data. This method effectively accounts for spatial correlation while incorporating dependencies on geographical characteristics in a highly flexible manner. Indeed, using latent Gaussian processes, indexed by spatial coordinates and topographical features, the model integrates spatial dependencies and environmental characteristics within a nonparametric framework. Posterior inference is conducted using an efficient rejection-free Markov Chain Monte Carlo algorithm, which eliminates the need for tuning parameter calibration, ensuring smoother and more reliable estimation. The model's flexibility is evaluated through a series of simulation studies, involving different rainfall and spatial correlation scenarios, to demonstrate its robustness across various conditions. We then apply the model to a large dataset of rainfall events collected from the Italian regions of Veneto and Trentino-Alto Adige, these areas are known for their complex orography and diverse meteorological drivers. By analyzing this data, we generate detailed maps that illustrate the mean and variance of rainfall and rainy days. The method is implemented in a new R package available on GitHub.

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arXiv2024

A Bayesian Model for Co-clustering Ordinal Data with Informative Missing Entries

Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population characteristics. To address this gap, we introduce a Bayesian nonparametric model for co-clustering multivariate ordinal data that treats censored observations as informative, rather than merely missing. We demonstrate that this offers a significant improvement in understanding the underlying structure of the data. Our model exploits the flexibility of two independent Dirichlet processes, allowing us to infer potentially distinct subpopulations that characterize the latent structure of both subjects and variables. The ordinal nature of the data is addressed by introducing latent variables, while a matrix factorization specification is adopted to handle the high dimensionality of the data in a parsimonious way. The conjugate structure of the model enables an explicit derivation of the full conditional distributions of all the random variables in the model, which facilitates seamless posterior inference using a Gibbs sampling algorithm. We demonstrate the method's performance through simulations and by analyzing politician and movie ratings data.

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arXiv2024

Bayesian Nonparametrics for Principal Stratification with Continuous Post-Treatment Variables

Principal stratification provides a causal inference framework for investigating treatment effects in the presence of a post-treatment variable. Principal strata play a key role in characterizing the treatment effect by identifying groups of units with the same or similar values for the potential post-treatment variable at all treatment levels. The literature has focused mainly on binary post-treatment variables. Few papers considered continuous post-treatment variables. In the presence of a continuous post-treatment, a challenge is how to identify and characterize meaningful coarsening of the latent principal strata that lead to interpretable principal causal effects. This paper introduces the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with binary treatment and continuous post-treatment variables. CASBAH leverages Bayesian nonparametric priors with an innovative hierarchical structure for the potential post-treatment outcomes that overcomes some of the limitations of previous works. Specifically, the novel features of our method allow for (i) identifying coarsened principal strata through a data-adaptive approach and (ii) providing a comprehensive quantification of the uncertainty surrounding stratum membership. Through Monte Carlo simulations, we show that the proposed methodology performs better than existing methods in characterizing the principal strata and estimating principal effects of the treatment. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

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arXiv2023

Confounder-Dependent Bayesian Mixture Model: Characterizing Heterogeneity of Causal Effects in Air Pollution Epidemiology

Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (PM2.5) increases mortality risk. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the Group Average Treatment Effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this work, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of PM2.5 on mortality are heterogeneous.

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arXiv2023

Structured factorization for single-cell gene expression data

Single-cell gene expression data are often characterized by large matrices, where the number of cells may be lower than the number of genes of interest. Factorization models have emerged as powerful tools to condense the available information through a sparse decomposition into lower rank matrices. In this work, we adapt and implement a recent Bayesian class of generalized factor models to count data and, specifically, to model the covariance between genes. The developed methodology also allows one to include exogenous information within the prior, such that recognition of covariance structures between genes is favoured. In this work, we use biological pathways as external information to induce sparsity patterns within the loadings matrix. This approach facilitates the interpretation of loadings columns and the corresponding latent factors, which can be regarded as unobserved cell covariates. We demonstrate the effectiveness of our model on single-cell RNA sequencing data obtained from lung adenocarcinoma cell lines, revealing promising insights into the role of pathways in characterizing gene relationships and extracting valuable information about unobserved cell traits.

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arXiv2023

A hierarchical Bayesian non-asymptotic extreme value model for spatial data

Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the asymptotic assumption, typical of the traditional extreme value theory, is relaxed. We introduce a Bayesian hierarchical model that accounts for the possible underlying variability in the distribution of event magnitudes and occurrences, which are described through latent temporal and spatial processes. Spatial dependence is characterized by geographical covariates and effects not fully described by the covariates are captured by spatial structure in the hierarchies. The performance of the approach is illustrated through simulation studies and an application to daily rainfall extremes across North Carolina (USA). The results show that we significantly reduce the estimation uncertainty with respect to state of the art techniques.

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arXiv2022

Accelerated structured matrix factorization

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

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arXiv2022

Escaping the curse of dimensionality in Bayesian model based clustering

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too few clusters. This article explains this behavior by studying the random partition posterior in a non-standard setting with a fixed sample size and increasing data dimensionality. We provide conditions under which the finite sample posterior tends to either assign every observation to a different cluster or all observations to the same cluster as the dimension grows. Interestingly, the conditions do not depend on the choice of clustering prior, as long as all possible partitions of observations into clusters have positive prior probabilities, and hold irrespective of the true data-generating model. We then propose a class of latent mixtures for Bayesian clustering (Lamb) on a set of low-dimensional latent variables inducing a partition on the observed data. The model is amenable to scalable posterior inference and we show that it can avoid the pitfalls of high-dimensionality under mild assumptions. The proposed approach is shown to have good performance in simulation studies and an application to inferring cell types based on scRNAseq.

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arXiv2022

Efficient posterior sampling for Bayesian Poisson regression

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient sampling from the posterior distribution of parameters, and standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo algorithms, are typically used. Herein, we developed an efficient Metropolis-Hastings algorithm and importance sampler to simulate from the posterior distribution of the parameters of Poisson log-linear models under conditional Gaussian priors with superior performance with respect to the state-of-the-art alternatives. The key for both algorithms is the introduction of a proposal density based on a Gaussian approximation of the posterior distribution of parameters. Specifically, our result leverages the negative binomial approximation of the Poisson likelihood and the successful Pólya-gamma data augmentation scheme. Via simulation, we obtained that the time per independent sample of the proposed samplers is competitive with that obtained using the successful Hamiltonian Monte Carlo sampling, with the Metropolis-Hastings showing superior performance in all scenarios considered.

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arXiv2022

Semiparametric Functional Factor Models with Bayesian Rank Selection

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To correct for model misspecification, we augment the parametric template with an infinite-dimensional nonparametric functional basis. The nonparametric basis functions are learned from the data and constrained to be orthogonal to the parametric template, which preserves distinctness between the parametric and nonparametric terms. This distinctness is essential to prevent functional confounding, which otherwise induces severe bias for the parametric terms. The nonparametric factors are regularized with an ordered spike-and-slab prior that provides consistent rank selection and satisfies several appealing theoretical properties. The versatility of the proposed approach is illustrated through applications to synthetic data, human motor control data, and dynamic yield curve data. Relative to parametric and semiparametric alternatives, the proposed semiparametric functional factor model eliminates bias, reduces excessive posterior and predictive uncertainty, and provides reliable inference on the effective number of nonparametric terms--all with minimal additional computational costs.

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arXiv2022

Numerical evaluation of dual norms via the MM algorithm

We deal with the problem of numerically computing the dual norm, which is important to study sparsity-inducing regularizations (Jenatton et al. 2011,Bach et al. 2012). The dual norms find application in optimization and statistical learning, for example, in the design of working-set strategies, for characterizing dual gradient methods, for dual decompositions and in the definition of augmented Lagrangian functions. Nevertheless, the dual norm of some well-known sparsity-inducing regolarization methods are not analytically available. Examples are the overlap group $\ell_2$-norm of (Jenatton et al. 2011) and the elastic net norm of Zhou and Hastie (2005). Therefore we resort to the Majorization-Minimization principle of Lange (2016) to provide an efficient algorithm that leverages a reparametrization of the dual constrained optimization problem as unconstrained optimization with barrier. Extensive simulation experiments have been performed in order to verify the correctness of operation, and evaluate the performance of the proposed method. Our results demonstrate the effectiveness of the algorithm in retrieving the dual norm even for large dimensions.

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arXiv2022

Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data

Recent advancements in miniaturized fluorescence microscopy have made it possible to investigate neuronal responses to external stimuli in awake behaving animals through the analysis of intra-cellular calcium signals. An on-going challenge is deconvolving the temporal signals to extract the spike trains from the noisy calcium signals' time-series. In this manuscript, we propose a nested Bayesian finite mixture specification that allows the estimation of spiking activity and, simultaneously, reconstructing the distributions of the calcium transient spikes' amplitudes under different experimental conditions. The proposed model leverages two nested layers of random discrete mixture priors to borrow information between experiments and discover similarities in the distributional patterns of neuronal responses to different stimuli. Furthermore, the spikes' intensity values are also clustered within and between experimental conditions to determine the existence of common (recurring) response amplitudes. Simulation studies and the analysis of a data set from the Allen Brain Observatory show the effectiveness of the method in clustering and detecting neuronal activities.

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