arXiv subjects

Alessandro Casa

Publications and source records attributed to Alessandro Casa.

16 recordsLinked to original sources

arXiv2025

A latent variable model for identifying and characterizing food adulteration

Recently, growing consumer awareness of food quality and sustainability has led to a rising demand for effective food authentication methods. Vibrational spectroscopy techniques have emerged as a promising tool for collecting large volumes of data to detect food adulteration. However, spectroscopic data pose significant challenges from a statistical viewpoint, highlighting the need for more sophisticated modeling strategies. To address these challenges, in this work we propose a latent variable model specifically tailored for food adulterant detection, while accommodating the features of spectral data. Our proposal offers greater granularity with respect to existing approaches, since it does not only identify adulterated samples but also estimates the level of adulteration, and detects the spectral regions most affected by the adulterant. Consequently, the methodology offers deeper insights, and could facilitate the development of portable and faster instruments for efficient data collection in food authenticity studies. The method is applied to both synthetic and real honey mid-infrared spectroscopy data, delivering precise estimates of the adulteration level and accurately identifying which portions of the spectra are most impacted by the adulterant.

stat.ME↗

arXiv2025

Addressing Phase Discrepancies in Functional Data: A Bayesian Approach for Accurate Alignment and Smoothing

In many real-world applications, functional data exhibit considerable variability in both amplitude and phase. This is especially true in biomechanical data such as the knee flexion angle dataset motivating our work, where timing differences across curves can obscure meaningful comparisons. Curves of this study also exhibit substantial variability from one another. These pronounced differences make the dataset particularly challenging to align properly without distorting or losing some of the individual curves characteristics. Our alignment model addresses these challenges by eliminating phase discrepancies while preserving the individual characteristics of each curve and avoiding distortion, thanks to its flexible smoothing component. Additionally, the model accommodates group structures through a dedicated parameter. By leveraging the Bayesian approach, the new prior on the warping parameters ensures that the resulting warping functions automatically satisfy all necessary validity conditions. We applied our model to the knee flexion dataset, demonstrating excellent performance in both smoothing and alignment, particularly in the presence of high inter-curve variability and complex group structures.

stat.ME↗

arXiv2025

Confidence set for mixture order selection

A fundamental challenge in approximating an unknown density using finite Gaussian mixture models is selecting the number of mixture components, also known as order. Traditional approaches choose a single best model using information criteria. However, often models with different orders yield similar fits, leading to substantial model selection uncertainty and making it challenging to identify the optimal number of components. In this paper, we introduce the Model Selection Confidence Set (MSCS) for order selection in Gaussian mixtures - a set-valued estimator that, with a predefined confidence level, includes the true mixture order across repeated samples. Rather than selecting a single model, our MSCS identifies all plausible orders by determining whether each candidate model is at least as plausible as the best-selected one, using a screening based on a penalized likelihood ratio statistic. We provide theoretical guarantees for asymptotic coverage, and demonstrate its practical advantages through simulations and real data analysis.

stat.ME↗

arXiv2024

Model-based clustering for covariance matrices via penalized Wishart mixture models

Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly adopted distance-based approaches tend to rely primarily on mean levels to characterize and differentiate between groups. Recently, there have been promising efforts to cluster covariance matrices directly, thereby distinguishing groups solely based on the relationships between variables. From a model-based perspective, a probabilistic formalization has been provided by considering a mixture model with component densities following a Wishart distribution. Notwithstanding, this approach faces challenges when dealing with a large number of variables, as the number of parameters to be estimated increases quadratically. To address this issue, we propose a sparse Wishart mixture model, which assumes that the component scale matrices possess a cluster-dependent degree of sparsity. Model estimation is performed by maximizing a penalized log-likelihood, enforcing a covariance graphical lasso penalty on the component scale matrices. This penalty not only reduces the number of non-zero parameters, mitigating the challenges of high-dimensional settings, but also enhances the interpretability of results by emphasizing the most relevant relationships among variables. The proposed methodology is tested on both simulated and real data, demonstrating its ability to unravel the complexities of neuroimaging data and effectively cluster subjects based on the relational patterns among distinct brain regions.

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arXiv2024

High-dimensional Covariance Estimation by Pairwise Likelihood Truncation

Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making estimation more manageable. In certain models, including the Gaussian model, both pairwise and full likelihoods are maximized by the same parameter values, thus retaining optimal statistical efficiency, when the number of variables is fixed. Leveraging on this insight, we introduce estimation of sparse high-dimensional covariance matrices by maximizing a truncated version of the pairwise likelihood function, obtained by including pairwise terms corresponding to nonzero covariance elements. To achieve a meaningful truncation, we propose to minimize the $L_2$-distance between pairwise and full likelihood scores plus an $L_1$-penalty discouraging the inclusion of uninformative terms. Differently from other regularization approaches, our method focuses on selecting whole pairwise likelihood objects rather than shrinking individual covariance parameters, thus retaining the inherent unbiasedness of the pairwise likelihood estimating equations. This selection procedure is shown to have the selection consistency property as the covariance dimension increases exponentially fast. Consequently, the implied pairwise likelihood estimator is consistent and converges to the oracle maximum likelihood estimator assuming knowledge of nonzero covariance entries.

stat.ME↗

arXiv2023

An adaptive functional regression framework for spatially heterogeneous signals in spectroscopy

The attention towards food products characteristics, such as nutritional properties and traceability, has risen substantially in the recent years. Consequently, we are witnessing an increased demand for the development of modern tools to monitor, analyse and assess food quality and authenticity. Within this framework, an essential set of data collection techniques is provided by vibrational spectroscopy. In fact, methods such as Fourier near infrared and mid infrared spectroscopy have been often exploited to analyze different foodstuffs. Nonetheless, existing statistical methods often struggle to deal with the challenges presented by spectral data, such as their high dimensionality, paired with strong relationships among the wavelengths. Therefore, the definition of proper statistical procedures accounting for the peculiarities of spectroscopy data is paramount. In this work, motivated by two dairy science applications, we propose an adaptive functional regression framework for spectroscopy data. The method stems from the trend filtering literature, allowing the definition of a highly flexible and adaptive estimator able to handle different degrees of smoothness. We provide a fast optimization procedure that is suitable for both Gaussian and non Gaussian scalar responses, and allows for the inclusion of scalar covariates. Moreover, we develop inferential procedures for both the functional and the scalar component thus enhancing not only the interpretability of the results, but also their usability in real world scenarios. The method is applied to two sets of MIR spectroscopy data, providing excellent results when predicting milk chemical composition and cows' dietary treatments. Moreover, the developed inferential routine provides relevant insights, potentially paving the way for a richer interpretation and a better understanding of the impact of specific wavelengths on milk features.

stat.ME↗

arXiv2023

Sparse model-based clustering of three-way data via lasso-type penalties

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful application, this approach suffers from over-parameterization issues, making it less suitable even for matrix-variate data of moderate size. To overcome this drawback, we introduce a sparse model-based clustering approach for three-way data. Our approach assumes that the matrix mixture parameters are sparse and have different degree of sparsity across clusters, allowing to induce parsimony in a flexible manner. Estimation of the model relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties enable the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions and allow to capture cluster-specific association structures. The proposed methodology is tested extensively on synthetic data and its validity is demonstrated in application to time-dependent crime patterns in different US cities.

stat.CO↗

arXiv2022

Classification of cow diet based on milk mid infrared spectra: a data analysis competition at the "International workshop of spectroscopy and chemometrics 2022"

In April 2022, the Vistamilk SFI Research Centre organized the second edition of the "International Workshop on Spectroscopy and Chemometrics - Applications in Food and Agriculture". Within this event, a data challenge was organized among participants of the workshop. Such data competition aimed at developing a prediction model to discriminate dairy cows' diet based on milk spectral information collected in the mid-infrared region. In fact, the development of an accurate and reliable discriminant model for dairy cows' diet can provide important authentication tools for dairy processors to guarantee product origin for dairy food manufacturers from grass-fed animals. Different statistical and machine learning modelling approaches have been employed during the workshop, with different pre-processing steps involved and different degree of complexity. The present paper aims to describe the statistical methods adopted by participants to develop such classification model.

q-bio.QM↗

arXiv2022

Mid infrared spectroscopy and milk quality traits: a data analysis competition at the "International Workshop on Spectroscopy and Chemometrics 2021"

A chemometric data analysis challenge has been arranged during the first edition of the "International Workshop on Spectroscopy and Chemometrics", organized by the Vistamilk SFI Research Centre and held online in April 2021. The aim of the competition was to build a calibration model in order to predict milk quality traits exploiting the information contained in mid-infrared spectra only. Three different traits have been provided, presenting heterogeneous degrees of prediction complexity thus possibly requiring trait-specific modelling choices. In this paper the different approaches adopted by the participants are outlined and the insights obtained from the analyses are critically discussed.

q-bio.QM↗

arXiv2022

Group-wise shrinkage estimation in penalized model-based clustering

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where they tend to be over-parameterized. As a consequence, different solutions have been proposed, often relying on matrix decompositions or variable selection strategies. Recently, a methodological link between Gaussian graphical models and finite mixtures has been established, paving the way for penalized model-based clustering in the presence of large precision matrices. Notwithstanding, current methodologies implicitly assume similar levels of sparsity across the classes, not accounting for different degrees of association between the variables across groups. We overcome this limitation by deriving group-wise penalty factors, which automatically enforce under or over-connectivity in the estimated graphs. The approach is entirely data-driven and does not require additional hyper-parameter specification. Analyses on synthetic and real data showcase the validity of our proposal.

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arXiv2021

Advances in Multi-Variate Analysis Methods for New Physics Searches at the Large Hadron Collider

Between the years 2015 and 2019, members of the Horizon 2020-funded Innovative Training Network named "AMVA4NewPhysics" studied the customization and application of advanced multivariate analysis methods and statistical learning tools to high-energy physics problems, as well as developed entirely new ones. Many of those methods were successfully used to improve the sensitivity of data analyses performed by the ATLAS and CMS experiments at the CERN Large Hadron Collider; several others, still in the testing phase, promise to further improve the precision of measurements of fundamental physics parameters and the reach of searches for new phenomena. In this paper, the most relevant new tools, among those studied and developed, are presented along with the evaluation of their performances.

hep-ex↗

arXiv2021

Co-clustering of time-dependent data via Shape Invariant Model

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data we need to account for relations among both time instants and variables and, at the same time, for subjects heterogeneity. We propose a new co-clustering methodology for clustering individuals and variables simultaneously that is designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the Shape Invariant Model in the Latent Block Model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that could be chosen on substantive grounds and provides parsimonious summaries of complex longitudinal or functional data by partitioning data matrices into homogeneous blocks.

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arXiv2021

Parsimonious Bayesian Factor Analysis for modelling latent structures in spectroscopy data

In recent years animal diet has been receiving increased attention, in particular examining the impact of pasture-based feeding strategies on the quality of milk and dairy products, in line with the increased prevalence of grass-fed dairy products appearing on market shelves. To date, there are limited testing methods available for the verification of grass-fed dairy therefore these products are susceptible to food fraud and adulteration. Hence statistical tools studying potential differences among milk samples coming from animals on different feeding systems are required, thus providing increased security around the authenticity of the products. Infrared spectroscopy techniques are widely used to collect data on milk samples and to predict milk related traits. While these data are routinely used to predict the composition of the macro components of milk, each spectrum provides a reservoir of unharnessed information about the sample. The interpretation of these data presents a number of challenges due to their high-dimensionality and the relationships amongst the spectral variables. In this work we propose a modification of the standard factor analysis to induce a parsimonious summary of spectroscopic data. The procedure maps the observations into a low-dimensional latent space while simultaneously clustering observed variables. The method indicates possible redundancies in the data and it helps disentangle the complex relationships among the wavelengths. A flexible Bayesian estimation procedure is proposed for model fitting, providing reasonable values for the number of latent factors and clusters. The method is applied on milk mid-infrared spectroscopy data from dairy cows on different pasture and non-pasture based diets, providing accurate modelling of the data correlation, the clustering of variables and information on differences between milk samples from cows on different diets.

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arXiv2020

Better than the best? Answers via model ensemble in density-based clustering

With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging landscape. In fact, basing predictions and inference on a single model may be limiting if not harmful; ensemble approaches, which combine different models, have been proposed to overcome the selection step, and proven fruitful especially in the supervised learning framework. Conversely, these approaches have been scantily explored in the unsupervised setting. In this work we focus on the model-based clustering formulation, where a plethora of mixture models, with different number of components and parametrizations, is typically estimated. We propose an ensemble clustering approach that circumvents the single best model paradigm, while improving stability and robustness of the partitions. A new density estimator, being a convex linear combination of the density estimates in the ensemble, is introduced and exploited for group assignment. As opposed to the standard case, where clusters are typically associated to the components of the selected mixture model, we define partitions by borrowing the modal, or nonparametric, formulation of the clustering problem, where groups are linked with high-density regions. Staying in the density-based realm we thus show how blending together parametric and nonparametric approaches may be beneficial from a clustering perspective.

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arXiv2019

Nonparametric semisupervised classification for signal detection in high energy physics

Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a deviation from the background, representing the known physics. Information available on the background can be incorporated in the search, in order to identify potential anomalies. From a statistical perspective, the problem is recasted to a peculiar classification one where only partial information is accessible. Therefore a semisupervised approach shall be adopted, either by strengthening or by relaxing assumptions underlying clustering or classification methods respectively. In this work, following the first route, we semisupervise nonparametric clustering in order to identify a possible signal. The main contribution consists in tuning a nonparametric estimate of the density underlying the experimental data with the aid of the available information on the physical theory. As a side contribution, a variable selection procedure is presented. The whole procedure is tested on a dataset mimicking proton-proton collisions performed within a particle accelerator. While finding motivation in the field of particle physics, the approach is applicable to various science domains, where similar problems of anomaly detection arise.

stat.AP↗

arXiv2019

Modal clustering asymptotics with applications to bandwidth selection

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.

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