arXiv subjects

Fabio Centofanti

Publications and source records attributed to Fabio Centofanti.

At least 19 recordsLinked to original sources

arXiv2026

Cellwise and Casewise Robust Covariance in High Dimensions

The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating cells (entries) of the data matrix. Recently some robust covariance estimators have been developed that can handle both types of outliers, but their computation is only feasible up to at most 20 dimensions. To remedy this we propose the cellRCov method, a robust covariance estimator that simultaneously handles casewise outliers, cellwise outliers, and missing data. It relies on a decomposition of the covariance on principal and orthogonal subspaces, leveraging recent work on robust PCA. It also employs a ridge-type regularization to stabilize the estimated covariance matrix. We establish some theoretical properties of cellRCov, including its casewise and cellwise influence functions as well as consistency and asymptotic normality. A simulation study demonstrates the superior performance of cellRCov in contaminated and missing data scenarios. Furthermore, its practical utility is illustrated in a real-world application to anomaly detection. We also construct and illustrate the cellRCCA method for robust and regularized canonical correlation analysis.

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arXiv2026

Cellwise Robust Discriminant Analysis

Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far away. But nowadays there is increasing interest in cellwise outliers, that are unexpected entries in the data matrix. Removing an entire case because it has one or a few outlying cells would lose much information. Cellwise robust methods aim to detect the outlying cells and to preserve the information in the other cells. We propose a DA method that is trained by estimating the location and covariance of each class by cellwise and casewise robust estimators, that can also handle NA's. The main novelty of our approach is in the prediction on test data, that may contain outlying cells and NA's themselves. The new robust discriminant function is derived from a novel statistical model by penalized maximum likelihood. We focus on quadratic DA, but also cover the setting of linear DA. The new cellQDA and cellLDA methods perform well in simulation. The approach is illustrated on real data, and the results are interpreted with the help of graphical displays.

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arXiv2026

Cellwise and Casewise Robust Multivariate Regression with Inference

Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying cells, that are individual contaminated entries in the predictor and/or response matrix. Moreover, modern datasets frequently contain missing values and are high-dimensional. To address these challenges we propose the cellwise multivariate regression (cellMR) estimator, a robust regression method that simultaneously accommodates casewise and cellwise outliers, missing data, and high dimensionality. The approach builds on a cellwise robust covariance estimator and uses ridge regularization for numerical stability. We further introduce cellBoot, a novel bootstrap-based inference procedure tailored to the cellMR framework. Relying on indirect inference, cellBoot provides asymptotically valid confidence intervals that are robust to casewise and cellwise contamination. We derive influence functions of the regression estimator and prove the asymptotic validity of the cellBoot confidence intervals. Simulations and a real genomics application illustrate the strong finite-sample performance of the proposed methods.

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arXiv2026

Robust Tensor-on-Tensor Regression

Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers, which may be present in both the response and the predictor. It can be affected by casewise outliers, which are observations that deviate from the bulk of the data, as well as by cellwise outliers, which are individual anomalous cells within the tensors. The latter are particularly common due to the typically large number of cells in tensor data. This paper introduces a novel robust TOT regression method, named ROTOT, that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers in the response. The outliers in the predictor are handled using a robust Multilinear Principal Component Analysis method. Graphical diagnostic tools are also proposed to identify the different types of outliers detected. The performance of ROTOT is evaluated through extensive simulations and further illustrated using the Labeled Faces in the Wild dataset, where ROTOT is applied to predict facial attributes.

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arXiv2026

Casewise and Cellwise Robust Multilinear Principal Component Analysis

Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as tensors typically consist of many cells. This paper introduces a novel robust MPCA method that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers. The solution that minimizes this loss function is computed using an iteratively reweighted least squares algorithm with a robust initialization. Graphical diagnostic tools are also proposed to identify the different types of outliers that have been found by the new robust MPCA method. The performance of the method and associated graphical displays is assessed through simulations and illustrated on two real datasets.

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arXiv2025

Robust Principal Components by Casewise and Cellwise Weighting

Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be strongly affected by the presence of outliers. Traditional robust approaches consider casewise outliers, that is, cases generated by an unspecified outlier distribution that differs from that of the clean cases. But there may also be cellwise outliers, which are suspicious entries that can occur anywhere in the data matrix. Another common issue is that some cells may be missing. This paper proposes a new robust PCA method, called cellPCA, that can simultaneously deal with casewise outliers, cellwise outliers, and missing cells. Its single objective function combines two robust loss functions, that together mitigate the effect of casewise and cellwise outliers. The objective function is minimized by an iteratively reweighted least squares (IRLS) algorithm. Residual cellmaps and enhanced outlier maps are proposed for outlier detection. The casewise and cellwise influence functions of the principal subspace are derived, and its asymptotic distribution is obtained. Extensive simulations and two real data examples illustrate the performance of cellPCA.

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arXiv2025

Statistical Process Monitoring based on Functional Data Analysis

In modern industrial settings, advanced acquisition systems allow for the collection of data in the form of profiles, that is, as functional relationships linking responses to explanatory variables. In this context, statistical process monitoring (SPM) aims to assess the stability of profiles over time in order to detect unexpected behavior. This review focuses on SPM methods that model profiles as functional data, i.e., smooth functions defined over a continuous domain, and apply functional data analysis (FDA) tools to address limitations of traditional monitoring techniques. A reference framework for monitoring multivariate functional data is first presented. This review then offers a focused survey of several recent FDA-based profile monitoring methods that extend this framework to address common challenges encountered in real-world applications. These include approaches that integrate additional functional covariates to enhance detection power, a robust method designed to accommodate outlying observations, a real-time monitoring technique for partially observed profiles, and two adaptive strategies that target the characteristics of the out-of-control distribution. These methods are all implemented in the R package funcharts, available on CRAN. Finally, a review of additional existing FDA-based profile monitoring methods is also presented, along with suggestions for future research.

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arXiv2025

An Adaptive Multivariate Functional Control Chart

New data acquisition technologies allow one to gather huge amounts of data that are best represented as functional data. In this setting, profile monitoring assesses the stability over time of both univariate and multivariate functional quality characteristics. The detection power of profile monitoring methods could heavily depend on parameter selection criteria, which usually do not take into account any information from the out-of-control (OC) state. This work proposes a new framework, referred to as adaptive multivariate functional control chart (AMFCC), capable of adapting the monitoring of a multivariate functional quality characteristic to the unknown OC distribution, by combining $p$-values of the partial tests corresponding to Hotelling $T^2$-type statistics calculated at different parameter combinations. Through an extensive Monte Carlo simulation study, the performance of AMFCC is compared with methods that have already appeared in the literature. Finally, a case study is presented in which the proposed framework is used to monitor a resistance spot welding process in the automotive industry. AMFCC is implemented in the R package funcharts, available on CRAN.

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arXiv2024

funcharts: Control charts for multivariate functional data in R

Modern statistical process monitoring (SPM) applications focus on profile monitoring, i.e., the monitoring of process quality characteristics that can be modeled as profiles, also known as functional data. Despite the large interest in the profile monitoring literature, there is still a lack of software to facilitate its practical application. This article introduces the funcharts R package that implements recent developments on the SPM of multivariate functional quality characteristics, possibly adjusted by the influence of additional variables, referred to as covariates. The package also implements the real-time version of all control charting procedures to monitor profiles partially observed up to an intermediate domain point. The package is illustrated both through its built-in data generator and a real-case study on the SPM of Ro-Pax ship CO2 emissions during navigation, which is based on the ShipNavigation data provided in the Supplementary Material.

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arXiv2024

An Adaptive Multivariate Functional EWMA Control Chart

In many modern industrial scenarios, the measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in the monitoring of the quality of a resistance spot welding process in the automotive industry through the online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and recognized as the full technological signature of the process.

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arXiv2024

Functional Mixture Regression Control Chart

Industrial applications often exhibit multiple in-control patterns due to varying operating conditions, which makes a single functional linear model (FLM) inadequate to capture the complexity of the true relationship between a functional quality characteristic and covariates, which gives rise to the multimode profile monitoring problem. This issue is clearly illustrated in the resistance spot welding (RSW) process in the automotive industry, where different operating conditions lead to multiple in-control states. In these states, factors such as electrode tip wear and dressing may influence the functional quality characteristic differently, resulting in distinct FLMs across subpopulations. To address this problem, this article introduces the functional mixture regression control chart (FMRCC) to monitor functional quality characteristics with multiple in-control patterns and covariate information, modeled using a mixture of FLMs. A monitoring strategy based on the likelihood ratio test is proposed to monitor any deviation from the estimated in-control heterogeneous population. An extensive Monte Carlo simulation study is performed to compare the FMRCC with competing monitoring schemes that have already appeared in the literature, and a case study in the monitoring of an RSW process in the automotive industry, which motivated this research, illustrates its practical applicability.

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arXiv2024

Robust Multivariate Functional Control Chart

In modern Industry 4.0 applications, a huge amount of data is acquired during manufacturing processes that are often contaminated with anomalous observations in the form of both casewise and cellwise outliers. These can seriously reduce the performance of control charting procedures, especially in complex and high-dimensional settings. To mitigate this issue in the context of profile monitoring, we propose a new framework, referred to as robust multivariate functional control chart (RoMFCC), that is able to monitor multivariate functional data while being robust to both functional casewise and cellwise outliers. The RoMFCC relies on four main elements: (I) a functional univariate filter to identify functional cellwise outliers to be replaced by missing components; (II) a robust multivariate functional data imputation method of missing values; (III) a casewise robust dimensionality reduction; (IV) a monitoring strategy for the multivariate functional quality characteristic. An extensive Monte Carlo simulation study is performed to compare the RoMFCC with competing monitoring schemes already appeared in the literature. Finally, a motivating real-case study is presented where the proposed framework is used to monitor a resistance spot welding process in the automotive industry.

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arXiv2023

Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this paper a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

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arXiv2022

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named S-LASSO, is proposed for the coefficient function of the Function-on-Function linear regression model. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating regions where the coefficient function is zero, and to smoothly estimate non-zero values of the coefficient function. The sparsity of the estimator is ensured by a \textit{functional LASSO penalty}, which pointwise shrinks toward zero the coefficient function, while the smoothness is provided by two roughness penalties that penalize the curvature of the final estimator. The resulting estimator is proved to be estimation and pointwise sign consistent. Via an extensive Monte Carlo simulation study, the estimation and predictive performance of the S-LASSO estimator are shown to be better than (or at worst comparable with) competing estimators already presented in the literature before. Practical advantages of the S-LASSO estimator are illustrated through the analysis of the \textit{Canadian weather}, \textit{Swedish mortality} and \textit{ship CO\textsubscript{2} emission data}. The S-LASSO method is implemented in the \textsf{R} package \textsf{slasso}, openly available online on CRAN.

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arXiv2022

Sparse and Smooth Functional Data Clustering

A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. The proposed method is referred to as sparse and smooth functional clustering (SaS-Funclust) and relies on a general functional Gaussian mixture model whose parameters are estimated by maximizing a log-likelihood function penalized with a functional adaptive pairwise penalty and a roughness penalty. The former allows identifying the noninformative portion of domain by shrinking the means of separated clusters to some common values, whereas the latter improves the interpretability by imposing some degree of smoothing to the estimated cluster means. The model is estimated via an expectation-conditional maximization algorithm paired with a cross-validation procedure. Through a Monte Carlo simulation study, the SaS-Funclust method is shown to outperform other methods already appeared in the literature, both in terms of clustering performance and interpretability. Finally, three real-data examples are presented to demonstrate the favourable performance of the proposed method. The SaS-Funclust method is implemented in the $\textsf{R}$ package $\textsf{sasfunclust}$, available online at https://github.com/unina-sfere/sasfunclust.

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arXiv2022

Real-time Monitoring of Functional Data

With the rise of Industry 4.0, huge amounts of data are now generated that are apt to be modelled as functional data. In this setting, standard profile monitoring methods aim to assess the stability over time of a completely observed functional quality characteristic. However, in some practical situations, evaluating the process state in real-time, i.e., as the process is running, could be of great interest to significantly improve the effectiveness of monitoring. To this aim, we propose a new method, referred to as functional real-time monitoring (FRTM), that is able to account for both phase and amplitude variation through the following steps: (i) registration; (ii) dimensionality reduction; (iii) monitoring of a partially observed functional quality characteristic. An extensive Monte Carlo simulation study is performed to quantify the performance of FRTM with respect to two competing methods. Finally, an example is presented where the proposed method is used to monitor batches from a penicillin production process in real-time.

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arXiv2021

Robust Functional ANOVA with Application to Additive Manufacturing

The development of data acquisition systems is facilitating the collection of data that are apt to be modelled as functional data. In some applications, the interest lies in the identification of significant differences in group functional means defined by varying experimental conditions, which is known as functional analysis of variance (FANOVA). With real data, it is common that the sample under study is contaminated by some outliers, which can strongly bias the analysis. In this paper, we propose a new robust nonparametric functional ANOVA method (RoFANOVA) that reduces the weights of outlying functional data on the results of the analysis. It is implemented through a permutation test based on a test statistic obtained via a functional extension of the classical robust $ M $-estimator. By means of an extensive Monte Carlo simulation study, the proposed test is compared with some alternatives already presented in the literature, in both one-way and two-way designs. The performance of the RoFANOVA is demonstrated in the framework of a motivating real-case study in the field of additive manufacturing that deals with the analysis of spatter ejections. The RoFANOVA method is implemented in the R package rofanova, available online at https://github.com/unina-sfere/rofanova.

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arXiv2020

Adaptive Smoothing Spline Estimator for the Function-on-Function Linear Regression Model

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also on two real-data benchmark examples.

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