arXiv subjects

Marzia A. Cremona

Publications and source records attributed to Marzia A. Cremona.

8 recordsLinked to original sources

arXiv2026

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models

In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. Such a subspace can be a Reproducing Kernel Hilbert Space (RKHS) to ensure the desired regularity characteristics, such as smoothness or periodicity, for the coefficient estimates. Our procedure, called SOFIA (Scalar-On-Function Integrated Adaptive Lasso), is based on an adaptive penalized least squares algorithm that leverages functional subgradients to efficiently solve the minimization problem. We demonstrate that the proposed method satisfies the functional oracle property, even when the number of predictors exceeds the sample size. SOFIA's effectiveness in variable selection and coefficient estimation is evaluated through extensive simulation studies and a real-data application to GDP growth prediction.

stat.ME↗

arXiv2026

Globally aligned Principal Component Analysis for multi-group data

We propose a novel principal component analysis (PCA) for multi-group datasets, where the same numerical variables are measured across different groups of observations. Existing approaches either ignore group structure entirely by working with global (pooled) data, focus exclusively on local structure (group-wise PCA), or impose restrictive assumptions of common principal components. Our approach respects the multi-group nature of data while improving global comparability of components. We combine group-specific principal components with global ones through an explicit alignment mechanism based on regularized optimization. We introduce the notion of globally aligned covariance matrix, incorporating weighted contributions from global principal directions in the group-wise covariance matrix. The alignment strength is controlled by regularization parameters that can be tuned to achieve the desired trade-off. Through a comprehensive simulation study, we demonstrate that the proposed aligned PCA achieves a favorable compromise between capturing local variation within groups and maintaining interpretability and stability across groups. Furthermore, in an application to the 2021 Canadian Census socioeconomic data, the proposed aligned PCA yields more comparable and stable region-specific components than pooled or region-wise PCA.

stat.ME↗

arXiv2024

Analyzing Taiwanese traffic patterns on consecutive holidays through forecast reconciliation and prediction-based anomaly detection techniques

This study explores traffic patterns on Taiwanese highways during consecutive holidays and focuses on understanding Taiwanese highway traffic behavior. We propose a prediction-based detection method for finding highway traffic anomalies using reconciled ordinary least squares (OLS) forecasts and bootstrap prediction intervals. Two fundamental features of traffic flow time series -- namely, seasonality and spatial autocorrelation -- are captured by adding Fourier terms in OLS models, spatial aggregation (as a hierarchical structure mimicking the geographical division in regions, cities, and stations), and a reconciliation step. Our approach, although simple, is able to model complex traffic datasets with reasonable accuracy. Being based on OLS, it is efficient and permits avoiding the computational burden of more complex methods. Analyses of Taiwan's consecutive holidays in 2019, 2020, and 2021 (73 days) showed strong variations in anomalies across different directions and highways. Specifically, we detected some areas and highways comprising a high number of traffic anomalies (north direction-central and southern regions-highways No. 1 and 3, south direction-southern region-highway No.3), and others with generally normal traffic (east and west direction). These results could provide important decision-support information to traffic authorities.

stat.AP↗

arXiv2023

Contrasting pre-vaccine COVID-19 waves in Italy through Functional Data Analysis

We use data from 107 Italian provinces to characterize and compare mortality patterns in the first two COVID-19 epidemic waves, which occurred prior to the introduction of vaccines. We also associate these patterns with mobility, timing of government restrictions, and socio-demographic, infrastructural, and environmental covariates. Notwithstanding limitations in the accuracy and reliability of publicly available data, we are able to exploit information in curves and shapes through Functional Data Analysis techniques. Specifically, we document differences in magnitude and variability between the two waves; while both were characterized by a co-occurrence of 'exponential' and 'mild' mortality patterns, the second spread much more broadly and asynchronously through the country. Moreover, we find evidence of a significant positive association between local mobility and mortality in both epidemic waves and corroborate the effectiveness of timely restrictions in curbing mortality. The techniques we describe could capture additional signals of interest if applied, for instance, to data on cases and positivity rates. However, we show that the quality of such data, at least in the case of Italian provinces, was too poor to support meaningful analyses.

stat.AP↗

arXiv2023

funBIalign: a hierachical algorithm for functional motif discovery based on mean squared residue scores

Motif discovery is gaining increasing attention in the domain of functional data analysis. Functional motifs are typical "shapes" or "patterns" that recur multiple times in different portions of a single curve and/or in misaligned portions of multiple curves. In this paper, we define functional motifs using an additive model and we propose funBIalign for their discovery and evaluation. Inspired by clustering and biclustering techniques, funBIalign is a multi-step procedure which uses agglomerative hierarchical clustering with complete linkage and a functional distance based on mean squared residue scores to discover functional motifs, both in a single curve (e.g., time series) and in a set of curves. We assess its performance and compare it to other recent methods through extensive simulations. Moreover, we use funBIalign for discovering motifs in two real-data case studies; one on food price inflation and one on temperature changes.

stat.ME↗

arXiv2020

The shapes of an epidemic: using Functional Data Analysis to characterize COVID-19 in Italy

We investigate patterns of COVID-19 mortality across 20 Italian regions and their association with mobility, positivity, and socio-demographic, infrastructural and environmental covariates. Notwithstanding limitations in accuracy and resolution of the data available from public sources, we pinpoint significant trends exploiting information in curves and shapes with Functional Data Analysis techniques. These depict two starkly different epidemics; an "exponential" one unfolding in Lombardia and the worst hit areas of the north, and a milder, "flat(tened)" one in the rest of the country -- including Veneto, where cases appeared concurrently with Lombardia but aggressive testing was implemented early on. We find that mobility and positivity can predict COVID-19 mortality, also when controlling for relevant covariates. Among the latter, primary care appears to mitigate mortality, and contacts in hospitals, schools and work places to aggravate it. The techniques we describe could capture additional and potentially sharper signals if applied to richer data.

stat.AP↗

arXiv2020

Probabilistic $K$-mean with local alignment for clustering and motif discovery in functional data

We develop a new method to locally cluster curves and discover functional motifs, i.e.~typical ``shapes'' that may recur several times along and across the curves capturing important local characteristics. In order to identify these shared curve portions, our method leverages ideas from functional data analysis (joint clustering and alignment of curves), bioinformatics (local alignment through the extension of high similarity seeds) and fuzzy clustering (curves belonging to more than one cluster, if they contain more than one typical ``shape''). It can employ various dissimilarity measures and incorporate derivatives in the discovery process, thus exploiting complex facets of shapes. We demonstrate the performance of our method with an extensive simulation study, and show how it generalizes other clustering methods for functional data. Finally, we provide real data applications to Berkeley growth data, Italian Covid-19 death curves and ``Omics'' data related to mutagenesis.

stat.ME↗

arXiv2019

On the bias of H-scores for comparing biclusters, and how to correct it

In the last two decades several biclustering methods have been developed as new unsupervised learning techniques to simultaneously cluster rows and columns of a data matrix. These algorithms play a central role in contemporary machine learning and in many applications, e.g. to computational biology and bioinformatics. The H-score is the evaluation score underlying the seminal biclustering algorithm by Cheng and Church, as well as many other subsequent biclustering methods. In this paper, we characterize a potentially troublesome bias in this score, that can distort biclustering results. We prove, both analytically and by simulation, that the average H-score increases with the number of rows/columns in a bicluster. This makes the H-score, and hence all algorithms based on it, biased towards small clusters. Based on our analytical proof, we are able to provide a straightforward way to correct this bias, allowing users to accurately compare biclusters.

stat.ME↗