4 research outputs found
FAStEN: an efficient adaptive method for feature selection and estimation in high-dimensional functional regressions
Functional regression analysis is an established tool for many contemporary
scientific applications. Regression problems involving large and complex data
sets are ubiquitous, and feature selection is crucial for avoiding overfitting
and achieving accurate predictions. We propose a new, flexible, and
ultra-efficient approach to perform feature selection in a sparse high
dimensional function-on-function regression problem, and we show how to extend
it to the scalar-on-function framework. Our method combines functional data,
optimization, and machine learning techniques to perform feature selection and
parameter estimation simultaneously. We exploit the properties of Functional
Principal Components, and the sparsity inherent to the Dual Augmented
Lagrangian problem to significantly reduce computational cost, and we introduce
an adaptive scheme to improve selection accuracy. Through an extensive
simulation study, we benchmark our approach to the best existing competitors
and demonstrate a massive gain in terms of CPU time and selection performance
without sacrificing the quality of the coefficients' estimation. Finally, we
present an application to brain fMRI data from the AOMIC PIOP1 study
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
Covariance‐based low‐dimensional registration for function‐on‐function regression
We propose a new low-dimensional registration procedure that exploits the relation- ship between the response and the predictor in a function-on-function regression. In this context, functional covariance components (FCCs) provide a flexible and powerful tool to represent the data in a low-dimensional space, capturing the most meaningful modes of dependency between the two set of curves. Based on this reduced representation, our procedure aligns simultaneously the two sets of curves, in a way that optimizes the subsequent regression analysis. To implement our procedure, we use both the continuous registration (CR) algorithm and a novel parallel algorithm coded in R. We then compare it to other common registration approaches via simulations and an application to the AneuRisk data