1,721,029 research outputs found
Functional principal component analysis for incomplete space–time data
Full text linkEnvironmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable
Estimating Spatial Anisotropy in Semiparametric Regression with Differential Regularization
No full textSpatial regression models play a crucial role in analyzing environmental data and predicting spatially distributed phenomena. However, traditional approaches often struggle to capture the complex spatial dependencies and non-stationarities present in real-world datasets. In this paper, we propose a novel parameter cascading algorithm for spatial regression. The algorithm allows for the simultaneous estimation of the unknown spatial parameters describing the anisotropy and the spatial field itself, while incorporating physical and domain knowledge. We illustrate the proposed algorithm through an application to the analysis of rainfall data in Switzerland. The parameter cascading algorithm enables more accurate and localized predictions of spatially distributed variables
Some first results on the consistency of spatial regression with partial differential equation regularization
Full text linkWe study the consistency of the estimator in spatial regression with partial differential equation (PDE) regularization. This new smoothing technique allows to accurately estimate spatial fields over complex two-dimensional domains, starting from noisy observations; the regularizing term involves a PDE that formalizes problem specific information about the phenomenon at hand. Differently from classical smoothing methods, the solution of the infinite-dimensional estimation problem cannot be computed analytically. An approximation is obtained via the finite element method, considering a suitable triangulation of the spatial domain. We first consider the consistency of the estimator in the infinite-dimensional setting. We then study the consistency of the finite element estimator, resulting from the approximated PDE. We study the bias and variance of the estimators, with respect to the sample size and to the value of the smoothing parameter. Some final simulation studies provide numerical evidence of the rates derived for the bias, variance and mean square error
Modeling spatially dependent functional data via regression with differential regularization
Full text linkWe propose a method for modelling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to effciently handle data distributed over complex domains and where the shape of the domain influences the phenomenon behavior. Moreover, the method can comply with specific conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood-flow velocity field in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data.CSQ
A Multi-Domain Model with Partial Differential Regularization: An Application to Neuroimaging Data
No full textIn the framework of physics-informed statistical models, this work proposes a multi-domain spatial regression method with a regularization term involving the Laplace-Beltrami operator, specifically designed for data observed over surface domains.
To illustrate its application, we employ the proposed method on high-dimensional resting-state fMRI signals from various subjects, with the precuneus designated as the Region of Interest for computing the Functional Connectivity maps. Here, we treat the Functional Connectivity Map of each subject as the response variable, with available data on cortical thickness serving as the regressor
Generalized Spatio-Temporal Regression with PDE Penalization
No full textWe develop a novel generalised linear model for the analysis of data distributed over space and time. The model involves a nonparametric term 5, a smooth function over space and time. The estimation is carried out by the minimization of an appropriate penalized negative log-likelihood functional, with a roughness penalty on 5 that involves space and time differential operators, in a separable fashion, or an evolution partial differential equation. The model can include covariate information in a semi-parametric setting. The functional is discretized by means of finite elements in space, and B-splines or finite differences in time. Thanks to the use of finite elements, the proposed method is able to efficiently model data sampled over irregularly shaped spatial domains, with complicated boundaries. To illustrate the proposed model we present an application to study the criminality in the city of Portland, from 2015 to 2020
Analysis of Complex Spatio-Temporal Neuroimaging Signals by Functional Principal Component Analysis
No full textWe propose a novel methodology to extract the main sources of variability from a collection of space-time dependent signals observed over complicated geometries. The methodology is developed in the context of functional Principal Component Analysis (fPCA), and proposes an estimation problem combining a rank-one approximation of the data matrix with a roughness penalty. The computed principal components are smooth spatio-temporal functions over the domain of interest, which are easy to interpret and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. The model is applied to the study of neuroimaging data. In particular, we explore the main sources of variability in neuronal connectivity in a population of healthy and pathological subjects, starting from functional Magnetic Resonance Imaging scans
A Nonparametric Approach to Model Event-Data on Linear Networks
No full textIn this article, we focus on spatio-temporal point patterns observed on linear networks and recorded continuously over time. We present a nonparametric methodology for spatio-temporal intensity estimation in inhomogeneous Poisson point processes. The approach combines maximum likelihood estimation with roughness penalties based on differential operators in time and in space, the latter defined over the linear network domains. This balances data adaptation and smoothness of the estimate. We establish theoretical properties related to the proposed estimator. For the implementation, we rely on advanced techniques coming from optimization and numerical analysis. The discretization of the estimation problem combines finite elements in space, designed for linear networks, and --splines in time, ensuring flexibility at feasible computational costs. We present an application to real data concerning road accidents occurred in Bergamo, Italy, in 2015-2022. This offers the opportunity to validate the proposed method, and to assess its performance in comparison with state-of-the-art techniques
Analyzing data in complicated 3D domains: Smoothing, semiparametric regression, and functional principal component analysis
Full text linkIn this work, we introduce a family of methods for the analysis of data observed at locations scattered in three-dimensional (3D) domains, with possibly complicated shapes. The proposed family of methods includes smoothing, regression, and functional principal component analysis for functional signals defined over (possibly nonconvex) 3D domains, appropriately complying with the nontrivial shape of the domain. This constitutes an important advance with respect to the literature, because the available methods to analyze data observed in 3D domains rely on Euclidean distances, which are inappropriate when the shape of the domain influences the phenomenon under study. The common building block of the proposed methods is a nonparametric regression model with differential regularization. We derive the asymptotic properties of the methods and show, through simulation studies, that they are superior to the available alternatives for the analysis of data in 3D domains, even when considering domains with simple shapes. We finally illustrate an application to a neurosciences study, with neuroimaging signals from functional magnetic resonance imaging, measuring neural activity in the gray matter, a nonconvex volume with a highly complicated structure
Efficient Parametric Tests in Semiparametric Regression with Differential Regularization
No full textIn this work we consider the problem of making inference on
the nonparametric component within a semiparametric regression model
with differential regularization. The parametric inference methods so far
introduced in the literature perform poorly, due to the variance mis-
specification induced by the penalization term. Nonparametric inference
procedures may instead be excessively computationally demanding. We
hereby propose two new parametric approaches, that are robust to the
effect of the penalization, while retaining a reduced computational cost.
The first method relies on an appropriate undersmoothing strategy, com-
bined with a bootstrap approach. The second one leverages instead on
the asymptotic properties of the scores of the model. The resulting tests
have better control of Type-I error, with respect to the existing alterna-
tives, and reduced computational cost. We apply the novel approaches
to the study chlorophyll-a concentrations in the Mediterranean sea
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