arXiv subjects

Ana Carolina da Cruz

Publications and source records attributed to Ana Carolina da Cruz.

3 recordsLinked to original sources

arXiv2026

Variational Inference for Variable Selection in Scalar-on-Function Regression

In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction accuracy. In this work, we develop a variational inference approach for estimation and variable selection in scalar-on-function regression, involving only functional covariates, and in partially functional regression models that also include scalar covariates. Specifically, we develop a variational expectation-maximization (VEM) algorithm, with a variational Bayes procedure implemented in the E-step to obtain approximate marginal posterior distributions for most model parameters, except for the regularization parameters, which are updated in the M-step. Our method accurately identifies relevant covariates while maintaining strong predictive performance, as demonstrated through extensive simulation studies across diverse scenarios. Compared with alternative approaches, including BGLSS (Bayesian Group Lasso with Spike-and-Slab priors), grLASSO (group Least Absolute Shrinkage and Selection Operator), grMCP (group Minimax Concave Penalty), and grSCAD (group Smoothly Clipped Absolute Deviation), our approach achieves a superior balance between goodness-of-fit and sparsity in most scenarios. We further illustrate its practical utility through real-data applications involving spectral analysis of sugar samples and weather measurements from Japan.

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arXiv2025

Fast Bayesian Basis Selection for Functional Data Representation with Correlated Errors

Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a result, smoothing techniques are often used to approximate the observed data as functions. In this work, we propose a novel Bayesian approach for selecting basis functions for smoothing one or multiple curves simultaneously. Our method differentiates from other Bayesian approaches in two key ways: (i) by accounting for correlated errors and (ii) by developing a variational Expectation-Maximization (VEM) algorithm, which is faster than Markov chain Monte Carlo (MCMC) methods such as Gibbs sampling. Simulation studies demonstrate that our method effectively identifies the true underlying structure of the data across various scenarios, and it is applicable to different types of functional data. Our VEM algorithm not only recovers the basis coefficients and the correct set of basis functions but also estimates the existing within-curve correlation. When applied to the motorcycle, LIDAR (LIght Detection And Ranging) experiment and Canadian weather datasets, our method demonstrates comparable, and in some cases superior, performance in terms of adjusted R2 compared to regression splines, smoothing splines, least absolute shrinkage and selection operator (LASSO) and Bayesian LASSO. Our proposed method is implemented in R and codes are available at https://github.com/acarolcruz/VB-Bases-Selection

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arXiv2025

BayesCPclust: A Bayesian Approach for Clustering Constant-Wise Change-Point Data

Change-point models deal with ordered data sequences. Their primary goal is to infer the locations where an aspect of the data sequence changes. In this paper, we propose and implement a nonparametric Bayesian model for clustering observations based on their constant-wise change-point profiles via Gibbs sampler. Our model incorporates a Dirichlet Process on the constant-wise change-point structures to cluster observations while simultaneously performing multiple change-point estimation. Additionally, our approach controls the number of clusters in the model, not requiring the specification of the number of clusters a priori. Satisfactory clustering and estimation results were obtained when evaluating our method under various simulated scenarios and on a real dataset from single-cell genomic sequencing. Our proposed methodology is implemented as an R package called BayesCPclust and is available from the Comprehensive R Archive Network at https://CRAN.R-project.org/package=BayesCPclust.

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