arXiv subjects

Paula Castro

Publications and source records attributed to Paula Castro.

3 recordsLinked to original sources

arXiv2026

An Interpretable Recommendation Model for Psychometric Data, With an Application to Gerontological Primary Care

There are challenges that must be overcome to make recommender systems useful in healthcare settings. The reasons are varied: the lack of publicly available clinical data, the difficulty that users may have in understanding the reasons why a recommendation was made, the risks that may be involved in following that recommendation, and the uncertainty about its effectiveness. In this work, we address these challenges with a recommendation model that leverages the structure of psychometric data to provide visual explanations that are faithful to the model and interpretable by care professionals. We focus on a narrow healthcare niche, gerontological primary care, to show that the proposed recommendation model can assist the attending professional in the creation of personalised care plans. We report results of a comparative offline performance evaluation of the proposed model on healthcare datasets that were collected by research partners in Brazil, as well as the results of a user study that evaluates the interpretability of the visual explanations the model generates. The results suggest that the proposed model can advance the application of recommender systems in this healthcare niche, which is expected to grow in demand , opportunities, and information technology needs as demographic changes become more pronounced.

cs.AI↗

arXiv2023

Analysis of Four-Dimensional Variational Data Assimilation Problems in Low Regularity Spaces

We carry out a rigorous analysis of four-dimensional variational data assimilation ($4D$-VAR) problems for linear and semilinear parabolic partial differential equations. Continuity of the state with respect to the spatial variable is required since pointwise observations of the state variable appear in the cost functional. Using maximal parabolic regularity tools, we prove this regularity for initial conditions with $L^\beta$-regularity guaranteed by control constraints, rather than Sobolev regularity of the controls ensured by artificial cost terms. We obtain existence of optimal controls and first order necessary optimality conditions for both the convex and nonconvex problem with spatial dimension $d=2,3$, as well as second order sufficient optimality conditions for the nonconvex problem for $d=2$.

math.OC↗

arXiv2018

A bilevel learning approach for optimal observation placement in variational data assimilation

In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the lower-level task is the variational reconstruction of the initial condition of a semilinear system, and the upper-level problem solves the optimal placement with help of a sparsity inducing function. Due to the pointwise nature of the observations, an optimality system with regular Borel measures is obtained as necessary optimality condition for the lower-level problem. The latter is then considered as constraint for the upper-level instance, yielding an optimization problem constrained by a multi-state system with measures. We demonstrate existence of Lagrange multipliers and derive a necessary optimality system characterizing the optimal solution of the bilevel problem. The numerical solution is carried out also on two levels. The lower-level problem is solved using a standard BFGS method, while the upper-level one is solved by means of a projected BFGS algorithm based on the estimation of $\epsilon$-active sets. Finally some numerical experiments are presented to illustrate the main features of our approach.

math.OC↗