arXiv subjects

Rosa E. Lillo

Publications and source records attributed to Rosa E. Lillo.

At least 19 recordsLinked to original sources

arXiv2026

Asgl: A Python Package for Penalized Linear and Quantile Regression

asgl is an open-source Python package that offers a robust and versatile framework for fitting a variety of regression models including linear, logistic, and, notably, quantile regression. It implements a comprehensive suite of penalization techniques such as lasso, ridge, group lasso, sparse group lasso, elastic net, and their adaptive variants. A key contribution of \pkg{asgl} is its extensive support for adaptive penalizations, critically offering a range of built-in methodologies for estimating the necessary adaptive weights as proposed by Mendez-Civieta et al. (2020). This feature addresses a significant practical challenge -- the weight estimation process -- in applying advanced adaptive methods, especially in high-dimensional settings, and is largely absent from other packages. Furthermore, asgl offers penalized quantile regression, a less commonly available feature in statistical software. The primary class, Regressor, ensures seamless integration with the scikit-learn ecosystem, facilitating straightforward model evaluation and hyperparameter optimization. asgl has demonstrated utility in variable selection and prediction tasks across both low- and high-dimensional data, positioning it as a comprehensive tool for modern statistical modeling.

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arXiv2026

Adaptive sparse group LASSO in quantile regression

This paper studies the introduction of sparse group LASSO (SGL) to the quantile regression framework. Additionally, a more flexible version, an adaptive SGL is proposed based on the adaptive idea, this is, the usage of adaptive weights in the penalization. Adaptive estimators are usually focused on the study of the oracle property under asymptotic and double asymptotic frameworks. A key step on the demonstration of this property is to consider adaptive weights based on a initial $\sqrt{n}$-consistent estimator. In practice this implies the usage of a non penalized estimator that limits the adaptive solutions to low dimensional scenarios. In this work, several solutions, based on dimension reduction techniques PCA and PLS, are studied for the calculation of these weights in high dimensional frameworks. The benefits of this proposal are studied both in synthetic and real datasets.

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arXiv2026

Fast Partial Quantile Regression

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantile based estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example.

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arXiv2026

Geometrical fairness in graph neural networks

Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications. Among these, recent frameworks grounded in diffusion processes provide a unifying perspective that extends traditional graph neural network formulations while addressing limitations of standard message-passing mechanisms. Despite these advances, concerns remain regarding the fairness of such models, as they may propagate or amplify biases present in the data. In this work, we introduce a fairness-aware adaptation of graph-based diffusion by modifying the underlying Laplacian operator. Our approach incorporates multiple complementary transformations, including subspace projections, spectral adjustments, and frequency-based filtering, to mitigate bias-related components. Leveraging the intrinsic smoothing properties of graph diffusion, we provide a principled analysis of the resulting behavior and establish theoretical insights into fairness properties. We evaluate the proposed framework on both synthetic and real-world datasets, demonstrating that it achieves competitive performance while improving fairness metrics with limited additional computational cost.

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arXiv2026

On the use of graph models to achieve individual and group fairness

Machine Learning algorithms are ubiquitous in key decision-making contexts such as justice, healthcare and finance, which has spawned a great demand for fairness in these procedures. However, the theoretical properties of such models in relation with fairness are still poorly understood, and the intuition behind the relationship between group and individual fairness is still lacking. In this paper, we provide a theoretical framework based on Sheaf Diffusion to leverage tools based on dynamical systems and homology to model fairness. Concretely, the proposed method projects input data into a bias-free space that encodes fairness constrains, resulting in fair solutions. Furthermore, we present a collection of network topologies handling different fairness metrics, leading to a unified method capable of dealing with both individual and group bias. The resulting models have a layer of interpretability in the form of closed-form expressions for their SHAP values, consolidating their place in the responsible Artificial Intelligence landscape. Finally, these intuitions are tested on a simulation study and standard fairness benchmarks, where the proposed methods achieve satisfactory results. More concretely, the paper showcases the performance of the proposed models in terms of accuracy and fairness, studying available trade-offs on the Pareto frontier, checking the effects of changing the different hyper-parameters, and delving into the interpretation of its outputs.

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arXiv2025

Incentivized Network Dynamics in Digital Job Recruitment

Recruiting passive candidates, i.e., individuals not actively seeking jobs but open to compelling opportunities, remains one of the hardest challenges in digital recruitment. Motivated by a real collaboration with an industry partner, we introduce the Independent Halting Cascade (IHC) model: a simple but rich agent-based framework that couples network diffusion with the possibility of halting through job applications. Agents can either recommend vacancies to peers or apply themselves, and incentives increase the likelihood of recommendation, mobilizing otherwise passive candidates. The IHC bridges research on social network diffusion, coordinated task completion, and labor economics by modeling heterogeneous skills, job specificities, and network structures, including homophily. We derive analytical boundaries that characterize diffusion and failure regimes, and we show, through simulations, that the IHC reproduces the empirical chain-length distributions of Travers and Milgram, and of Dodds, with only coarse calibration. Across synthetic (ER, BA, homophilic) and real networks (SMS, e-mail, Twitter), the IHC achieves comparable or higher success rates than direct-recommendation baselines, while requiring fewer applicants. Our findings suggest that the IHC captures core mechanisms of coordinated task completion, offering both a theoretical contribution and a practical foundation for recruitment systems designed to reach and engage passive candidates.

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arXiv2025

FairLangProc: A Python package for fairness in NLP

The rise in usage of Large Language Models to near ubiquitousness in recent years has risen societal concern about their applications in decision-making contexts, such as organizational justice or healthcare. This, in turn, poses questions about the fairness of these models in critical settings, which leads to the developement of different procedures to address bias in Natural Language Processing. Although many datasets, metrics and algorithms have been proposed to measure and mitigate harmful prejudice in Natural Language Processing, their implementation is diverse and far from centralized. As a response, this paper presents FairLangProc, a comprehensive Python package providing a common implementation of some of the more recent advances in fairness in Natural Language Processing providing an interface compatible with the famous Hugging Face transformers library, aiming to encourage the widespread use and democratization of bias mitigation techniques. The implementation can be found on https://github.com/arturo-perez-peralta/FairLangProc.

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arXiv2025

Area-based epigraph and hypograph indices for functional outlier detection

Detecting outliers in Functional Data Analysis is challenging because curves can stray from the majority in many different ways. The Modified Epigraph Index (MEI) and Modified Hypograph Index (MHI) rank functions by the fraction of the domain on which one curve lies above or below another. While effective for spotting shape anomalies, their construction limits their ability to flag magnitude outliers. This paper introduces two new metrics, the Area-Based Epigraph Index (ABEI) and Area-Based Hypograph Index (ABHI) that quantify the area between curves, enabling simultaneous sensitivity to both magnitude and shape deviations. Building on these indices, we present EHyOut, a robust procedure that recasts functional outlier detection as a multivariate problem: for every curve, and for its first and second derivatives, we compute ABEI and ABHI and then apply multivariate outlier-detection techniques to the resulting feature vectors. Extensive simulations show that EHyOut remains stable across a wide range of contamination settings and often outperforms established benchmark methods. Moreover, applications to Spanish weather data and United Nations world population data further illustrate the practical utility and meaningfulness of this methodology.

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arXiv2025

Comparing Lasso and Adaptive Lasso in High-Dimensional Data: A Genetic Survival Analysis in Triple-Negative Breast Cancer

In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets where covariates far outnumber observations. We propose and evaluate four weight calculation strategies for adaptive lasso specifically designed for high-dimensional settings: ridge regression, principal component analysis (PCA), univariate Cox regression, and random survival forest (RSF) based weights. To address the inherent variability in high dimensional model selection, we develop a robust procedure that evaluates performance across multiple data partitions and selects variables based on a novel importance index. Extensive simulation studies demonstrate that adaptive lasso with ridge and PCA weights significantly outperforms standard lasso in variable selection accuracy while maintaining similar or better predictive performance across various correlation structures, censoring proportions (0-80%), and dimensionality settings. These improvements are particularly pronounced in highly-censored scenarios, making our approach valuable for real-world genetic studies with limited observed events. We apply our methodology to triple-negative breast cancer data with 234 patients, over 19500 variables and 82% censoring, identifying key genetic and clinical prognostic factors. Our findings demonstrate that adaptive lasso with appropriate weight calculation provides more stable and interpretable models for high-dimensional survival analysis.

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arXiv2025

The more the merrier: logical and multistage processors in credit scoring

Machine Learning algorithms are ubiquitous in key decision-making contexts such as organizational justice or healthcare, which has spawned a great demand for fairness in these procedures. In this paper we focus on the application of fair ML in finance, more concretely on the use of fairness techniques on credit scoring. This paper makes two contributions. On the one hand, it addresses the existent gap concerning the application of established methods in the literature to the case of multiple sensitive variables through the use of a new technique called logical processors (LP). On the other hand, it also explores the novel method of multistage processors (MP) to investigate whether the combination of fairness methods can work synergistically to produce solutions with improved fairness or accuracy. Furthermore, we examine the intersection of these two lines of research by exploring the integration of fairness methods in the multivariate case. The results are very promising and suggest that logical processors are an appropriate way of handling multiple sensitive variables. Furthermore, multistage processors are capable of improving the performance of existing methods.

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arXiv2025

Health Prognostics in Multi-sensor Systems Based on Multivariate Functional Data Analysis

Recent developments in big data analysis, machine learning, Industry 4.0, and IoT applications have enabled the monitoring and processing of multi-sensor data collected from systems, allowing for the prediction of the "Remaining Useful Life" (RUL) of system components. Particularly in the aviation industry, Prognostic Health Management (PHM) has become one of the most important practices for ensuring reliability and safety. Not only is the accuracy of RUL prediction important, but the implementability of techniques, domain adaptability, and interpretability of system degradation behaviors have also become essential. In this paper, the data collected from the multi-sensor environment of complex systems are processed using a Functional Data Analysis (FDA) approach to predict when the systems will fail and to understand and interpret the systems' life cycles. The approach is applied to the C-MAPSS datasets shared by National Aeronautics and Space Administration, and the behaviors of the sensors in aircraft engine failures are adaptively modeled with Multivariate Functional Principal Component Analysis (MFPCA). While the results indicate that the proposed method predicts the RUL competitively compared to other methods in the literature, it also demonstrates how multivariate Functional Data Analysis is useful for interpretability in prognostic studies within multi-sensor environments.

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arXiv2024

Clustering multivariate functional data using the epigraph and hypograph indices: a case study on Madrid air quality

With the rapid growth of data generation, advancements in functional data analysis (FDA) have become essential, especially for approaches that handle multiple variables at the same time. This paper introduces a novel formulation of the epigraph and hypograph indices, along with their generalized expressions, specifically designed for multivariate functional data (MFD). These new definitions account for interrelationships between variables, enabling effective clustering of MFD based on the original data curves and their first two derivatives. The methodology developed here has been tested on simulated datasets, demonstrating strong performance compared to state-of-the-art methods. Its practical utility is further illustrated with two environmental datasets: the Canadian weather dataset and a 2023 air quality study in Madrid. These applications highlight the potential of the method as a great tool for analyzing complex environmental data, offering valuable insights for researchers and policymakers in climate and environmental research.

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arXiv2024

nn2poly: An R Package for Converting Neural Networks into Interpretable Polynomials

The nn2poly package provides the implementation in R of the NN2Poly method to explain and interpret feed-forward neural networks by means of polynomial representations that predict in an equivalent manner as the original network.Through the obtained polynomial coefficients, the effect and importance of each variable and their interactions on the output can be represented. This capabiltiy of capturing interactions is a key aspect usually missing from most Explainable Artificial Intelligence (XAI) methods, specially if they rely on expensive computations that can be amplified when used on large neural networks. The package provides integration with the main deep learning framework packages in R (tensorflow and torch), allowing an user-friendly application of the NN2Poly algorithm. Furthermore, nn2poly provides implementation of the required weight constraints to be used during the network training in those same frameworks. Other neural networks packages can also be used by including their weights in list format. Polynomials obtained with nn2poly can also be used to predict with new data or be visualized through its own plot method. Simulations are provided exemplifying the usage of the package alongside with a comparison with other approaches available in R to interpret neural networks.

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arXiv2024

A bivariate two-state Markov modulated Poisson process for failure modelling

Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). The novel two-dimensional MMPP allows for dependence between the two sequences of inter-failure times, while at the same time preserves the MMPP properties, marginally. The generalization is based on the Marshall-Olkin exponential distribution. Inference is undertaken for the new model through a method combining a matching moments approach with an Approximate Bayesian Computation (ABC) algorithm. The performance of the method is shown on simulated and real datasets representing times and distances covered between consecutive failures in a public transport company. For the real dataset, some quantities of importance associated with the reliability of the system are estimated as the probabilities and expected number of failures at different times and distances covered by trains until the occurrence of a failure.

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arXiv2024

Fitting procedure for the two-state Batch Markov modulated Poisson process

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which has been proposed for the modeling of dependent events occurring in batches (as group arrivals, failures or risk events). This paper focuses on exploring the possibilities of the BMMPP for the modeling of real phenomena involving point processes with group arrivals. The first result in this sense is the characterization of the two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of moments related to the inter-event time and batch size distributions. This characterization leads to a sequential fitting approach via a moments matching method. The performance of the novel fitting approach is illustrated on both simulated and a real teletraffic data set, and compared to that of the EM algorithm. In addition, as an extension of the inference approach, the queue length distributions at departures in the queueing system BMMPP/M/1 is also estimated.

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arXiv2023

NN2Poly: A polynomial representation for deep feed-forward artificial neural networks

Interpretability of neural networks and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work, NN2Poly is proposed: a theoretical approach to obtain an explicit polynomial model that provides an accurate representation of an already trained fully-connected feed-forward artificial neural network (a multilayer perceptron or MLP). This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks, to work with arbitrarily deep MLPs in both regression and classification tasks. NN2Poly uses a Taylor expansion on the activation function, at each layer, and then applies several combinatorial properties to calculate the coefficients of the desired polynomials. Discussion is presented on the main computational challenges of this method, and the way to overcome them by imposing certain constraints during the training phase. Finally, simulation experiments as well as applications to real tabular data sets are presented to demonstrate the effectiveness of the proposed method.

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arXiv2022

Multivariate Functional Outlier Detection using the FastMUOD Indices

We present definitions and properties of the fast massive unsupervised outlier detection (FastMUOD) indices, used for outlier detection (OD) in functional data. FastMUOD detects outliers by computing, for each curve, an amplitude, magnitude and shape index meant to target the corresponding types of outliers. Some methods adapting FastMUOD to outlier detection in multivariate functional data are then proposed. These include applying FastMUOD on the components of the multivariate data and using random projections. Moreover, these techniques are tested on various simulated and real multivariate functional datasets. Compared with the state of the art in multivariate functional OD, the use of random projections showed the most effective results with similar, and in some cases improved, OD performance.

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arXiv2021

Outlier Detection for Functional Data with R Package fdaoutlier

Outlier detection is one of the standard exploratory analysis tasks in functional data analysis. We present the R package fdaoutlier which contains implementations of some of the latest techniques for detecting functional outliers. The package makes it easy to detect different types of outliers (magnitude, shape, and amplitude) in functional data, and some of the implemented methods can be applied to both univariate and multivariate functional data. We illustrate the main functionality of the R package with common functional datasets in the literature.

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