arXiv subjects

Marcos Matabuena

Publications and source records attributed to Marcos Matabuena.

At least 19 recordsLinked to original sources

arXiv2026

Capturing the Curve: Functional Data Analysis for Validated Digital Outcome Measures

Digital health technologies enable high-frequency collection of data in near-continuous time and capture rich information about the health of individuals. The raw data collected by these devices often have a hierarchical functional structure: repeated physiological functions are observed over time and on multiple time scales (seconds, days, weeks). While many summaries can be derived from digital data, typically, only a small subset of pre-defined scalars is validated as outcome measures in clinical trials. We explore data-driven summaries based on between-subject scores from Multilevel Functional Principal Component Analysis (MFPCA), which are low-dimensional representations of functional data with robust statistical properties. Specifically, we compute MFPCA projection scores with respect to a reference population, summarising how individuals differ from the dominant directions of variation at each hierarchical level. Through a simulation study based on smartwatch electrocardiogram (ECG) signals, we compare MFPCA scores with pre-specified summaries in terms of validation criteria, including test-retest reliability and known-groups discrimination. We demonstrate that MFPCA scores generally have high reliability and can discriminate between groups across simulated scenarios of change. This offers an advantage when digital tools enable the measurement of novel physiological signals and the characteristics of the change are not yet defined. Finally, using knee flexion-extension data from individuals living with Parkinson's disease, we demonstrate that one of the MFPCA scores more strongly correlates with established gold-standard metrics and can detect clinical change, compared to a pre-specified scalar. We conclude that MFPCA-derived scores retain more information than typical outcome measures and open the door to using learning representation strategies in clinical trial settings.

stat.AP↗

arXiv2026

Gaussian mixture models in Hilbert spaces via kernel methods

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.

stat.ML↗

arXiv2026

Random-Effects Algorithm for Random Objects in Metric Spaces

Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random effects is a critical modeling step for efficient estimation and personalized prediction. Although mixed-effects models are well established for scalar outcomes and, more recently, for functional data in Hilbert spaces, general random-effects frameworks for objects in metric spaces remain underdeveloped. In this paper, we propose a nonlinear Fr\'echet-based algorithm for random-effects modeling of arbitrary random objects defined on a metric space. Using M-estimation theory, we establish conditions under which the proposed metric-space prediction target is consistently estimated under a working random-effects formulation. We then evaluate the empirical performance of the proposed method using both synthetic data and digital health datasets that require practical tools for analyzing random objects in metric spaces, such as multivariate probability distributions and random graphs. We show that, although our method is developed beyond Hilbert spaces, it can outperform existing Hilbert space-based methods.

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arXiv2026

Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes

Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression and treatment response that conventional summary measures miss. Motivated by a 26-week clinical trial comparing the closed-loop insulin delivery system t:slim X2 with standard therapy in children with type 1 diabetes, we propose a probabilistic framework to model the continuous-time evolution of time-indexed distributions using continuous glucose monitoring data (CGM) collected every five minutes. We represent the glucose distribution as a Gaussian mixture, with time-varying mixture weights governed by a neural ODE. We estimate the model parameter using a distribution-matching criterion based on the maximum mean discrepancy. The resulting framework is interpretable, computationally efficient, and sensitive to subtle temporal distributional changes. Applied to CGM trial data, the method detects treatment-related improvements in glucose dynamics that are difficult to capture with traditional analytical approaches.

stat.ML↗

arXiv2025

Distributional Random Forests for Complex Survey Designs

We study estimation of the conditional law $P(Y|X = x)$ and continuous measurable maps of it when $Y \in \mathcal{Y}$ takes values in a locally compact Polish space (e.g., $\mathbb{R}^d$), $X \in \mathbb{R}^p$, and the observations arise from a complex survey design: a single- or multi-stage sampling scheme that may involve unequal selection, stratification, and clustering. We propose a survey-calibrated distributional random forest (SDRF) that incorporates complex-design features via the pseudo-population bootstrap, PSU-level honesty, and a Maximum Mean Discrepancy (MMD) split criterion computed from kernel mean embeddings of design-weighted node distributions. We provide a framework for analyzing forest-based estimators under various survey designs; establish consistency for both finite- and super-population conditional laws under explicit conditions on the design, kernel, resampling multipliers, and tree partitions. As far as we are aware, these are the first results on model-free estimation of conditional distributions under survey designs. Simulations under a stratified two-stage cluster design expose the systematic bias incurred by ignoring survey structure. We illustrate the broad applicability of SDRF on NHANES, estimating the conditional joint tolerance regions for two diabetes biomarkers, revealing subgroup-level distributional heterogeneity relevant to diabetes risk profiling in the U.S. population.

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arXiv2025

ROC Analysis with Covariate Adjustment Using Neural Network Models: Evaluating the Role of Age in the Physical Activity-Mortality Association

The receiver operating characteristic (ROC) curve and its summary measure, the Area Under the Curve (AUC), are well-established tools for evaluating the efficacy of biomarkers in biomedical studies. Compared to the traditional ROC curve, the covariate-adjusted ROC curve allows for individual evaluation of the biomarker. However, the use of machine learning models has rarely been explored in this context, despite their potential to develop more powerful and sophisticated approaches for biomarker evaluation. The goal of this paper is to propose a framework for neural network-based covariate-adjusted ROC modeling that allows flexible and nonlinear evaluation of the effectiveness of a biomarker to discriminate between two reference populations. The finite-sample performance of our method is investigated through extensive simulation tests under varying dependency structures between biomarkers, covariates, and referenced populations. The methodology is further illustrated in a clinically case study that assesses daily physical activity - measured as total activity time (TAC), a proxy for daily step count-as a biomarker to predict mortality at three, five and eight years. Analyzes stratified by sex and adjusted for age and BMI reveal distinct covariate effects on mortality outcomes. These results underscore the importance of covariate-adjusted modeling in biomarker evaluation and highlight TAC's potential as a functional capacity biomarker based on specific individual characteristics.

stat.ME↗

arXiv2025

Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces

This paper introduces a framework for uncertainty quantification in regression models defined on metric spaces. Using a proposed notion of homoscedasticity, we define a conformal prediction algorithm that provides finite-sample marginal coverage guarantees and fast convergence rates to the oracle prediction region. For heteroscedastic settings, we introduce a kNN procedure that yields locally adaptive prediction radii in general metric spaces. Although this procedure does not provide the same finite-sample guarantees as the conformal algorithm, it is designed to improve local coverage calibration without imposing smoothing assumptions. Both procedures are compatible with a broad range of regression algorithms and scale to large datasets, allowing practitioners to use their preferred models and incorporate domain-specific knowledge. Building on the heteroscedastic $k$NN approach, we also develop a flexible sequential extension for metric-space-valued time series based on nearest-neighbor expert aggregation. We establish the consistency of the proposed estimators under minimal conditions. Finally, we illustrate the practical utility of our framework in personalized medicine applications involving random objects such as probability distributions and graph Laplacians.

stat.ML↗

arXiv2025

Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spaces

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties, the integration of depth measures into regression modeling to provide prediction regions remains a largely underexplored area of research. To address this gap, we propose a novel, model-free uncertainty quantification algorithm based on conditional depth measures--specifically, conditional kernel mean embeddings and an integrated depth measure. These new algorithms can be used to define prediction and tolerance regions when predictors and responses are defined in separable Hilbert spaces. The use of kernel mean embeddings ensures faster convergence rates in prediction region estimation. To enhance the practical utility of the algorithms with finite samples, we also introduce a conformal prediction variant that provides marginal, non-asymptotic guarantees for the derived prediction regions. Additionally, we establish both conditional and unconditional consistency results, as well as fast convergence rates in certain homoscedastic settings. We evaluate the finite--sample performance of our model in extensive simulation studies involving various types of functional data and traditional Euclidean scenarios. Finally, we demonstrate the practical relevance of our approach through a digital health application related to physical activity, aiming to provide personalized recommendations

stat.ML↗

arXiv2025

Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data

Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over time and how these changes may reflect the progression of chronic diseases such as diabetes. We introduce a probabilistic model based on a Gaussian mixture that captures the evolution of a continuous-time stochastic process. Our approach combines a nonparametric estimate of the distribution, obtained with Maximum Mean Discrepancy (MMD), and a Neural Ordinary Differential Equation (Neural ODE) that governs the temporal evolution of the mixture weights. The model is highly interpretable, detects subtle distribution shifts, and remains computationally efficient. We illustrate the broad utility of our approach in a 26-week clinical trial that treats all continuous glucose monitoring (CGM) time series as the primary outcome. This method enables rigorous longitudinal comparisons between the treatment and control arms and yields characterizations that conventional summary-based clinical trials analytical methods typically do not capture.

stat.ML↗

arXiv2025

Variable Selection for Fixed and Random Effects in Multilevel Functional Mixed Effects Models

We develop a new method for simultaneously selecting fixed and random effects in a multilevel functional regression model. The proposed method is motivated by accelerometer-derived physical activity data from the 2011-12 cohort of the National Health and Nutrition Examination Survey (NHANES), where we are interested in identifying age and race-specific heterogeneity in covariate effects on the diurnal patterns of physical activity across the lifespan. Existing methods for variable selection in function-on-scalar regression have primarily been designed for fixed effect selection and for single-level functional data. In high-dimensional multilevel functional regression, the presence of cluster-specific heterogeneity in covariate effects could be detected through sparsity in fixed and random effects, and for this purpose, we propose a multilevel functional mixed effects selection (MuFuMES) method. The fixed and random functional effects are modelled using splines, with spike-and-slab group lasso (SSGL) priors on the unknown parameters of interest and a computationally efficient MAP estimation approach is employed for mixed effect selection through an Expectation Conditional Maximization (ECM) algorithm. Numerical analysis using simulation study illustrates the satisfactory selection accuracy of the variable selection method in having a negligible false-positive and false-negative rate. The proposed method is applied to the accelerometer data from the NHANES 2011-12 cohort, where it effectively identifies age and race-specific heterogeneity in covariate effects on the diurnal patterns of physical activity, recovering biologically meaningful insights.

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arXiv2025

Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age

Many problems within personalized medicine and digital health rely on the analysis of continuous-time functional biomarkers and other complex data structures emerging from high-resolution patient monitoring. In this context, this work proposes new optimization-based variable selection methods for multivariate, functional, and even more general outcomes in metrics spaces based on best-subset selection. Our framework applies to several types of regression models, including linear, quantile, or non parametric additive models, and to a broad range of random responses, such as univariate, multivariate Euclidean data, functional, and even random graphs. Our analysis demonstrates that our proposed methodology outperforms state-of-the-art methods in accuracy and, especially, in speed-achieving several orders of magnitude improvement over competitors across various type of statistical responses as the case of mathematical functions. While our framework is general and is not designed for a specific regression and scientific problem, the article is self-contained and focuses on biomedical applications. In the clinical areas, serves as a valuable resource for professionals in biostatistics, statistics, and artificial intelligence interested in variable selection problem in this new technological AI-era.

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arXiv2024

Denoising Data with Measurement Error Using a Reproducing Kernel-based Diffusion Model

The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement devices. Motivated by this challenge, we propose a denoising framework that employs diffusion models to generate denoised data whose distribution closely approximates the unobservable, error-free data, thereby permitting standard data analysis based on the denoised data. The key element of our framework is a novel Reproducing Kernel Hilbert Space-based method that trains the diffusion model with only error-contaminated data, admits a closed-form solution, and achieves a fast convergence rate in terms of estimation error. Furthermore, we verify the effectiveness of our method by deriving an upper bound on the Kullback--Leibler divergence between the distributions of the generated denoised data and the error-free data. A series of conducted simulations also verify the promising empirical performance of the proposed method compared to other state-of-the-art methods. To further illustrate the potential of this denoising framework in a real-world application, we apply it in a digital health context, showing how measurement error in continuous glucose monitors can influence conclusions drawn from a clinical trial on diabetes Mellitus disease.

stat.ME↗

arXiv2024

Glucodensity Functional Profiles Outperform Traditional Continuous Glucose Monitoring Metrics

Continuous glucose monitoring (CGM) data has revolutionized the management of type 1 diabetes, particularly when integrated with insulin pumps to mitigate clinical events such as hypoglycemia. Recently, there has been growing interest in utilizing CGM devices in clinical studies involving healthy and diabetes populations. However, efficiently exploiting the high temporal resolution of CGM profiles remains a significant challenge. Numerous indices -- such as time-in-range metrics and glucose variability measures -- have been proposed, but evidence suggests these metrics overlook critical aspects of glucose dynamic homeostasis. As an alternative method, this paper explores the clinical value of glucodensity metrics in capturing glucose dynamics -- specifically the speed and acceleration of CGM time series -- as new biomarkers for predicting long-term glucose outcomes. Our results demonstrate significant information gains, exceeding 20\% in terms of adjusted $R^2$, in forecasting glycosylated hemoglobin (HbA1c) and fasting plasma glucose (FPG) at five and eight years from baseline AEGIS data, compared to traditional non-CGM and CGM glucose biomarkers. These findings underscore the importance of incorporating more complex CGM functional metrics, such as the glucodensity approach, to fully capture continuous glucose fluctuations across different time-scale resolutions.

stat.AP↗

arXiv2024

Conformal Prediction in Dynamic Biological Systems

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial because it addresses the challenges posed by nonlinearity and parameter sensitivity, allowing us to properly understand and extrapolate the behavior of complex biological systems. Here, we focus on dynamic models represented by deterministic nonlinear ordinary differential equations. Many current UQ approaches in this field rely on Bayesian statistical methods. While powerful, these methods often require strong prior specifications and make parametric assumptions that may not always hold in biological systems. Additionally, these methods face challenges in domains where sample sizes are limited, and statistical inference becomes constrained, with computational speed being a bottleneck in large models of biological systems. As an alternative, we propose the use of conformal inference methods, introducing two novel algorithms that, in some instances, offer non-asymptotic guarantees, enhancing robustness and scalability across various applications. We demonstrate the efficacy of our proposed algorithms through several scenarios, highlighting their advantages over traditional Bayesian approaches. The proposed methods show promising results for diverse biological data structures and scenarios, offering a general framework to quantify uncertainty for dynamic models of biological systems.The software for the methodology and the reproduction of the results is available at https://zenodo.org/doi/10.5281/zenodo.13644870.

stat.ML↗

arXiv2024

Uncertainty quantification for intervals

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating outcomes with a range format. As interest in automating healthcare decisions grows, uncertainty quantification via predictive regions becomes essential for developing reliable and trustworthy predictive algorithms. However, the statistical literature currently lacks a general methodology for interval targets, especially when these outcomes are incomplete due to censoring. We propose an uncertainty quantification algorithm for interval responses and establish its theoretical properties using empirical process arguments based on a newly developed class of functions specifically designed for these interval data structures. Although this paper primarily focuses on deriving predictive regions for interval-censored data, the approach can also be applied to other statistical modeling tasks, such as goodness-of-fit assessments. Finally, the applicability of the method is demonstrated through simulations, showing up to a 60\% improvement in conditional coverage. Our new algorithm is also applied to various biomedical contexts, including two clinical examples: i) sleep duration and its association with cardiovascular diseases, and ii) survival time in relation to physical activity levels.

stat.ME↗

arXiv2024

Functional Time Transformation Model with Applications to Digital Health

The advent of wearable and sensor technologies now leads to functional predictors which are intrinsically infinite dimensional. While the existing approaches for functional data and survival outcomes lean on the well-established Cox model, the proportional hazard (PH) assumption might not always be suitable in real-world applications. Motivated by physiological signals encountered in digital medicine, we develop a more general and flexible functional time-transformation model for estimating the conditional survival function with both functional and scalar covariates. A partially functional regression model is used to directly model the survival time on the covariates through an unknown monotone transformation and a known error distribution. We use Bernstein polynomials to model the monotone transformation function and the smooth functional coefficients. A sieve method of maximum likelihood is employed for estimation. Numerical simulations illustrate a satisfactory performance of the proposed method in estimation and inference. We demonstrate the application of the proposed model through two case studies involving wearable data i) Understanding the association between diurnal physical activity pattern and all-cause mortality based on accelerometer data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 and ii) Modelling Time-to-Hypoglycemia events in a cohort of diabetic patients based on distributional representation of continuous glucose monitoring (CGM) data. The results provide important epidemiological insights into the direct association between survival times and the physiological signals and also exhibit superior predictive performance compared to traditional summary based biomarkers in the CGM study.

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arXiv2024

Beyond Scalar Metrics: Functional Data Analysis of Postprandial Continuous Glucose Monitoring in the AEGIS Study

Postprandial glucose collected through continuous glucose monitoring (CGM) provides critical information for assessing metabolic capacity and guiding dietary recommendations. Traditional approaches summarize these data into scalar measures, such as 2-hour AUC or peak glucose, potentially overlooking temporal dynamics. We propose analyzing entire CGM trajectories using multilevel functional data analysis (FDA), which accounts for the smooth, hierarchical nature of glucose responses. Applying these methods to AEGIS study participants without diabetes, we illustrate how FDA characterizes variability in postprandial responses and links dietary/patient characteristics to glucose dynamics. We further extend the r-square metric to hierarchical functional models to quantify explanatory power. Our results show that dietary effects vary across the 6-hour postprandial window-for example, fiber blunts responses after 90 minutes, while fats reduce early rises within 50 minutes. Moreover, metabolic responses differ between normoglycemic and prediabetic individuals. These findings demonstrate that functional approaches reveal temporal and stratified insights into postprandial glucose regulation that scalar methods cannot capture.

q-bio.QM↗

arXiv2024

Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces

Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into regression modeling for establishing prediction regions remains underexplored. To address this gap, we propose a novel method utilizing a model-free uncertainty quantification algorithm based on conditional depth measures and conditional kernel mean embeddings. This enables the creation of tailored prediction and tolerance regions in regression models handling complex statistical responses and predictors in separable Hilbert spaces. Our focus in this paper is exclusively on examples where the response is a functional data object. To enhance practicality, we introduce a conformal prediction algorithm, providing non-asymptotic guarantees in the derived prediction region. Additionally, we establish both conditional and unconditional consistency results and fast convergence rates in some special homoscedastic cases. We evaluate the model finite sample performance in extensive simulation studies with different function objects as probability distributions and functional data. Finally, we apply the approach in a digital health application related to physical activity, aiming to offer personalized recommendations in the US. population based on individuals' characteristics.

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