arXiv subjects

Marcos Matabuena

Publications and source records attributed to Marcos Matabuena.

At least 19 recordsLinked to original sources

arXiv2026

Joint Modeling of Conditional Mean and Variability in Multilevel Functional Data: Application to Postprandial Glucose Trajectories in the AEGIS Study

Functional data analysis provides a framework for studying time-varying associations between covariates and high-frequency biological signals. In digital health, participants often contribute repeated functional trajectories, yet existing multilevel regression methods largely focus on the conditional mean, overlooking variability and its role in biological heterogeneity. We propose a heteroskedastic functional mixed-effects regression framework that jointly models the conditional mean and variance of repeated trajectories, with participant-specific random effects in both components. We also develop a participant-level bootstrap to quantify uncertainty in estimated functional parameters. We apply the method to postprandial glucose trajectories from the AEGIS study. Premeal glucose, carbohydrate intake, and meal type show distinct time-dependent associations with glucose variability, whereas HbA1c is more strongly associated with the conditional mean than with variability. Substantial between-participant differences in residual variability remain even after accounting for observed covariates. These findings show that modeling conditional variability alongside the mean provides insights into glucose regulation and individual heterogeneity that mean-focused analyses may miss. More broadly, the proposed framework enables joint characterization of average responses, variability, and participant-specific heterogeneity in repeated biological signals.

stat.ML↗

arXiv2026

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

Recent advancements in measurement technologies have facilitated the acquisition of high-resolution data in fields such as engineering, biology, and medicine. However, these observations are frequently corrupted by measurement noise. To address this challenge, we propose a denoising framework that employs diffusion models to recover the underlying error-free data distribution, thereby enabling reliable downstream analysis. Central to our framework is a novel Reproducing Kernel Hilbert Space (RKHS)-based method that trains the diffusion model using only error-contaminated data. This method admits a closed-form solution and achieves a fast convergence rate in terms of estimation error. Theoretically, we validate our approach by deriving an upper bound on the total variation distance between the distributions of the generated denoised data and the true error-free data. Extensive simulations demonstrate the superior empirical performance of our method compared to state-of-the-art baselines. Finally, we illustrate the framework's practical utility in digital health and epidemiology by applying it to Continuous Glucose Monitor (CGM) data and the association analysis between blood lipids and coronary heart disease.

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arXiv2026

Deep Learning for Random Objects in Metric Spaces: Beyond Manifold Assumptions

Deep learning (DL) methods have substantially improved predictive performance across a wide range of downstream prediction tasks, enabling new discoveries in multiple domains. However, principled DL methods for non-Euclidean random objects remain relatively scarce, despite the growing importance of modern biomedical outcomes taking the form of probability distributions, random graphs, functions, and other random objects in metric spaces. Motivated by a new generation of digital and clinical biomarkers, we propose a deep learning framework for regression with random objects in metric spaces. Our approach operates directly on the metric structure of the response space, avoiding restrictive manifold or Euclidean embedding assumptions imposed by many existing methods. At the same time, it retains modern statistical guarantees under the stated statistical assumptions. We establish statistical consistency and convergence rates for the proposed estimator, and characterize conditions under which it can mitigate the curse of dimensionality for hierarchically compositional regression functions. Extensive simulation studies demonstrate competitive predictive performance, with gains over several competing approaches in multiple Euclidean and non-Euclidean configurations. Finally, we demonstrate the practical utility of the proposed framework in two digital health case studies with distribution-valued outcomes in Wasserstein spaces, using high-resolution accelerometry and continuous glucose monitoring data. Embedding-based deep-learning methods may be less suitable when no informative low-dimensional representation exists or when the learned embedding does not adequately preserve the intrinsic geometry of the response space.

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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.

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arXiv2026

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.

stat.ME↗

arXiv2026

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↗

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.

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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 Fréchet-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.

stat.ML↗

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

Conditional Mean and Variance Estimation via \textit{k}-NN Algorithm with Automated Variance Selection

We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities of classical non-parametric \textit{k}-NN models, while integrating a data-driven variable selection step that improves empirical performance. By accurately estimating both conditional mean and variance regression functions, the method effectively reconstructs the conditional distribution and density functions for multiple families of scale-and-localization generative models. We show that our estimator can achieve fast convergence rates, and we derive practical rules for selecting the smoothing parameter~$k$ that enhance the precision of the algorithm in finite sample regimes. Extensive simulations for low, moderate and large-dimensional covariate spaces, together with a real-world biomedical application, demonstrate that the proposed method can consistently outperform the conventional \textit{k-NN} regression algorithm while being more interpretable in the model output.

stat.ME↗

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

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

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

Multilevel functional distributional models with application to continuous glucose monitoring in diabetes clinical trials

Continuous glucose monitoring (CGM) is a minimally invasive technology that measures blood glucose every few minutes for weeks or months at a time. CGM data are often collected in the free-living environment and is strongly related to sleep, physical activity and meal intake. As the timing of these activities varies substantially within- and between-individuals, it is difficult to model CGM trajectories as a function of time of day. Therefore, in practice, CGM trajectories are often reduced to one or two scalar summaries of the thousands of measurements collected for a study participant. To alleviate the potential loss of information, the cumulative distribution function (cdf) of the CGM time series was proposed as an alternative. Here we address the problem of conducting inference on cdfs in clinical trials with long follow up and frequent measurements. Our approach provides three major innovations: (1) modeling the entire cdf and preserving its monotonicity; (2) accounting for the cdfs correlation (because they are measured on the same individual), continuity (results are robust to the choice of the probability grid), and differential error (e.g., medians have lower variability than $0.99$ quantiles); and (3) preserving the family-wise error when the observed data are longitudinal samples of cdfs. We focus on modeling data collected by The Juvenile Diabetes Research Foundation Continuous Glucose Monitoring Group in a large clinical trial that collected CGM data every few minutes for 26 weeks. Our basic observation unit is the distribution of CGM observations in a four-week interval. The scientific goals are to: (1) identify and quantify the effects of factors that affect glycaemic control in type 1 diabetes patients (T1D); and (2) identify and characterize the patients who respond to treatment.

stat.ME↗

arXiv2025

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↗

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

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↗

arXiv2025

Screening for Diabetes Mellitus in the U.S. Population Using Neural Network Models and Complex Survey Designs

Complex survey designs are commonly employed in many medical cohorts. In such scenarios, developing case-specific predictive risk score models that reflect the unique characteristics of the study design is essential for minimizing selective biases in the statistical results. The objectives of this paper are to: (i) propose a general predictive framework for regression and classification using neural network (NN) modeling that incorporates survey weights into the estimation process; (ii) introduce an uncertainty quantification algorithm for model prediction tailored to data from complex survey designs; and (iii) apply this method to develop robust risk score models for assessing the risk of Diabetes Mellitus in the US population, utilizing data from the NHANES 2011-2014 cohort. The results indicate that models of varying complexity, each utilizing a different set of variables, demonstrate different discriminative power for predicting diabetes (with different economic cost), yet yield generalizable results at the population level. Although the focus is on diabetes, this NN predictive framework is adaptable for developing clinical models across a diverse range of diseases and medical cohorts. The software and data used in this paper are publicly available on GitHub.

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