arXiv subjects

Irina Gaynanova

Publications and source records attributed to Irina Gaynanova.

At least 19 recordsLinked to original sources

arXiv2026

Fast distance computation of multivariate distributions via nonparanormal transport

With the increasing availability of data objects in the form of probability distributions, there is a growing need for statistical methods tailored to distributional data. Distance measures, especially the pairwise distance matrix between data objects, provide the foundation for a wide range of modern data analysis methods, such as clustering, multidimensional scaling, and distance-based regression, among others. The Wasserstein distance is commonly used with distributional data due to its compelling optimal transport property. However, while the Wasserstein distance can be efficiently computed for univariate distributions, its application to multivariate distributions is limited due to high computational costs. To address these scalability issues, we introduce the Nonparanormal Transport (NPT) metric, a closed-form distance based on the flexible nonparanormal distribution family for modeling skewed and non-Gaussian multivariate data. Simulation studies demonstrate that NPT maintains a high level of agreement with the Wasserstein distance, while being at least 1000 times faster than its efficient variants when computing a 100-distribution pairwise distance matrix in both 2 and 5 dimensions. We illustrate the utility of NPT through a multidimensional scaling analysis of bivariate oxygen desaturation distributions of 723 individuals with sleep apnea in the Sleep Heart Health Study.

stat.ME↗

arXiv2026

Fréchet regression of multivariate distributions with nonparanormal transport

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which additionally encode dependence across univariate marginals, have received less attention and pose computational and statistical challenges. In this work, we address these challenges with a new regression approach for multivariate distributional responses, in which distributions are modeled within the semiparametric nonparanormal family. By incorporating the nonparanormal transport (NPT) metric -- an efficient closed-form surrogate for the Wasserstein distance -- into the Fréchet regression framework, our approach decomposes the problem into separate regressions of marginal distributions and their dependence structure, facilitating both efficient estimation and granular interpretation of predictor effects. We provide theoretical justification for NPT, establishing its bi-Lipschitz equivalence to the Wasserstein distance and proving that it mitigates the curse of dimensionality. We further prove uniform convergence guarantees for regression estimators, both when distributional responses are fully observed and when they are estimated from empirical samples, attaining fast convergence rates comparable to the univariate case. The utility of our method is demonstrated via simulations and an application to continuous glucose monitoring data.

stat.ME↗

arXiv2026

Beyond fixed thresholds: optimizing summaries of wearable device data via piecewise linearization of quantile functions

Wearable devices, such as actigraphy monitors and continuous glucose monitors (CGMs), capture high-frequency data, which are often summarized by the percentages of time spent within fixed thresholds. For example, actigraphy data are categorized into sedentary, light, and moderate-to-vigorous activity, while CGM data are divided into hypoglycemia, normoglycemia, and hyperglycemia based on a standard glucose range of $70\unicode{x2013}180$ mg/dL. Although scientific and clinical guidelines inform the choice of thresholds, it remains unclear whether this choice is optimal and whether the same thresholds should be applied across different populations. In this work, we define threshold optimality with loss functions that quantify discrepancies between the full empirical distributions of wearable device measurements and their discretizations based on specific thresholds. We introduce two loss functions: one that aims to accurately reconstruct the original distributions and another that preserves the pairwise sample distances. Using the Wasserstein distance as the base measure, we reformulate the loss minimization as optimal piecewise linearization of quantile functions. We solve this optimization via stepwise algorithms and differential evolution. We also formulate semi-supervised approaches where some thresholds are predefined based on scientific rationale. Applications to CGM data from two distinct populations$\unicode{x2014}$individuals with type 1 diabetes and those with normal glycemic control$\unicode{x2014}$demonstrate that data-driven thresholds vary by population and improve discriminative power over fixed thresholds.

stat.ME↗

arXiv2026

A Sparse Linear Model for Positive Definite Estimation of Covariance Matrices

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several challenges such as the correlation among the elements in the sample covariance matrix, positive definiteness and unbiased estimation of the diagonal elements. To address these challenges, we formulate a linear covariance model for estimating sparse covariance matrices and propose a penalized regression. This method is general enough to encompass existing sparse covariance estimators and can additionally consider correlation among the elements in the sample covariance matrix while avoiding unnecessary bias in the diagonal elements and preserving positive definiteness. We develop a consensus ADMM algorithm for estimation and derive $\ell_2$ convergence rate of the proposed estimator. We apply our estimator to simulated data and real data from neuroscience and genetics to describe the efficacy of our proposed method.

stat.ME↗

arXiv2025

A spectral method for multi-view subspace learning using the product of projections

Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique (individual) signal subspaces from noisy, high-dimensional measurements. Despite many proposed methods, the conditions for reliably identifying joint and individual subspaces remain unclear. We rigorously quantify these conditions, which depend on the ratio of the signal rank to the ambient dimension, principal angles between true subspaces, and noise levels. Our approach characterizes how spectrum perturbations of the product of projection matrices, derived from each view's estimated subspaces, affect subspace separation. Using these insights, we provide an easy-to-use and scalable estimation algorithm. In particular, we employ rotational bootstrap and random matrix theory to partition the observed spectrum into joint, individual, and noise subspaces. Diagnostic plots visualize this partitioning, providing practical and interpretable insights into the estimation performance. In simulations, our method estimates joint and individual subspaces more accurately than existing approaches. Applications to multi-omics data from colorectal cancer patients and nutrigenomic study of mice demonstrate improved performance in downstream predictive tasks.

stat.ML↗

arXiv2025

Smooth tensor decomposition with application to ambulatory blood pressure monitoring data

Ambulatory blood pressure monitoring (ABPM) enables continuous measurement of blood pressure and heart rate over 24 hours and is increasingly used in clinical studies. However, ABPM data are often reduced to summary statistics, such as means or medians, which obscure temporal features like nocturnal dipping and individual chronotypes. Functional data analysis methods better capture these temporal dynamics but typically treat each ABPM measurement separately, limiting their ability to leverage correlations among matched measurements. In this work, we observe that aligning ABPM data along measurement type, time, and patient ID lends itself to a tensor representation--a multidimensional array. Although tensor learning has shown great potential in other fields, it has not been applied to ABPM data. Existing tensor learning approaches often lack temporal smoothing constraints, assume no missing data, and can be computationally demanding. To address these limitations, we propose a novel smooth tensor decomposition method that incorporates a temporal smoothing penalty and accommodates missing data. We also develop an automatic procedure for selecting the optimal smoothing parameter and tensor ranks. Simulation studies demonstrate that our method reliably reconstructs smooth temporal trends from noisy, incomplete data. Application to ABPM data from patients with concurrent obstructive sleep apnea and type 2 diabetes uncovers clinically relevant associations between patient characteristics and ABPM measurements, which are missed by summary-based approaches.

stat.ME↗

arXiv2025

Truncated Gaussian copula principal component analysis with application to pediatric acute lymphoblastic leukemia patients' gut microbiome

Increasing epidemiologic evidence suggests that the diversity and composition of the gut microbiome can predict infection risk in cancer patients. Infections remain a major cause of morbidity and mortality during chemotherapy. Analyzing microbiome data to identify associations with infection pathogenesis for proactive treatment has become a critical research focus. However, the high-dimensional nature of the data necessitates the use of dimension-reduction methods to facilitate inference and interpretation. Traditional dimension reduction methods, which assume Gaussianity, perform poorly with skewed and zero-inflated microbiome data. To address these challenges, we propose a semiparametric principal component analysis (PCA) method based on a truncated latent Gaussian copula model that accommodates both skewness and zero inflation. Simulation studies demonstrate that the proposed method outperforms existing approaches by providing more accurate estimates of scores and loadings across various copula transformation settings. We apply our method, along with competing approaches, to gut microbiome data from pediatric patients with acute lymphoblastic leukemia. The principal scores derived from the proposed method reveal the strongest associations between pre-chemotherapy microbiome composition and adverse events during subsequent chemotherapy, offering valuable insights for improving patient outcomes.

stat.ME↗

arXiv2025

fastfrechet: An R package for fast implementation of Fréchet regression with distributional responses

Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021) actigraphy (Ghosal et al., 2023), and continuous glucose monitoring (Coulter et al., 2024; Matabuena et al., 2021). To accommodate the complex structure of such problems, Petersen and Müller (2019) proposed a regression framework called Fréchet regression which allows non-Euclidean responses, including distributional responses. This regression framework was further extended for variable selection by Tucker et al. (2023), and Coulter et al. (2024) (arXiv:2403.00922 [stat.AP]) developed a fast variable selection algorithm for the specific setting of univariate distributional responses equipped with the 2-Wasserstein metric (2-Wasserstein space). We present "fastfrechet", an R package providing fast implementation of these Fréchet regression and variable selection methods in 2-Wasserstein space, with resampling tools for automatic variable selection. "fastfrechet" makes distribution-based Fréchet regression with resampling-supplemented variable selection readily available and highly scalable to large data sets, such as the UK Biobank (Doherty et al., 2017).

stat.CO↗

arXiv2024

GlucoBench: Curated List of Continuous Glucose Monitoring Datasets with Prediction Benchmarks

The rising rates of diabetes necessitate innovative methods for its management. Continuous glucose monitors (CGM) are small medical devices that measure blood glucose levels at regular intervals providing insights into daily patterns of glucose variation. Forecasting of glucose trajectories based on CGM data holds the potential to substantially improve diabetes management, by both refining artificial pancreas systems and enabling individuals to make adjustments based on predictions to maintain optimal glycemic range.Despite numerous methods proposed for CGM-based glucose trajectory prediction, these methods are typically evaluated on small, private datasets, impeding reproducibility, further research, and practical adoption. The absence of standardized prediction tasks and systematic comparisons between methods has led to uncoordinated research efforts, obstructing the identification of optimal tools for tackling specific challenges. As a result, only a limited number of prediction methods have been implemented in clinical practice. To address these challenges, we present a comprehensive resource that provides (1) a consolidated repository of curated publicly available CGM datasets to foster reproducibility and accessibility; (2) a standardized task list to unify research objectives and facilitate coordinated efforts; (3) a set of benchmark models with established baseline performance, enabling the research community to objectively gauge new methods' efficacy; and (4) a detailed analysis of performance-influencing factors for model development. We anticipate these resources to propel collaborative research endeavors in the critical domain of CGM-based glucose predictions. {Our code is available online at github.com/IrinaStatsLab/GlucoBench.

q-bio.QM↗

arXiv2024

Learning Joint and Individual Structure in Network Data with Covariates

Datasets consisting of a network and covariates associated with its vertices have become ubiquitous. One problem pertaining to this type of data is to identify information unique to the network, information unique to the vertex covariates and information that is shared between the network and the vertex covariates. Existing techniques for network data and vertex covariates focus on capturing structure that is shared but are usually not able to differentiate structure that is unique to each dataset. This work formulates a low-rank model that simultaneously captures joint and individual information in network data with vertex covariates. A two-step estimation procedure is proposed, composed of an efficient spectral method followed by a refinement optimization step. Theoretically, we show that the spectral method is able to consistently recover the joint and individual components under a general signal-plus-noise model. Simulations and real data examples demonstrate the ability of the methods to recover accurate and interpretable components. In particular, the application of the methodology to a food trade network between countries with economic, developmental and geographical country-level indicators as covariates yields joint and individual factors that explain the trading patterns.

stat.ME↗

arXiv2024

Bayesian segmented Gaussian copula factor model for single-cell sequencing data

Single-cell sequencing technologies have significantly advanced molecular and cellular biology, offering unprecedented insights into cellular heterogeneity by allowing for the measurement of gene expression at an individual cell level. However, the analysis of such data is challenged by the prevalence of low counts due to dropout events and the skewed nature of the data distribution, which conventional Gaussian factor models struggle to handle effectively. To address these challenges, we propose a novel Bayesian segmented Gaussian copula model to explicitly account for inflation of zero and near-zero counts, and to address the high skewness in the data. By employing a Dirichlet-Laplace prior for each column of the factor loadings matrix, we shrink the loadings of unnecessary factors towards zero, which leads to a simple approach to automatically determine the number of latent factors, and resolve the identifiability issue inherent in factor models due to the rotational invariance of the factor loadings matrix. Through simulation studies, we demonstrate the superior performance of our method over existing approaches in conducting factor analysis on data exhibiting the characteristics of single-cell data, such as excessive low counts and high skewness. Furthermore, we apply the proposed method to a real single-cell RNA-sequencing dataset from a lymphoblastoid cell line, successfully identifying biologically meaningful latent factors and detecting previously uncharacterized cell subtypes.

stat.ME↗

arXiv2024

Fast variable selection for distributional regression with application to continuous glucose monitoring data

With the growing prevalence of diabetes and the associated public health burden, it is crucial to identify modifiable factors that could improve patients' glycemic control. In this work, we seek to examine associations between medication usage, concurrent comorbidities, and glycemic control, utilizing data from continuous glucose monitor (CGMs). CGMs provide interstitial glucose measurements, but reducing data to simple statistical summaries is common in clinical studies, resulting in substantial information loss. Recent advancements in the Frechet regression framework allow to utilize more information by treating the full distributional representation of CGM data as the response, while sparsity regularization enables variable selection. However, the methodology does not scale to large datasets. Crucially, variable selection inference using subsampling methods is computationally infeasible. We develop a new algorithm for sparse distributional regression by deriving a new explicit characterization of the gradient and Hessian of the underlying objective function, while also utilizing rotations on the sphere to perform feasible updates. The updated method is up to 10000-fold faster than the original approach, opening the door for applying sparse distributional regression to large-scale datasets and enabling previously unattainable subsampling-based inference. Applying our method to CGM data from patients with type 2 diabetes and obstructive sleep apnea, we found a significant association between sulfonylurea medication and glucose variability without evidence of association with glucose mean. We also found that overnight oxygen desaturation variability showed a stronger association with glucose regulation than overall oxygen desaturation levels.

stat.AP↗

arXiv2023

Gluformer: Transformer-Based Personalized Glucose Forecasting with Uncertainty Quantification

Deep learning models achieve state-of-the art results in predicting blood glucose trajectories, with a wide range of architectures being proposed. However, the adaptation of such models in clinical practice is slow, largely due to the lack of uncertainty quantification of provided predictions. In this work, we propose to model the future glucose trajectory conditioned on the past as an infinite mixture of basis distributions (i.e., Gaussian, Laplace, etc.). This change allows us to learn the uncertainty and predict more accurately in the cases when the trajectory has a heterogeneous or multi-modal distribution. To estimate the parameters of the predictive distribution, we utilize the Transformer architecture. We empirically demonstrate the superiority of our method over existing state-of-the-art techniques both in terms of accuracy and uncertainty on the synthetic and benchmark glucose data sets.

cs.LG↗

arXiv2022

singR: An R package for Simultaneous non-Gaussian Component Analysis for data integration

This paper introduces an R package that implements Simultaneous non-Gaussian Component Analysis for data integration. SING uses a non-Gaussian measure of information to extract feature loadings and scores (latent variables) that are shared across multiple datasets. We describe and implement functions through two examples. The first example is a toy example working with images. The second example is a simulated study integrating functional connectivity estimates from a restingstate functional magnetic resonance imaging dataset and task activation maps from a working memory functional magnetic resonance imaging dataset. The SING model can produce joint components that accurately reflect information shared by multiple datasets, particularly for datasets with non-Gaussian features such as neuroimaging.

stat.AP↗

arXiv2022

Sparse semiparametric discriminant analysis for high-dimensional zero-inflated data

Sequencing-based technologies provide an abundance of high-dimensional biological datasets with skewed and zero-inflated measurements. Classification of such data with linear discriminant analysis leads to poor performance due to the violation of the Gaussian distribution assumption. To address this limitation, we propose a new semiparametric discriminant analysis framework based on the truncated latent Gaussian copula model that accommodates both skewness and zero inflation. By applying sparsity regularization, we demonstrate that the proposed method leads to the consistent estimation of classification direction in high-dimensional settings. On simulated data, the proposed method shows superior performance compared to the existing method. We apply the method to discriminate healthy controls from patients with Crohn's disease based on microbiome data and to identify genera with the most influence on the classification rule.

stat.ME↗

arXiv2022

Exponential canonical correlation analysis with orthogonal variation

Canonical correlation analysis (CCA) is a standard tool for studying associations between two data sources; however, it is not designed for data with count or proportion measurement types. In addition, while CCA uncovers common signals, it does not elucidate which signals are unique to each data source. To address these challenges, we propose a new framework for CCA based on exponential families with explicit modeling of both common and source-specific signals. Unlike previous methods based on exponential families, the common signals from our model coincide with canonical variables in Gaussian CCA, and the unique signals are exactly orthogonal. These modeling differences lead to a non-trivial estimation via optimization with orthogonality constraints, for which we develop an iterative algorithm based on a splitting method. Simulations show on par or superior performance of the proposed method compared to the available alternatives. We apply the method to analyze associations between gene expressions and lipids concentrations in nutrigenomic study, and to analyze associations between two distinct cell-type deconvolution methods in prostate cancer tumor heterogeneity study.

stat.CO↗

arXiv2022

Hierarchical nuclear norm penalization for multi-view data

The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose signal matrices from each view into the sum of shared and individual structures, which are further used for dimension reduction, exploratory analyses, and quantifying associations across views. However, existing methods have limitations in modeling partially-shared structures due to either too restrictive models, or restrictive identifiability conditions. To address these challenges, we formulate a new model for partially-shared signals based on grouping the views into so-called hierarchical levels. The proposed hierarchy leads us to introduce a new penalty, hierarchical nuclear norm (HNN), for signal estimation. In contrast to existing methods, HNN penalization avoids scores and loadings factorization of the signals and leads to a convex optimization problem, which we solve using a dual forward-backward algorithm. We propose a simple refitting procedure to adjust the penalization bias and develop an adapted version of bi-cross-validation for selecting tuning parameters. Extensive simulation studies and analysis of the genotype-tissue expression data demonstrate the advantages of our method over existing alternatives.

stat.ME↗

arXiv2022

A case study of glucose levels during sleep using fast function on scalar regression inference

Continuous glucose monitors (CGMs) are increasingly used to measure blood glucose levels and provide information about the treatment and management of diabetes. Our motivating study contains CGM data during sleep for 174 study participants with type II diabetes mellitus measured at a 5-minute frequency for an average of 10 nights. We aim to quantify the effects of diabetes medications and sleep apnea severity on glucose levels. Statistically, this is an inference question about the association between scalar covariates and functional responses. However, many characteristics of the data make analyses difficult, including (1) non-stationary within-day patterns; (2) substantial between-day heterogeneity, non-Gaussianity, and outliers; 3) large dimensionality due to the number of study participants, sleep periods, and time points. We evaluate and compare two methods: fast univariate inference (FUI) and functional additive mixed models (FAMM). We introduce a new approach for calculating p-values for testing a global null effect of covariates using FUI, and provide practical guidelines for speeding up FAMM computations, making it feasible for our data. While FUI and FAMM are philosophically different, they lead to similar point estimators in our study. In contrast to FAMM, FUI is fast, accounts for within-day correlations, and enables the construction of joint confidence intervals. Our analyses reveal that: (1) biguanide medication and sleep apnea severity significantly affect glucose trajectories during sleep, and (2) the estimated effects are time-invariant.

stat.AP↗