720 citations · 1.5k across the 26 of their papers we have counts for
31 papers
Wasserstein Regression with Empirical Measures and Density Estimation for Sparse Data
Yidong Zhou, Hans-Georg Müller
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods c…
Geodesic Mixed Effects Models for Repeatedly Observed/Longitudinal Random Objects
Satarupa Bhattacharjee, Hans-Georg Müller
Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear…
Functional linear and single-index models: A unified approach via Gaussian Stein identity
Krishnakumar Balasubramanian, Hans-Georg Müller, Bharath K. Sriperumbudur
Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when…
Metric Statistics: Exploration and Inference for Random Objects With Distance Profiles
Paromita Dubey, Yaqing Chen, Hans-Georg Müller
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be describe…
Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States
Paromita Dubey, Yaqing Chen, Álvaro Gajardo +5
Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasin…
Network Regression with Graph Laplacians
Yidong Zhou, Hans-Georg Müller
Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks where a network as a whole is viewed as a data point…
Predictive Distributions and the Transition from Sparse to Dense Functional Data
Álvaro Gajardo, Xiongtao Dai, Hans-Georg Müller
A representation of Gaussian distributed sparsely sampled longitudinal data in terms of predictive distributions for their functional principal component scores (FPCs) maps availab…
Single Index Fréchet Regression
Satarupa Bhattacharjee, Hans-Georg Müller
Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a directi…
Conditional Wasserstein Barycenters and Interpolation/Extrapolation of Distributions
Jianing Fan, Hans-Georg Müller
Increasingly complex data analysis tasks motivate the study of the dependency of distributions of multivariate continuous random variables on scalar or vector predictors. Statistic…
Latent Deformation Models for Multivariate Functional Data and Time Warping Separability
Cody Carroll, Hans-Georg Müller
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component func…
Autoregressive Optimal Transport Models
Changbo Zhu, Hans-Georg Müller
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field o…
Modeling Time-Varying Random Objects and Dynamic Networks
Paromita Dubey, Hans-Georg Müller
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common…
Concurrent Object Regression
Satarupa Bhattacharjee, Hans-Georg Mueller
Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations…
Uniform convergence of local Fréchet regression, with applications to locating extrema and time warping for metric space valued trajectories
Yaqing Chen, Hans-Georg Müller
Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajec…
Wasserstein Regression
Yaqing Chen, Zhenhua Lin, Hans-Georg Müller
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate prob…
Cox Point Process Regression
Álvaro Gajardo, Hans-Georg Müller
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in…
Functional Models for Time-Varying Random Objects
Paromita Dubey, Hans-Georg Müller
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elem…
Total Variation Regularized Fréchet Regression for Metric-Space Valued Data
Zhenhua Lin, Hans-Georg Müller
Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random…
Rank Dynamics for Functional Data
Yaqing Chen, Matthew Dawson, Hans-Georg Müller
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yi…
Wasserstein Gradients for the Temporal Evolution of Probability Distributions
Yaqing Chen, Hans-Georg Müller
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model th…
Fréchet Analysis Of Variance For Random Objects
Paromita Dubey, Hans-Georg Müller
Fréchet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects tha…
Principal Component Analysis for Functional Data on Riemannian Manifolds and Spheres
Xiongtao Dai, Hans-Georg Müller
Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface…
Fréchet Regression for Random Objects with Euclidean Predictors
Alexander Petersen, Hans-Georg Müller
Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statisti…
Dynamic Modeling with Conditional Quantile Trajectories for Longitudinal Snippet Data, with Application to Cognitive Decline of Alzheimer's Patients
Matthew Dawson, Hans-Georg Müller
Longitudinal data are often plagued with sparsity of time points where measurements are available. The functional data analysis perspective has been shown to provide an effective a…