The focus is on the statistical analysis of non-Euclidean data, where random objects denote random variables and data samples that take values in general metric spaces. Data of such general type are increasingly prevalent in statistics and machine learning. The workshop covers theory, methodology and applications, with emphasis on applications to brain connectomics. Methodology for metric statistics is aimed at samples of networks, distributions, compositional data, covariance matrices and surfaces, tree data and data on manifolds, as well as complex Euclidean data such as high-dimensional and functional data that can be viewed as elements of a metric space.
Topics of interest include quantification of means, barycenters and variance and conditional Fréchet means and their implementation by regression models such as Fréchet regression and its variants. The workshop will also cover extensions of metric statistics and the analysis of random objects towards metric versions of principal component analysis, uncertainty quantification, deep learning, causal inference and longitudinal and time series methodology.
Lightning Talks and Poster Session
This workshop will include lightning talks and a poster session for early career researchers (including graduate students). If accepted, you will be asked to do both. In order to propose a lightning session talk and a poster, you must first register for the workshop, and then submit a proposal using the form that will become available on this page after you register. The registration form should not be used to propose a lightning session talk or poster.
The deadline for proposing is September 30, 2026. If your proposal is accepted, you should plan to attend the event in-person.
In-Person Registration
Seats are limited at the venue, which means that in-person registration may be capped prior to the workshop start date. If capacity is reached, a waitlist will be imposed, which the registration form will reflect. Early registration is strongly encouraged.
All in-person registrants must wait to receive an invitation to attend in-person from IMSI before traveling, which generally begin to be sent out 4-6 weeks in advance.
All registrants (online and in-person) will receive zoom links and are welcome to attend online.
Registration Fee
A non-refundable registration fee will be payable by credit card or debit card for any participants invited to attend this workshop in-person. In-person participants agree to pay the non-refundable fee by the deadline given by IMSI. Failure to pay the fee by the deadline may mean that the invitation to attend in-person is revoked.
Nabarun Deb
University of Chicago Booth School of Business
D
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Daisuke Kuriso
University of Tokyo, Graduate School of Economics
K
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Kuang-Yao Lee
Temple University
H
L
Hongzhe Li
University of Pennsylvania
E
L
Eardi Lila
University of Washington
T
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Tom Nye
University of Newcastle
B
P
Byeong Park
Seoul National University
A
P
Alex Petersen
Brigham Young University
X
S
Xiaofeng Shao
Washington University in St. Louis
B
S
Bharath Sriperumbudur
Pennsylvania State University
Z
Y
Zhigang Yao
National University of Singapore
H
Z
Hang Zhou
University of North Carolina
Y
Z
Yidong Zhou
University of California, Davis
C
Z
Changbo Zhu
University of Notre Dame
H
Z
Hongtu Zhu
University of North Carolina
V
Z
Vadim Zipunnikov
Johns Hopkins University
Y
W
Yichao Wu
University of Illinois Chicago
R
O
Ryo Okano
University of Tokyo
Z
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Zhengwu Zhang
University of North Carolina
Schedule
Monday, November 30, 2026
8:30-8:55 CST
Registration & Light Refreshments
8:55-9:00 CST
Welcome & Housekeeping
9:00-9:45 CST
Lifted PCA in the Wasserstein Space
Speaker: Jérémie Bigot (University of Bordeaux)
Principal Component Analysis (PCA) is one of the fundamental tools for statistical dimension reduction. Nevertheless, no canonical extension of PCA to distribution-valued data has emerged within the framework of optimal transport. While Wasserstein barycenters and Wasserstein least-squares regression have recently been shown to arise as canonical liftings in the Wasserstein space of Euclidean averaging and standard linear regression, an analogous lifting principle for PCA has not been considered so far. In this paper, we introduce Lifted PCA, a canonical extension of Euclidean PCA to the Wasserstein space obtained through the framework of lifting functionals in the space of probability measures by convex extension. Starting from the classical variational formulations of PCA on the Stiefel and Grassmann manifolds, we derive two equivalent minimization problems over probability measures supported on these manifolds that correspond to Wasserstein barycenters with generalized costs. We prove that these formulations are linked by an exact analogue of the equivalence between the Stiefel and Grassmann formulations of Euclidean PCA, thereby preserving the original variational structure of PCA on these manifolds after lifting. Building upon the generalized Wasserstein barycenter problem, our analysis further shows that Lifted PCA admits dual formulations and optimality conditions for its characterization, as well as equivalent multimarginal optimal transport and matching-for-teams formulations. We also establish statistical consistency for empirical estimators and develop computational algorithms based on the Wasserstein barycenter formulation over the Stiefel manifold. Our results show that while Euclidean PCA summarizes a collection of vectors by projections onto an optimal low-dimensional linear subspace, Lifted PCA summarizes a collection of probability distributions using an optimal probability measure supported on multiple low-dimensional subspaces. Numerical experiments on distributional datasets illustrate the practical performance of the proposed methodology and its benefits for distributional data analysis.
9:45-9:55 CST
Tech Break
9:55-10:40 CST
Additive Frechet Regression for Random Objects
Speaker: Byeong U. Park (Seoul National University)
Regression analysis for complex data taking values in a general metric space has gained increasing attention in recent years, particularly in the context of Frechet regression with Euclidean predictors $bX in R^{p}$. However, local Frechet regression, while more flexible than global Frechet regression, suffers from the curse of dimensionality for the case of multivariate predictors. To address this issue while maintaining model flexibility, we introduce a framework of additive structured nonparametric regression when responses are situated in a general metric space. Overcoming the challenge of the
lack of vector space structure in general metric spaces where the responses reside requires a novel approach that incorporates the additive structure via projection operators. This leads to a unified framework of additive regression for a wide range of response types, including one-dimensional distributions in Wasserstein space, network data represented by graph Laplacians and spherical data equipped with geodesic distances, among others. We establish pointwise and uniform consistency, including convergence rates, for the proposed additive Frechet regression estimators, using smooth backfitting. The practical utility of this additive model is demonstrated through applications to brain connectivity network analysis using resting-state fMRI data and distributional physical activity data.
10:40-11:15 CST
Coffee Break
11:15-12:00 CST
Which Point on My Brain Matches Which Point on Yours? Registering Cortical Surfaces by Structural Connectivity
Speaker: Zhengwu Zhang (University of North Carolina, Chapel Hill)
"Comparing brain Connectivity across people presupposes that cortical locations correspond, yet stand registration matches folding patterns, which are only loosely related to the brain wiring. This talk presents two methods that align cortical surfaces using structural connectivity itself. Representing connectivity as a continuous atlas-free density over pairs of cortical locations, encore uses a square-root transform and Fisher-Rao geometry to obtain an inverse-consistent penalty-free registration on the product of two spheres. ConSeal keeps that geometry but moves the observed streamline endpoints directly, making the alignment grid-robust and diffeomorphic by construction. On Human Connectome Project data, alignment by wiring improves prediction of cognition. I will end with open statistical problems on registration uncertainty and point processes on manifolds. "
12:00-13:00 CST
Lunch Break
13:00-13:45 CST
TBA
Speaker: Yidong Zhou
13:45-13:55 CST
Tech Break
13:55-14:40 CST
TBA
Speaker: Hongtu Zhu (University of North Carolina, Chapel Hill)
14:40-15:15 CST
Coffee Break
15:15-16:00 CST
TBA
Speaker: Karthik Bharath (University of Nottingham)
Tuesday, December 1, 2026
8:30-9:00 CST
Check-In & Light Refreshments
9:00-9:45 CST
Regression and Inference on the Bures–Wasserstein Manifold
Speaker: Hongzhe Li (University of Pennsylvania)
Covariance matrices are increasingly used to summarize complex relationships in modern biomedical data, such as gene co-expression in single-cell studies and connectivity patterns in neuroscience. An important challenge is to understand how these matrix-valued features vary with subject-level characteristics such as age, disease status, or other clinical covariates. In this talk, I will present a regression framework for covariance matrix-valued outcomes based on the Bures–Wasserstein geometry. The framework provides a principled way to model how covariance structures change with covariates and, importantly, to perform statistical inference on those changes. I will discuss methods for testing whether a covariate is associated with the covariance structure, as well as whether it has an effect after adjusting for other variables. Theoretical results justify the proposed procedures, and simulation studies demonstrate their practical performance. I will illustrate the methods using single-cell gene expression data, where covariance matrices represent gene co-expression patterns across individuals. The analysis reveals age-related changes in gene co-expression structure and demonstrates how these methods can help identify systematic changes in complex biological networks.
9:45-9:55 CST
Tech Break
9:55-10:40 CST
Fréchet Kriging for Metric Space-Valued Spatial Data
Speaker: Ryo Okano (Hitotsubashi University)
Spatial prediction of non-Euclidean data, such as probability distributions, symmetric positive definite matrices, and networks, arises in many modern applications. Such data can be naturally modeled as elements of general metric spaces, where classical kriging methods relying on vector space structures are not directly applicable. We propose Fréchet kriging, a general framework for spatial prediction of metric space-valued data. The proposed method replaces the weighted average in classical ordinary kriging with a weighted Fréchet mean, where the weights are determined from the spatial dependence structure characterized by a generalized variogram. This approach preserves the intrinsic geometry of the response space without requiring an embedding into a linear space. We establish theoretical properties of the proposed predictor and demonstrate its effectiveness through simulations and real data applications.
10:40-11:15 CST
Coffee Break
11:15-12:00 CST
Variable Selection for Partially Global Frechet Regression
Speaker: Yichao Wu (University of Illinois at Chicago)
Variable selection for Fréchet regression presents a unique challenge, as the model is defined via a weighted Fréchet mean without explicit regression coefficients. In this talk, I will review variable selection techniques for global Fréchet regression and Nadaraya-Watson Fréchet regression first. After that, I will introduce our new variable selection method for partially global Fréchet regression.
12:00-13:00 CST
Lunch Break
13:00-13:45 CST
From limits of the matrix exponential to a geodesic metric space of graphs
Speaker: Tom Nye (Newcastle University)
I will describe the construction and geometry of pipework space, a stratified geodesic metric space of edge-weighted
graphs. A key step is understanding limits of transition matrices of random walks on the vertices of graphs.
13:45-13:55 CST
Tech Break
13:55-14:40 CST
Geometry as Signal: Manifold Fitting and the Structure of Data
Speaker: Zhigang Yao (National University of Singapore)
14:40-15:15 CST
Coffee Break
15:15-16:00 CST
TBA
Speaker: Hao Chen (University of California, Davis (UC Davis))
Wednesday, December 2, 2026
8:30-9:00 CST
Check-In & Light Refreshments
9:00-9:45 CST
TBA
Speaker: Hongtu Zhu (University of North Carolina, Chapel Hill)
9:45-9:55 CST
Tech Break
9:55-10:40 CST
Functional linear and single-index regression via RKHS spectral regularization
Speaker: Bharath Sriperumbudur (Pennsylvania State University)
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 the covariates are random functions coupled with scalar responses. In this work, we consider the estimation of the index vector of a functional single-index model that relates the functional covariate, which is a sample path of a zero-mean Gaussian process, to a scalar-valued response. Based on the infinite-dimensional extension of Gaussian Stein's identity, which allows for estimating the index while being oblivious to the link function, we propose an estimator that involves solving a spectral regularized regression problem in a reproducing kernel Hilbert space (RKHS). We establish convergence rates for this estimator in the regimes of commutativity and non-commutativity of the kernel integral operator and the covariance operator of the Gaussian process. Moreover, when the model is linear, we show these rates to be minimax optimal for both the prediction and estimation errors.
10:40-11:15 CST
Coffee Break
11:15-12:00 CST
Criterion-based Object Inference
Speaker: Daisuke Kurisu (The University of Tokyo)
We propose a unified approach to constructing confidence regions and conducting hypothesis tests for random objects in general metric spaces. The proposed method bases inference on the criterion used for estimation. Under regularity conditions, we establish asymptotically exact coverage and consistent rejection of fixed alternatives. Our method can be applied to inference for Fréchet means and medians, as well as global and local Fréchet regression. Our results also include two-sample comparisons of population centers and simultaneous confidence regions for global regression. We illustrate the proposed method through applications to several real-world datasets.
12:00-13:00 CST
Lunch Break
13:00-13:50 CST
Special Discussion: Artificial Intelligence and the Future of Non-Euclidean Data Analysis
13:50-13:55 CST
Tech Break
13:55-14:55 CST
Lightning Talks
15:00-16:00 CST
Poster Session/Social Hour at IMSI
Thursday, December 3, 2026
8:30-9:00 CST
Check-In & Light Refreshments
9:00-9:45 CST
TBA
Speaker: Eardi Lila (University of Washington)
9:45-9:55 CST
Tech Break
9:55-10:40 CST
TBA
Speaker: Alex Petersen (Brigham Young University)
10:40-11:15 CST
Coffee Break
11:15-12:00 CST
TBA
Speaker: Hang Zhou (University of North Carolina, Chapel Hill)
12:00-13:00 CST
Lunch Break
13:00-13:45 CST
Hypothesis Testing for Metric Point Processes
Speaker: Kuang-Yao Lee (Temple University)
Point process data arise widely in scientific applications, however, existing methods have been developed primarily for Euclidean domains, and there is few solution for replicated point processes observed on general metric spaces. We propose a novel, unified and fully nonparametric framework for hypothesis testing on metric point processes. We represent each process as a random finite counting measure and develop a two-layer kernel embedding architecture: the first layer embeds individual counting measures into a reproducing kernel Hilbert space to test equality of metric intensity measures, while the second layer embeds their probability laws into a nested Hilbert space to test equality of the full distributions. We establish integrally strictly positive definite kernels on broad classes of Polish spaces, and formulate the resulting procedures as maximum mean discrepancy tests. We derive asymptotic null distributions for both independent and paired two-sample designs. Extensive simulations across several metric spaces demonstrate accurate size control and strong power against a range of alternatives. We further illustrate the methodology with a neuroimaging application, where the proposed approach identifies structural differences that are not captured by conventional count-based summaries. (This is joint work with Zhengwu Zhang (University of North Carolina at Chapel Hill) and Lexin Li (University of California at Berkeley)).
13:45-13:55 CST
Tech Break
13:55-14:40 CST
TBA
Speaker: Nabarun Deb (University of Chicago Booth School of Business)
14:40-15:15 CST
Coffee Break
15:15-16:00 CST
Distributional Data Analysis for Digital Health Technologies Data
Wearables, heart rate sensors, continuous glucose monitors, and smartphones produce dense data streams that are usually reduced to a few summary statistics, losing much of their information. The same data can be viewed in three ways at once: as a time series, as a function of time of day, and as a distribution of values. Each view captures different structure. This talk reviews these approaches for digital health. It covers how to choose among representations of a distribution (density, quantile, hazard, and others) and the geometry each one implies. It surveys regression methods and discusses how to combine the distributional view with the time-series and functional views. Applications include physical activity, heart rate, glucose monitoring, sleep, and mental health. I will close with open problems and connections to metric statistics for random objects.
Friday, December 4, 2026
8:30-9:00 CST
Check-In & Light Refreshments
9:00-9:45 CST
Online Monitoring for Object-valued Time Series
Speaker: Xiaofeng Shao (Washington University in St. Louis)
9:45-10:15 CST
Coffee Break
10:15-11:00 CST
Optimal Transport in Statistics: Barycenter Optimization and Regression Analysis
Speaker: Changbo Zhu (University of Notre Dame)
Optimal transport provides a geometric framework for analyzing distribution-valued data. This talk explores two fundamental tasks: averaging probability distributions and modeling their relationships with covariates. I first present scalable algorithms for computing unregularized Wasserstein barycenters of distributions represented on high-resolution grids. I then introduce Kantorovich regression, which uses transport potentials relative to Wasserstein barycenters to model distribution-valued responses with mixed distributional and Euclidean predictors. Numerical examples and applications illustrate the computational advantages and interpretability of these methods.
11:00-11:30 CST
Closing Remarks & Survey
Registration
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