SCoDA Workshop: Statistics on Complex Data - Seoul 2026

24 Jun 2026, 09:35 → 27 Jun 2026, 19:30 Asia/Seoul

Seoul National University

Jörn Schulz (University of Stavanger), Sungkyu Jung (Seoul National University)

Join us in Seoul in 2026, June 25th - 27th, for the SCoDA workshop on Statistics for Complex Data, a global forum bringing together researchers and practitioners to discuss methodologies and challenges in non-linear and geometric statistics, including shape analysis, topological data analysis (TDA), and high-dimensional, low-sample-size (HDLSS) settings.

The SCoDA project is a collaboration between Norway (University of Stavanger, Stavanger University Hospital, University of Tromsø), South Korea (Seoul National University), and Japan (University of Tsukuba). More information about the project can be found here: SCoDA - Statistics on Complex Data.

Set in the vibrant city of Seoul on the campus of Seoul National University (SNU), the event offers an inspiring environment for exchanging ideas, fostering collaborations, and exploring the future of statistics in a world with an increasing amount of complex data.

Prior to the workshop, a Complex Data School will be held from June 24th to 25th, offering focused training in shape and geometric statistics for Master’s and PhD students.

We look forward to welcoming you to an exciting program of talks and discussions. If interested in participating, please contact the organizer as soon as possible.

 

Confirmed speakers:

Keynote speakers

• Ian Dryden (University of Nottingham, UK)
• Jae-Hun Jung (Postech, Korea)

   

Invited speakers

• Shogo Kato (Institute of Statistical Mathematics , Japan)
• Zhigang Yao (National University of Singapore, Singapore)
• Kipoong Kim (Changwon National University, Korea)
• Jongmin Lee (Pusan National University, Korea)
• Mohsen Taheri Shalmani (Kristiania University, Norway)
• Jan Terje Kvaløy (University of Stavanger, Norway)
• Daisuke Kurisu (University of Tokyo, Japan)
• Keunsu Kim (Kyushu University, Japan)
• Jeong Min Jeon (Seoul National University, Korea)
• Yvo Pokern (University College London, U.K.)
• Ho Yun (EPFL, Switzerland)
• Almond Stöcker (EPFL, Switzerland)

 

Practical information:

Participation is free, but advance registration for the workshop and/or the Complex Data School is required. Please note that only registered and confirmed participants can attend, and the workshop is offered in person only.

 

SCoDA Workshop Organizers 

Jörn Schulz (University of Stavanger, Norway)

Sungkyu Jung (Seoul National University, Korea)

Kazuyoshi Yata (University of Tsukuba, Japan)

Jisu Kim (Seoul National University, Korea)

Linda Natalie Borho (University of Stavanger, Norway)

 

Support

The ScoDA workshop will be hosted by the Institute of Data Innovation in Science of SNU, and is made possible by generous support from the SCoDA project as part of the UTFORSK programme, project number UTF-2024-10203, and the Seoul National University G-LAMP project. 

 

 

 

 

Wednesday 24 June

10:00 → 10:30 Registration: Complex Data School

10:30 → 12:00 Complex Data School: Special Topic on Shapes by Prof. Ian Dryden

12:00 → 13:30 Lunch

13:30 → 15:00 Complex Data School: Special Topic on Shapes by Prof. Ian Dryden

15:00 → 15:30 Break

15:30 → 17:00 Complex Data School: From Skeletal Model Generation to Analysis by Mohsen Taheri Shalmani & Jörn Schulz

Thursday 25 June

09:30 → 11:00 Complex Data School: From Skeletal Model Generation to Analysis by Mohsen Taheri Shalmani & Jörn Schulz

11:30 → 12:40 Lunch

12:40 → 13:00 Registration: SCoDA Workshop

13:00 → 13:10 Opening Remarks

13:10 → 14:30 Session: 1

Convener: Jaesung Park (Seoul National University)

13:10 Robust Intrinsic Scale Estimation on Metric Spaces

We formulate a general notion of intrinsic scale on metric spaces that encompasses the classical notion of dispersion on the real line. Moreover, we identify various robust examples such as intrinsic $\mathcal{S}_n$ and $\mathcal{Q}_n$ scales. Theoretical properties, including robustness, are established.

Speaker: Jongmin Lee (Department of Statistics, Pusan National University)

Jongmin Lee_SCoDA_260625.pdf

13:50 Estimation on Complex Projective Space for Electron Nuclear Double Resonance Spectroscopy

Electron-nuclear double resonance (ENDOR) spectroscopy is a sophisticated method to indirectly measure intra-molecular distances and orientations for complex biomolecules. Experimental limitations mean that the complex microwave echo signal, recorded as a real (in-phase) and imaginary (in-quadrature) component for each of the different frequencies used to excite the system, has an unidentifiable global phase and magnitude factor. Quotienting this out leads to the natural parameter space on which to perform inference: complex projective space. This work presents estimation methodology, parametric testing and nonparametric estimation based on ENDOR measurements including numerical and first theoretical results on consistency.

Speaker: Yvo Pokern (University College London)

14:30 → 14:50 Break

14:50 → 16:10 Session: 2

Convener: JEONG MIN JEON (Seoul National University)

14:50 Geodesic Difference-in-Differences

In this talk, we propose geodesic difference-in-differences (GDID), a novel DID framework for outcomes in geodesic metric spaces, such as distributions, networks, and manifold-valued data. To address the absence of algebraic operations in these spaces, we use geodesics as proxies for differences and introduce the geodesic average treatment effect on the treated (ATT) as the causal estimand. We establish the identification of the geodesic ATT and derive the convergence rate of its sample versions, employing tools from metric geometry and empirical process theory. To illustrate the practical utility of geodesic DID, we analyze health impacts of the Soviet Union’s collapse using age-at-death distributions and assess effects of U.S. electricity market liberalization on electricity generation compositions. (Joint work with Yidong Zhou, Taisuke Otsu, and Hans-Georg Mueller)

Speaker: Daisuke Kurisu (The University of Tokyo)

15:30 Regression for spherical responses with linear and spherical covariates using a scaled link function

We propose a regression model in which the responses are spherical variables and the covariates include linear and/or spherical variables. A novel link function is introduced by extending the Möbius transformation on the sphere. This link function is an anisotropic mapping that enables scale control along each axis of the spherical covariates and for each linear covariate. It generalizes several well-known link functions for circular or linear covariates. Each parameter of the link function is clearly interpretable. For the error distribution, we consider a general class of elliptically symmetric distributions, which includes the Kent distribution, the elliptically symmetric angular Gaussian distribution, and the scaled von Mises-Fisher distribution. Axes of symmetry of the error distribution are determined using a method involving parallel transport. Maximum likelihood estimation is feasible via reparameterization of the proposed model. Moreover, the parameters of the link function and the shape/scale parameters of the error distribution are orthogonal in the sense of the Fisher information matrix. The proposed regression model is illustrated using a Mid-Atlantic Ridge dataset.

Speaker: Dr Shogo Kato (Institute of Statistical Mathematics)

16:10 → 16:20 Break

16:20 → 17:40 Session: 3

Convener: Jisu KIM (Seoul National University)

16:20 Generalized Linear Model for Spherical Responses with Projection-Based Inference

Spherical observations arise in a variety of scientific disciplines, most notably in medical imaging, and yet the regression models for responses on the sphere remain relatively underdeveloped. A particular shortcoming of the existing literature lies in the absence of a rigorous framework for statistical inference. Many proposals emphasize model flexibility at the expense of theoretical tractability, while others rely on tangent-space approximations that undermine the validity of inference. In this paper, a generalized linear model for spherical responses is proposed, which is based on a canonical reparameterization of the von Mises–Fisher distribution that casts the model into the exponential family form. This formulation permits likelihood-based inference to be developed in a principled manner. Under mild regularity conditions, it is shown that the maximum likelihood estimator is consistent and asymptotically normal. A projection-based inference procedure is further developed, in which the estimated regression coefficient is decomposed into components parallel and orthogonal to the estimated mean direction, yielding asymptotically valid Wald tests for the directional and concentration effects separately. The robustness and power advantages of the proposed method over conventional procedures are confirmed through Monte Carlo simulations, and its practical utility is illustrated through an application to a LP-ds-rep dataset.

Speaker: Kipoong Kim (Changwon National University)

17:00 Robust Estimation for Directional Data via Minimum Hellinger Distance

Directional data consist of observations that lie on a unit sphere. Although the sample space is compact, outliers can still occur in practice, particularly when the data are highly concentrated. This motivates the development of robust estimation methods for directional models. Robust inference for directional data has therefore become a popular topic in recent statistical research. In this study, we propose a minimum Hellinger distance estimator (MHDE) for directional data on a sphere. While MHDE estimators are well understood in Euclidean settings, where they achieve robustness and first-order efficiency, their theoretical properties on the sphere remain largely unexplored. We establish the asymptotic normality of the proposed estimator under suitable regularity conditions. Our results show that the MHDE retains efficiency when the model is correctly specified while providing robustness against model deviations. This confirms that, as in the Euclidean setting, the estimator achieves robustness without sacrificing efficiency. Additionally, we conduct numerical experiments to investigate the finite-sample performance of the proposed method. The results corroborate the theoretical findings and demonstrate the estimator's practical effectiveness.

Speaker: Prof. Yasuhito Tsuruta (Meiji University)

Friday 26 June

09:30 → 10:30 Keynote: 1

Convener: Jörn Schulz (University of Stavanger)

09:30 Shape Analysis of Dynamic Object Data

Object oriented data analysis (OODA) provides a framework for the statistical analysis of a wide variety of highly structured data. Shapes, images, functions, covariance matrices, networks and other manifold-valued data are all examples of object data that can be analyzed using OODA methods. Shapes of 3D objects are a type of manifold-valued data, invariant to translation, rotation and scale. It is often of interest to summarize the dynamic evolution of object shapes in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres (PNS) gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the PNS methodology to 3D subshape spaces and provide some practical fitting algorithms. Further relevant approaches include smoothing splines on manifolds. The methodology is applied to placenta shape change, a sliding clamp multi-protein complex, and dynamic peptide analysis.

Speaker: Ian Dryden

10:30 → 10:50 Break

10:50 → 12:00 Session: 4

Convener: Sungkyu Jung (Seoul National University)

10:50 Kernel Ridge Regression for Spherical Responses

The aim is to propose a novel nonlinear regression framework for responses taking values on a hypersphere. Rather than performing tangent space regression, where all the sphere responses are lifted to a single tangent space on which the regression is performed, we estimate conditional Fréchet means by minimizing squared distances on the nonlinear manifold. Yet, the tangent space serves as a linear predictor space where the regression function takes values. The framework integrates Riemannian geometry techniques with functional data analysis by modelling the regression function using methods from vector-valued reproducing kernel Hilbert space theory. This formulation enables the reduction of the infinite-dimensional estimation problem to a finite-dimensional one via a representer theorem and leads to an estimation algorithm by means of Riemannian gradient descent. Explicit checkable conditions on the data that ensure the existence and uniqueness of the minimizing estimator are given.

Speaker: Almond Stoecker (EPFL)

11:25 Nike Swoosh for Cross-Subspace Alignment in PCA

Comparing empirical subspaces of mismatched dimensions is a tricky problem that naturally arises in modern high-dimensional PCA, particularly within cross-validation and distributed learning frameworks. Traditional heuristics like the scree plot often yield ambiguous "elbows," leaving the true number of underlying signals up to guesswork.
In this talk, I will present the asymptotic geometric behavior between independent empirical subspaces. By tracking the chordal (or Wasserstein) distance across varying candidate dimensions, we introduce an alternative approach to PCA rank selection. Instead of a vague scree plot elbow, our geometric risk curve forms a distinct "Nike Swoosh". The definitive global minimum - the exact bottom of the swoosh—pinpoints the true number of significant signals.

To justify this visual heuristic, we formulate the exact deterministic macroscopic phase transition between independent empirical subspaces under data splitting. In a high-dimensional regime, we prove that a half-split is strictly optimal, yielding an explicit closed-form boundary for signal recovery. Practically, our "Nike Swoosh" risk curve provides a robust metric for consistent signal extraction, and the geometric distortion of the swoosh serves as a direct indicator of whether a given finite sample (usually a few hundred) has already fallen into the high-dimensional regime.

Speaker: Ho Yun

12:00 → 13:30 Lunch

13:30 → 15:30 Session: 5

Convener: Kipoong Kim (Changwon National University)

13:30 Intrinsic Shape Statistics via Skeletal Representations

Statistical shape analysis relies fundamentally on the establishment of correspondence and the definition of suitable shape representations to detect and explain local dissimilarities between groups of objects. Most existing approaches are based on extrinsic or noninvariant properties, requiring alignment and often leading to biased results. Moreover, providing a mathematical interpretation of deformation types such as bending, twisting, or stretching remains challenging. To address these issues, we introduce an intrinsic and invariant framework based on hierarchical, locally parameterized representations using local coordinate systems, enabling reliable detection and interpretation of locational dissimilarities.
Building on this perspective, we focus on slab-shaped objects such as hippocampi and propose a locally parameterized discrete swept skeletal representation that ensures meaningful correspondence across samples. The model fitting procedure is constructed via boundary division and surface flattening, producing skeletal structures that reflect the underlying geometry of swept regions. The quality of the fitted models is evaluated using geometric criteria, including skeletal symmetry, tidiness, and the volume coverage of the implied boundary. This representation supports both visual and statistical analysis and demonstrates improved performance over existing skeletal approaches.
A further challenge is the definition of shape spaces that contain only geometrically valid objects, excluding self-intersections and other inconsistencies. To address this, we study the shape space for tubular objects based on the Elliptical Tube Representation (ETRep), constrained by the Relative Curvature Condition (RCC). The proposed methodology guarantees that geodesic paths remain within the space of valid shapes restricted by the RCC, ensuring that Fréchet means are free of local self-intersections. The framework defines an intrinsic distance based on skeletal coordinate systems and enables consistent comparison of structural variation between groups. Applications to hippocampal data illustrate how the proposed methodology supports both global and localized hypothesis testing within a geometrically valid and interpretable Riemannian framework.

Speaker: Mohsen Taheri Shalmani (University of Stavanger)

14:10 Principal Nested Submanifolds

The study of the interplay between statistics and geometry has expanded rapidly in both scope and influence over recent decades. The idea of manifold fitting can be traced back to the pioneering work of Hassler Whitney in the early 1930s. A fundamental question in this area is the following: given a data set, under what conditions can we construct a smooth (d)-dimensional surface (or manifold) that provides a good approximation to the data, and how can the quality of such a fit be quantified in terms of distance and smoothness?

In this talk, I will provide an overview of the manifold fitting problem, with particular emphasis on our recent work on principal nested submanifolds. This framework offers a flexible nonlinear approach to capturing the intrinsic geometric structure of high-dimensional data. I will also discuss several recent insights and developments at the intersection of geometry, statistics, and data science.

Speaker: Zhigang Yao (National University of Singapore)

14:50 On goodness of fit testing based on measures of deviation from Brownian bridge

In various settings goodness of fit tests are constructed based on processes which under a null hypothesis of interest converges to a Brownian bridge. Examples include classical testing of distributional assumptions, testing goodness of fit in time series models, finance model testing, choosing hyper parameters in machine learning and also testing for trend in recurrent event data. Tests are then constructed based on various ways of measuring deviation from Brownian bridge behavior, and either asymptotic null distributions or resampling methods are used to approximate the distribution of the test statistic.

In this talk I will discuss various measures of deviation from Brownian bridge, some classical and some more recent suggestions, and consider their properties. Some illustrations will be shown for applications in trend testing.

Speaker: Jan Terje Kvaløy (University of Stavanger)

15:30 → 15:50 Break

15:50 → 17:30 Young Researcher Session

Convener: KAZUYOSHI YATA (U. Tsukuba)

15:50 Inference on High-Dimensional Mean Vectors and Their Applications via Automatic Sparse Estimation Methodology

High-dimensional, low-sample-size (HDLSS) data are now common in modern scientific fields, such as genomics and medical imaging, where the number of variables significantly exceeds the number of observations. In this talk, we consider the estimation of linear combinations of high-dimensional mean vectors in multi-sample settings. Such inference is a fundamental component of various multivariate analysis techniques, including multi-sample tests and discriminant analysis. In high-dimensional regimes, classical estimators often suffer from severe noise accumulation, leading to inconsistency. To address this problem, sparse estimation techniques, such as thresholding and $L_1$-penalization, have been extensively studied, and their asymptotic properties and practical effectiveness have been discussed in several contexts. However, the performance of these methods depends heavily on the selection of tuning parameters. Common selection procedures, such as cross-validation or information criteria, can be problematic in HDLSS settings due to their heavy computational cost or the deviations from theoretical assumptions. We find that the key to improving estimation accuracy lies in understanding the geometric relationship between the estimation target and high-dimensional noise. Based on this geometric structure, we propose a novel sparse estimation method for high-dimensional mean vectors. The proposed approach effectively mitigates the parameter selection problem, operates with low computational cost, and achieves consistency under HDLSS conditions, as demonstrated both theoretically and through numerical simulations. Finally, we apply our methodology to high-dimensional discriminant analysis and evaluate its performance using real-world high-dimensional datasets.

Speaker: Tetsuya Umino (Degree Programs in Pure and Applied Sciences, Graduate School of Science and Technology, University of Tsukuba, Ibaraki, Japan)

16:15 Generalized Frechet mean with random minimizing domain

This paper introduces a novel extension of Fréchet means, referred to as generalized Fréchet means, as a comprehensive framework for describing the characteristics of random elements. The generalized Fréchet mean is defined as the minimizer of a cost function, and the framework encompasses various extensions of Fréchet means that have appeared in the literature. The most distinctive feature of the proposed framework is that it allows the domain of minimization for the empirical generalized Fréchet means to be random and different from that of its population counterpart. This flexibility broadens the applicability of the Fréchet mean framework to various statistical scenarios, including sequential dimension reduction for non-Euclidean data. We establish a strong consistency theorem for generalized Fréchet means and demonstrate the utility of the proposed framework by verifying the consistency of principal geodesic analysis on the hypersphere.

Speaker: Jaesung Park (Seoul National University)

16:40 Data Analysis with Information Centrality

Information centrality is a vertex measure of a graph, which is a harmonic mean of effective conductances defined between a given vertex and all other connected vertices. As the reciprocal of effective resistance, effective conductance serves as a higher-order connectivity measure and has a connection with a renowned mathematical data analysis technique, spectral embedding, by the graph Laplacian. The connection suggests possibility of data analysis with information centrality, by considering a data point as a vertex in a graph formed by data points. Depending on the objective, one can fix a graph and calculate an information centrality of a temporarily appended test point and consider it as an affinity measure of the test point to the data points forming the graph. This metric, which we may term test information centrality, can be interpreted as a non-linear affinity criterion for identifying normal data points in outlier detection tasks. In this talk, we will look into a demonstration of this approach to outlier detection and continuity result of test effective conductance.

Speaker: Siwon Kim (Seoul National University)

slides.pdf

17:05 Linking Cancer and Density Representations in Mammography via AJIVE and Explainability Methods

Mammography screening produces multiple images per patient, each assessed for cancer risk and breast density using the BI-RADS system. While these tasks are clinically related, density both increases cancer risk and reduces imaging sensitivity, multi-task learning models do not consistently outperform single-task baselines. This raises a natural question: how much information is truly shared between the two tasks at the level of learned neural network representations, and can explicitly separating shared from task-specific structure lead to improved predictions?

We investigate this question using Angle-Based Joint and Individual Variation Explained (AJIVE), a statistical method for decomposing shared and task-specific variation. Separate ResNet-based classifiers are trained for cancer risk and density prediction on the VinDr-Mammo dataset. Their learned feature representations are then decomposed into joint components and task-specific components. Our hypothesis being that cancer prediction may improve when using only the cancer-specific component, i.e., after removing density-related structure from the representation.

Preliminary results do not show a significant advantage of disentangled representations. This suggests either that the shared structure between the tasks is more deeply entangled than expected, or that current decomposition methods do not align well with task-relevant features in deep networks.

To interpret the decomposition in the image domain, we compare standard Grad-CAM saliency maps with a weighted variant informed by AJIVE loadings. This allows us to assess whether joint and individual components correspond to distinct anatomical or pathological regions. Alignment with annotated findings bounding boxes in VinDr-Mammo provides a clinically grounded evaluation.

Speaker: Jan Zavadil (UiT)

18:30 → 20:30 Dinner (participation by invitation only)

Saturday 27 June

09:30 → 10:30 Keynote: 2

Convener: Jisu KIM (Seoul National University)

09:30 Topological Regularization for Complex Data: Filtration Learning in Exact Multi-Parameter Persistent Homology

Abstract: The shape of complex data -- time series, functional observations, and multimodal measurements -- encodes structural information that classical statistical methods often fail to capture. Topological data analysis addresses this through persistent homology, which tracks the evolution of topological features across a filtration of the data. However, the outcome of any topological analysis depends on the choice of filtration. We present a framework for filtration learning in Exact Multi-Parameter Persistent Homology (EMPH), a method developed specifically for topological time-series analysis. Unlike conventional sliding window approaches, EMPH exploits the geometry of the Liouville torus via Fourier decomposition to derive an exact closed-form formula for the rank invariant, substantially reducing computational complexity while preserving full topological fidelity. Building on this, we formulate filtration selection as an optimization problem and propose an algorithm that learns the filtration minimizing a topological loss -- enabling data-adaptive, statistically grounded topology extraction for complex data. We demonstrate the framework on classification problems for time-series data, where the learned filtration in the multi-parameter persistence space yields improved discriminative performance over fixed filtrations. We further discuss extensions to topological regularization in generative modeling and multimodal learning, where persistence diagrams and persistence images serve as structural targets that constrain the learning objective. These results establish EMPH-based filtration learning as a flexible statistical tool for complex data analysis, providing interpretable topological summaries that are both computationally efficient and optimizable within learning frameworks.

Speaker: Jae-Hun Jung (POSTECH)

10:30 → 10:50 Break

10:50 → 12:10 Session: 6

Convener: KAZUYOSHI YATA (U. Tsukuba)

10:50 Nonnegative matrix factorization with topological regularization

Nonnegative Matrix Factorization (NMF) is a core tool for uncovering the latent structure of data. Since basis vectors encapsulate the essential features of the data, a central objective of this study is to learn them in a way that is both interpretable and structurally meaningful. In this talk, we quantify the intuition of what constitutes a “good basis” using persistent homology, and introduce Top-NMF, a novel framework that directly incorporates this topological criterion into the optimization process as a regularization term.

Speaker: Keunsu Kim

11:30 Deconvolution density estimation on Lie groups without auxiliary data

In this work, we introduce density estimation on a general Lie group when data contain measurement errors and the distribution of measurement error is unknown. We estimate the target density without additional observations, such as an observable random sample from the measurement error distribution or repeated measurements. To achieve this, we take a semiparametric approach assuming that the measurement error distribution belongs to a parametric family. We also discuss maximum likelihood estimation for the case where the target density is also parametric. We establish the identifiability of a measurement error model and derive various asymptotic properties for our estimators. The performance of our estimators is demonstrated via simulation studies.

Speaker: JEONG MIN JEON (Seoul National University)

12:10 → 12:20 Closing Remarks

12:20 → 13:30 Lunch

13:30 → 19:30 Sociel Activity (participation by invitation only)