arXiv subjects

Hee-Seok Oh

Publications and source records attributed to Hee-Seok Oh.

18 recordsLinked to original sources

arXiv2026

Dual-Homotopy Framework for Constrained EM Algorithm

We propose a new constrained EM algorithm that is applicable to general constrained estimation problems. The proposed method is based on a novel framework, the `dual-homotopy framework,' which combines deterministic annealing EM with a barrier-based optimization, enabling stable estimation under parameter constraints. Building on this framework, we further introduce an adaptive constrained EM algorithm that preserves likelihood monotonicity, regardless of the underlying distributional form or the specific structure of the constraints. Through simulation studies and a real-data analysis, both under parameter constraints, we demonstrate that the proposed algorithm yields more stable and accurate estimates than existing methods, including the standard EM algorithm.

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arXiv2026

Graph Canonical Coherence Analysis

We propose graph canonical coherence analysis (gCChA), a novel framework that extends canonical correlation analysis to multivariate graph signals in the graph frequency domain. The proposed method addresses challenges posed by the inherent features of graphs: discreteness, finiteness, and irregularity. It identifies pairs of canonical graph signals that maximize their coherence, enabling the exploration of relationships between two sets of graph signals from a spectral perspective. This framework shows how these relationships change across different structural scales of the graph. We demonstrate the usefulness of this method through applications to economic and energy datasets of G20 countries and the USPS handwritten digit dataset.

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arXiv2025

A Data-Adaptive Factor Model Using Composite Quantile Approach

This paper proposes a data-adaptive factor model (DAFM), a novel framework for extracting common factors that explain the structures of high-dimensional data. DAFM adopts a composite quantile strategy to adaptively capture the full distributional structure of the data, thereby enhancing estimation accuracy and revealing latent patterns that are invisible to conventional factor models. In this paper, we develop a practical algorithm for estimating DAFM by minimizing an objective function based on a weighted average of check functions across quantiles. We also establish the theoretical properties of the estimators, including their consistency and convergence rates. Furthermore, we derive their asymptotic distributions by introducing approximated estimators from a kernel-smoothed objective function, and propose two consistent methods for determining the number of factors. Simulation studies demonstrate that DAFM outperforms existing factor models across different data distributions, and real data analyses on volatility and forecasting further validate its effectiveness.

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arXiv2025

A data-based notion of quantiles on Hadamard spaces

This paper defines an alternative notion, described as data-based, of geometric quantiles on Hadamard spaces, in contrast to the existing methodology, described as parameter-based. In addition to having the same desirable properties as parameter-based quantiles, these data-based quantiles are shown to have several theoretical advantages related to large-sample properties like strong consistency and asymptotic normality, breakdown points, extreme quantiles and the gradient of the loss function. Using simulations, we explore some other advantages of the data-based framework, including simpler computation and better adherence to the shape of the distribution, before performing experiments with real diffusion tensor imaging data lying on a manifold of symmetric positive definite matrices. These experiments illustrate some of the uses of these quantiles by testing the equivalence of the generating distributions of different data sets and measuring distributional characteristics.

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arXiv2024

Principal Component Analysis in the Graph Frequency Domain

We propose a novel principal component analysis in the graph frequency domain for dimension reduction of multivariate data residing on graphs. The proposed method not only effectively reduces the dimensionality of multivariate graph signals, but also provides a closed-form reconstruction of the original data. In addition, we investigate several propositions related to principal components and the reconstruction errors, and introduce a graph spectral envelope that aids in identifying common graph frequencies in multivariate graph signals. We demonstrate the validity of the proposed method through a simulation study and further analyze the boarding and alighting patterns of Seoul Metropolitan Subway passengers using the proposed method.

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arXiv2024

L1 Prominence Measures for Directed Graphs

We introduce novel measures, L1 prestige and L1 centrality, for quantifying the prominence of each vertex in a strongly connected and directed graph by utilizing the concept of L1 data depth (Vardi and Zhang, Proc. Natl. Acad. Sci. U.S.A.\ 97(4):1423--1426, 2000). The former measure quantifies the degree of prominence of each vertex in receiving choices, whereas the latter measure evaluates the degree of importance in giving choices. The proposed measures can handle graphs with both edge and vertex weights, as well as undirected graphs. However, examining a graph using a measure defined over a single `scale' inevitably leads to a loss of information, as each vertex may exhibit distinct structural characteristics at different levels of locality. To this end, we further develop local versions of the proposed measures with a tunable locality parameter. Using these tools, we present a multiscale network analysis framework that provides much richer structural information about each vertex than a single-scale inspection. By applying the proposed measures to the networks constructed from the Seoul Mobility Flow Data, it is demonstrated that these measures accurately depict and uncover the inherent characteristics of individual city regions.

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arXiv2024

Cross-Spectral Analysis of Bivariate Graph Signals

With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent quantities is one of the important problems. To address this issue, we propose a cross-spectral analysis tool for bivariate graph signals. The main goal of this study is to extend the scope of spectral analysis of graph signals to multivariate graph signals. In this study, we define joint weak stationarity graph processes and introduce graph cross-spectral density and coherence for multivariate graph processes. We propose several estimators for the cross-spectral density and investigate the theoretical properties of the proposed estimators. Furthermore, we demonstrate the effectiveness of the proposed estimators through numerical experiments, including simulation studies and a real data application. Finally, as an interesting extension, we discuss robust spectral analysis of graph signals in the presence of outliers.

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arXiv2024

Geometric quantile-based measures of multivariate distributional characteristics

Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are reasonable measures of these distributional characteristics and computing confidence regions with the desired coverage.

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arXiv2024

Absolute average and median treatment effects as causal estimands on metric spaces

We define the notions of absolute average and median treatment effects as causal estimands on general metric spaces such as Riemannian manifolds, propose estimators using stratification, and prove several properties, including strong consistency. In the process, we also demonstrate the strong consistency of the weighted sample Fr\'echet means and geometric medians. Stratification allows these estimators to be utilized beyond the narrow constraints of a completely randomized experiment. After constructing confidence intervals using bootstrapping, we outline how to use the proposed estimates to test Fisher's sharp null hypothesis that the absolute average or median treatment effect is zero. Empirical evidence for the strong consistency of the estimators and the reasonable asymptotic coverage of the confidence intervals is provided through simulations in both randomized experiments and observational study settings. We also apply our methods to real data from an observational study to investigate the causal relationship between Alzheimer's disease and the shape of the corpus callosum, rejecting the aforementioned null hypotheses in cases where conventional Euclidean methods fail to do so. Our proposed methods are more generally applicable than past studies in dealing with general metric spaces.

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arXiv2024

On a Notion of Graph Centrality Based on L1 Data Depth

A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for graphical and multiscale analysis based on the L1 centrality. Specifically, the suggested analysis tools include the target plot, L1 centrality-based neighborhood, local L1 centrality, multiscale edge representation, and heterogeneity plot and index. Most importantly, our work is closely associated with the concept of data depth for multivariate data, which allows for a wide range of practical applications of the proposed measure. Throughout the paper, we demonstrate our tools with two interesting examples: the Marvel Cinematic Universe movie network and the bill cosponsorship network of the 21st National Assembly of South Korea.

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arXiv2024

Combined Quantile Forecasting for High-Dimensional Non-Gaussian Data

This study proposes a novel method for forecasting a scalar variable based on high-dimensional predictors that is applicable to various data distributions. In the literature, one of the popular approaches for forecasting with many predictors is to use factor models. However, these traditional methods are ineffective when the data exhibit non-Gaussian characteristics such as skewness or heavy tails. In this study, we newly utilize a quantile factor model to extract quantile factors that describe specific quantiles of the data beyond the mean factor. We then build a quantile-based forecast model using the estimated quantile factors at different quantile levels as predictors. Finally, the predicted values at the various quantile levels are combined into a single forecast as a weighted average with weights determined by a Markov chain based on past trends of the target variable. The main idea of the proposed method is to incorporate a quantile approach to a forecasting method to handle non-Gaussian characteristics effectively. The performance of the proposed method is evaluated through a simulation study and real data analysis of PM2.5 data in South Korea, where the proposed method outperforms other existing methods in most cases.

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arXiv2023

Quantiles on global non-positive curvature spaces

This paper develops a notion of geometric quantiles on Hadamard spaces, also known as global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function at quantiles on Hadamard manifolds, we investigate asymptotic properties of sample quantiles on Hadamard manifolds, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space and, in particular, an explicit formula for the gradient of the quantile loss function, along with experiments using simulated and real single-cell RNA sequencing data.

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arXiv2023

Moving sum procedure for change point detection under piecewise linearity

We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.

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arXiv2022

Robust Geodesic Regression

This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables. The existing work on geodesic regression uses the sum-of-squared errors to find the solution, but as in the classical Euclidean case, the least-squares method is highly sensitive to outliers. In this paper, we use M-type estimators, including the $L_1$, Huber and Tukey biweight estimators, to perform robust geodesic regression, and describe how to calculate the tuning parameters for the latter two. We also show that, on compact symmetric spaces, all M-type estimators are maximum likelihood estimators, and argue for the overall superiority of the $L_1$ estimator over the $L_2$ and Huber estimators on high-dimensional manifolds and over the Tukey biweight estimator on compact high-dimensional manifolds. Results from numerical examples, including analysis of real neuroimaging data, demonstrate the promising empirical properties of the proposed approach.

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arXiv2021

Spherical Principal Curves

This paper presents a new approach for dimension reduction of data observed in a sphere. Several dimension reduction techniques have recently developed for the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted to implement principal curves on Riemannian manifolds. However, this approach uses approximations to deal with data on Riemannian manifolds, which causes distorted results. In this study, we propose a new approach to construct principal curves on a sphere by a projection of the data onto a continuous curve. Our approach lies in the same line of Hastie and Stuetzle (1989) that proposed principal curves for Euclidean space data. We further investigate the stationarity of the proposed principal curves that satisfy the self-consistency on a sphere. Results from real data analysis with earthquake data and simulation examples demonstrate the promising empirical properties of the proposed approach.

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arXiv2021

Lévy Adaptive B-spline Regression via Overcomplete Systems

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (Lévy Adaptive B-Spline regression) model, an extension of the LARK models, for the estimation of functions with varying degrees of smoothness. LABS model is a LARK with B-spline bases as generating kernels. The B-spline basis consists of piecewise k degree polynomials with k-1 continuous derivatives and can express systematically functions with varying degrees of smoothness. By changing the orders of the B-spline basis, LABS can systematically adapt the smoothness of functions, i.e., jump discontinuities, sharp peaks, etc. Results of simulation studies and real data examples support that this model catches not only smooth areas but also jumps and sharp peaks of functions. The proposed model also has the best performance in almost all examples. Finally, we provide theoretical results that the mean function for the LABS model belongs to the certain Besov spaces based on the orders of the B-spline basis and that the prior of the model has the full support on the Besov spaces.

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arXiv2020

Multi-feature Clustering of Step Data using Multivariate Functional Principal Component Analysis

This paper presents a new statistical method for clustering step data, a popular form of health record data easily obtained from wearable devices. Since step data are high-dimensional and zero-inflated, classical methods such as K-means and partitioning around medoid (PAM) cannot be applied directly. The proposed method is a novel combination of newly constructed variables that reflect the inherent features of step data, such as quantity, strength, and pattern, and a multivariate functional principal component analysis that can integrate all the features of the step data for clustering. The proposed method is implemented by applying a conventional clustering method such as K-means and PAM to the multivariate functional principal component scores obtained from these variables. Simulation studies and real data analysis demonstrate significant improvement in clustering quality.

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arXiv2019

Ensemble Patch Transformation: A New Tool for Signal Decomposition

This paper considers the problem of signal decomposition and data visualization. For this purpose, we introduce a new multiscale transform, termed `ensemble patch transformation' that enhances identification of local characteristics embedded in a signal and provides multiscale visualization according to different levels; hence, it is useful for data analysis and signal decomposition. In literature, there are data-adaptive decomposition methods such as empirical mode decomposition (EMD) by Huang et al. (1998). Along the same line of EMD, we propose a new decomposition algorithm that extracts meaningful components from a signal that belongs to a large class of signals, compared to the previous methods. Some theoretical properties of the proposed algorithm are investigated. To evaluate the proposed method, we analyze several synthetic examples and a real-world signal.

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