arXiv subjects

Hyeok Kyu Kwon

Publications and source records attributed to Hyeok Kyu Kwon.

4 recordsLinked to original sources

arXiv2026

Nonparametric undirected graphical model selection using diffusion models

Undirected graphical models provide a fundamental framework for representing conditional independence structures among high-dimensional random variables. While undirected graphical model selection has become a central problem in high-dimensional statistics, most existing methods are restricted to parametric settings. In this paper, we develop a nonparametric approach to undirected graphical model selection based on diffusion models. Recent work has shown that diffusion models can adapt to the unknown graph structure of the underlying distribution, yet utilizing these models for explicit graph estimation remains unexplored. To bridge this gap, we introduce a novel diffusion-based method for nonparametric undirected graphical model selection. We establish the model selection consistency of the proposed method and demonstrate its empirical performance through extensive simulations and two real data analyses.

stat.ME↗

arXiv2026

Nonparametric estimation of a factorizable density using diffusion models

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit approach to nonparametric density estimation and study them within a statistical framework to analyze their surprising performance. A key challenge in high-dimensional statistical inference is leveraging low-dimensional structures inherent in the data to mitigate the curse of dimensionality. We assume that the underlying density exhibits a low-dimensional structure by factorizing into low-dimensional components, a property common in examples such as Bayesian networks and Markov random fields. Under suitable assumptions, we demonstrate that an implicit density estimator constructed from diffusion models adapts to the factorization structure and achieves the minimax optimal rate with respect to the total variation distance. In constructing the estimator, we design a sparse weight-sharing neural network architecture, where sparsity and weight-sharing are key features of practical architectures such as convolutional neural networks and recurrent neural networks.

math.ST↗

arXiv2025

Rates of convergence for nonparametric estimation of singular distributions using generative adversarial networks

It is common in nonparametric estimation problems to impose a certain low-dimensional structure on the unknown parameter to avoid the curse of dimensionality. This paper considers a nonparametric distribution estimation problem with a structural assumption under which the target distribution is allowed to be singular with respect to the Lebesgue measure. In particular, we investigate the use of generative adversarial networks (GANs) for estimating the unknown distribution and obtain a convergence rate with respect to the $L^1$-Wasserstein metric. The convergence rate depends only on the underlying structure and noise level. More interestingly, under the same structural assumption, the convergence rate of GAN is strictly faster than the known rate of VAE in the literature. We also obtain a lower bound for the minimax optimal rate, which is conjectured to be sharp at least in some special cases. Although our upper and lower bounds for the minimax optimal rate do not match, the difference is not significant.

math.ST↗

arXiv2024

Minimax optimal density estimation using a shallow generative model with a one-dimensional latent variable

A deep generative model yields an implicit estimator for the unknown distribution or density function of the observation. This paper investigates some statistical properties of the implicit density estimator pursued by VAE-type methods from a nonparametric density estimation framework. More specifically, we obtain convergence rates of the VAE-type density estimator under the assumption that the underlying true density function belongs to a locally Hölder class. Remarkably, a near minimax optimal rate with respect to the Hellinger metric can be achieved by the simplest network architecture, a shallow generative model with a one-dimensional latent variable.

math.ST↗