Minwoo Chae
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Mitigating Spurious Correlation via Distributionally Robust Learning with Hierarchical Ambiguity Sets Open
Conventional supervised learning methods are often vulnerable to spurious correlations, particularly under distribution shifts in test data. To address this issue, several approaches, most notably Group DRO, have been developed. While thes…
A monotone single index model for spatially referenced multistate current status data Open
Assessment of multistate disease progression is commonplace in biomedical research, such as in periodontal disease (PD). However, the presence of multistate current status endpoints, where only a single snapshot of each subject’s progressi…
Online Bernstein-von Mises theorem Open
Online learning is an inferential paradigm in which parameters are updated incrementally from sequentially available data, in contrast to batch learning, where the entire dataset is processed at once. In this paper, we assume that mini-bat…
Nonparametric estimation of a factorizable density using diffusion models Open
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 implici…
Advances in Bayesian model selection consistency for high-dimensional generalized linear models Open
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian …
Minimax optimal density estimation using a shallow generative model with a one-dimensional latent variable Open
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 fro…
Rates of convergence for nonparametric estimation of singular distributions using generative adversarial networks Open
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 stru…
A likelihood approach to nonparametric estimation of a singular distribution using deep generative models Open
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are …
Posterior asymptotics in Wasserstein metrics on the real line Open
In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's Kullba…
Bayesian High-dimensional Semi-parametric Inference beyond sub-Gaussian Errors Open
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $β$-Hölder class with an exponentially decreasing tail, which doe…
Posterior asymptotics in Wasserstein metrics on the real line Open
In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's Kullba…
Bayesian consistency for a nonparametric stationary Markov model Open
We consider posterior consistency for a Markov model with a novel class of nonparametric prior. In this model, the transition density is parameterized via a mixing distribution function. Therefore, the Wasserstein distance between mixing m…
Bayesian sparse linear regression with unknown symmetric error Open
We study Bayesian procedures for sparse linear regression when the unknown error distribution is endowed with a non-parametric prior. Specifically, we put a symmetrized Dirichlet process mixture of Gaussian prior on the error density, wher…
A novel approach to Bayesian consistency Open
It is well-known that the Kullback–Leibler support condition implies posterior consistency in the weak topology, but is not sufficient for consistency in the total variation distance. There is a counter–example. Since then many authors hav…
A novel approach for solving an arbitrary sparse linear system Open
It has been an open problem [Saad (2003)] to find an iterative method that can solve an arbitrary sparse linear system $Ax = b$ in an efficient way (i.e. guaranteed convergence at geometric rate). We propose a novel iterative algorithm whi…