arXiv subjects

Jongmin Mun

Publications and source records attributed to Jongmin Mun.

4 recordsLinked to original sources

arXiv2026

Multifidelity Computer Model Emulation Via Diffusion Model Steering and Targeted Maximum Likelihood

We develop a multifidelity method for fusing low-resolution simulations with computationally expensive high-resolution simulations, which are run infrequently and are therefore prone to bias. We formulate this fusion as a constrained optimization under missing-not-at-random (MNAR) selection bias. This formulation searches for the exponentially tilted high-resolution distribution that minimizes KL divergence from the biased baseline, subject to moment constraints derived from low-resolution simulations. This optimization requires first estimating the biased baseline conditional density $f$ as a nuisance parameter. We estimate $f$ using a score-based diffusion model. To eliminate the generative model's regularization bias that harms the downstream task, we apply targeted maximum likelihood estimation (TMLE). TMLE debiases $\hat{f}$ via a targeted exponential tilting, rendering the target parameters insensitive to first-order nuisance estimation errors. To execute this computationally, we adapt generative model steering, a technique originally developed for human-preference alignment. Using Feynman-Kac steering with a reward function based on our formulation, we simultaneously execute the exponential tilts for MNAR and TMLE at inference time, avoiding expensive retraining costs. Code available [here](https://github.com/Jong-Min-Moon/multifidel_emul_by_FK).

stat.CO↗

arXiv2026

Hybrid Partial Least Squares Regression with Multiple Functional and Scalar Predictors

Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the presence of cross-modality correlations. The proposed approach embeds multiple functional and scalar predictors into a unified hybrid Hilbert space and rigorously extends the nonlinear iterative PLS (NIPALS) algorithm. This theoretical development is complemented by a sample-level algorithm that incorporates roughness penalties to control smoothness. By exploiting the rank-one structure of the resulting optimization problem, the algorithm admits a computationally efficient closed-form solution that requires solving only linear systems at each iteration. We establish fundamental geometric properties of the proposed framework, including orthogonality of the latent scores and PLS directions. Extensive numerical studies on synthetic data, together with an application to a renal imaging study, validate these theoretical results and demonstrate the method's ability to recover predictive structure under intermodal multicollinearity, yielding parsimonious low-dimensional representations.

stat.ME↗

arXiv2025

Iterative Exploration-Driven Sparse SDP Clustering via Thompson Sampling

High-dimensional sparse clustering is a combinatorial NP-hard problem that arises from the coupling between cluster assignment and variable selection. We demonstrate that semidefinite programming (SDP) relaxation of K-means is robust to variable over-selection by establishing minimax separation bounds. Leveraging this robustness, we propose a block-coordinate ascent framework that alternates between SDP-based clustering and conservative variable selection. To address the tendency of deterministic greedy methods to become trapped in local optima, we formulate the variable selection step as a bandit problem. Crucially, to reliably evaluate feature utility and generate stochastic rewards for Thompson sampling even under imperfect intermediate cluster assignments, we employ a robust maximum mean discrepancy (MMD) permutation test. This approach introduces adaptive memory by aggregating historical variable-selection outcomes into posterior distributions, and selects features via posterior sampling, enabling stochastic exploration that promotes the inclusion of underexplored features and facilitates escape from local maxima. We establish conditions for consistent variable selection and exact cluster recovery, and extend the method to settings with unknown covariance through a scalable estimation procedure. Synthetic experiments and a real-data application in document clustering demonstrate that the proposed memory-driven randomized approach consistently outperforms state-of-the-art sparse clustering methods.

stat.ME↗

arXiv2024

Minimax Optimal Two-Sample Testing under Local Differential Privacy

We explore the trade-off between privacy and statistical utility in private two-sample testing under local differential privacy (LDP) for both multinomial and continuous data. We begin by addressing the multinomial case, where we introduce private permutation tests using practical privacy mechanisms such as Laplace, discrete Laplace, and Google's RAPPOR. We then extend our multinomial approach to continuous data via binning and study its uniform separation rates under LDP over Hölder and Besov smoothness classes. The proposed tests for both discrete and continuous cases rigorously control the type I error for any finite sample size, strictly adhere to LDP constraints, and achieve minimax separation rates under LDP. The attained minimax rates reveal inherent privacy-utility trade-offs that are unavoidable in private testing. To address scenarios with unknown smoothness parameters in density testing, we propose an adaptive test based on a Bonferroni-type approach that ensures robust performance without prior knowledge of the smoothness parameters. We validate our theoretical findings with extensive numerical experiments and demonstrate the practical relevance and effectiveness of our proposed methods.

stat.ML↗