Jongmin Mun

Privacy

1. 

   Minimax optimal two-sample testing under local differential privacy

   Jongmin Mun, Seungwoo Kwak, and Ilmun Kim

   arxiv preprint, Nov 2024

   Summary Paper

   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 H}"older 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.

Imbalance

1. 

   Weighted support vector machine for extremely imbalanced data

   Jongmin Mun, Sungwan Bang, and Jaeoh Kim

   Computational Statistics & Data Analysis, Mar 2025

   Summary Paper

   Data augmentation and loss function adjustments are two common techniques for imbalanced classification. In cases of extreme class imbalance, it is often standard practice to combine these two approaches. However, determining the optimal oversampling ratio and the degree of asymmetry in the loss function typically relies on heuristics. We further consider the scenario where the minority class consists of subgroups and propose a straightforward method for combining data augmentation and loss function adjustments. This method serves as a sample-based approximation of the population-level asymptotically Bayes optimal oracle procedure.

Clustering

1. High-Dimensional Sparse Clustering via Iterative Semidefinite Programming Relaxed K-Means

   Jongmin Mun, Paromita Dubey, and Yingying Fan

   arxiv preprint, May 2025

   Summary Paper

   We propose an iterative algorithm for clustering high-dimensional data, where the true signal lies in a much lower-dimensional space. Our method alternates between feature selection and clustering, without requiring precise estimation of sparse model parameters. Feature selection is performed by thresholding a rough estimate of the discriminative direction, while clustering is carried out via a semidefinite programming (SDP) relaxation of K-means. In the isotropic case, the algorithm is motivated by the minimax separation bound for exact recovery of cluster labels using varying sparse subsets of features. This bound highlights the critical role of variable selection in achieving exact recovery. We further extend the algorithm to settings with unknown sparse precision matrices, avoiding full model parameter estimation by computing only the minimally required quantities. Across a range of simulation settings, we find that the proposed iterative approach outperforms several state-of-the-art methods, especially in higher dimensions.

Brain

1. 

   In-vivo integration of soft neural probes through high-resolution printing of liquid electronics on the cranium

   Young-Geun Park, Yong Won Kwon, Chin Su Koh, Enji Kim, Dong Ha Lee, Sumin Kim, Jongmin Mun, Yeon-Mi Hong, Sanghoon Lee, Ju-Young Kim, Jae-Hyun Lee, Hyun Ho Jung, Jinwoo Cheon, Jin Woo Chang, and Jang-Ung Park

   Nature Communications, Feb 2024

   Summary Paper

   Conventional neural probes are rigid, causing damages when implanted in freely moving animals. To address this issue, we present a soft, conformable neural interface system designed for long-term, stable monitoring of single-unit neural activity in freely moving subjects. This system integrates soft neural probes implanted in the brain with liquid metal-based electronics printed on the cranial surface. In-vivo mouse studies, employing dimensionality reduction, clustering analysis, and goodness-of-fit testing, provide statistical evidence of stable neural recordings over 33 weeks and behavior-induced activation across multiple brain regions during T-maze tests.