Jongmin Mun

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.

We study pricing policy learning from batched contextual bandit data under market

shift and privacy protection. Market shift is modeled as covariate shift, where

the relationship among treatments, features, and rewards remains invariant, while

privacy is enforced through local differential privacy (LDP), which perturbs each

data point before use. Viewing the off-policy setting, covariate shift, and LDP

collectively as forms of distributional shift, we develop a policy learning algorithm

based on a unified pessimism principle that addresses all three shifts. Without

privacy, we estimate the conditional reward via nonparametric regression and

quantify its variance to construct a pessimistic estimator, yielding a policy with

minimax-optimal decision error. Under LDP, we apply the Laplace mechanism and

adjust the pessimistic estimator to account for additional uncertainty from privacy

noise. The resulting doubly pessimistic objective is then optimized to determine

the final pricing policy.

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.

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.

Based on an asymptotically optimal weighted support vector machine (SVM) that introduces label shift, a systematic procedure is derived for applying oversampling and weighted SVM to extremely imbalanced datasets with a cluster-structured positive class. This method formalizes three intuitions: (i) oversampling should reflect the structure of the positive class; (ii) weights should account for both the imbalance and oversampling ratios; (iii) synthetic samples should carry less weight than the original samples. The proposed method generates synthetic samples from the estimated positive class distribution using a Gaussian mixture model. To prevent overfitting to excessive synthetic samples, different misclassification penalties are assigned to the original positive class, synthetic positive class, and negative class. The proposed method is numerically validated through simulations and an analysis of Republic of Korea Army artillery training data.