arXiv subjects

YoonHaeng Hur

Publications and source records attributed to YoonHaeng Hur.

9 recordsLinked to original sources

arXiv2026

Cluster-Aware Matching via Laplacian Optimal Transport

In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure. In such cases, as individual points are often interchangeable within a coherent region, finding a robust region-to-region alignment is more desirable than establishing a precise point-to-point correspondence. To this end, we propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT). The key idea is to regularize the optimal transport problem with quadratic Laplacian terms constructed from similarity graphs of the point clouds, which encourages the optimal coupling to respect the cluster structure of both point sets. We also introduce Refined Simultaneous Clustering (RSC), a method that leverages the cluster-aware coupling obtained from LapOT to produce consistent partitions across the point sets, which can overcome the limitations of independent clustering and yield more stable and interpretable results. We demonstrate the effectiveness of our approach through theoretical analysis and empirical experiments, showing that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.

stat.ML↗

arXiv2026

Weighted Conformal Clustering

Clustering is a central tool for discovering latent structure in unlabeled data; yet modern clustering pipelines often end with a hard assignment of each observation to a cluster without rigorous measures of assignment uncertainty. We propose a novel weighted conformal approach for constructing valid confidence sets for cluster labels. The key difficulty is that the labels available for calibration are not observed ground-truth labels, but synthetic labels produced by a data-dependent clustering algorithm. Our method develops a conformal inference algorithm that corrects the resulting mismatch with the latent target labels through weights by formulating conformal clustering as a conditional label-distribution shift problem. We first derive an oracle procedure that attains finite-sample marginal coverage and then develop a computationally tractable and implementable version using estimated conditional label probabilities and novel augmented calibration. We show that the coverage of the estimated-weight procedure depends on the estimator, giving an explicit bound on the loss relative to the nominal level. Empirical studies demonstrate that the proposed weighted approach offers improvements over the recently proposed split conformal clustering procedure in terms of informative confidence set size, especially in nonlinear and high-dimensional clustering applications.

stat.ME↗

arXiv2026

Inference for Clustering: Conformal Sets for Cluster Labels

While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence sets for cluster labels. The key challenge is that labels are unobserved and estimated from data, so naively using deterministic cluster labels can violate exchangeability and induce severe under-coverage. To address this, we propose split conformal clustering with stochastic labels, which samples labels from soft cluster labels, fits a soft classifier to predict these stochastic labels, and calibrates conformal scores to construct confidence sets for cluster labels at any query point. We establish a finite-sample lower bound on marginal coverage that reveals how under-coverage is controlled by two properties of the clustering algorithm: consistency of estimated soft labels and replace-one stability. Under mild conditions, we prove asymptotic coverage and verify these conditions for correctly specified parametric mixture models. Simulations for mixture models show that our method attains target coverage with informative set sizes, validating our theoretical results. Applications to clustering cell types in single-cell RNA-seq data demonstrate the practical utility and interpretability of our approach to quantifying cluster label uncertainty.

stat.ME↗

arXiv2024

A Convexified Matching Approach to Imputation and Individualized Inference

We introduce a new convexified matching method for missing value imputation and individualized inference inspired by computational optimal transport. Our method integrates favorable features from mainstream imputation approaches: optimal matching, regression imputation, and synthetic control. We impute counterfactual outcomes based on convex combinations of observed outcomes, defined based on an optimal coupling between the treated and control data sets. The optimal coupling problem is considered a convex relaxation to the combinatorial optimal matching problem. We estimate granular-level individual treatment effects while maintaining a desirable aggregate-level summary by properly constraining the coupling. We construct transparent, individual confidence intervals for the estimated counterfactual outcomes. We devise fast iterative entropic-regularized algorithms to solve the optimal coupling problem that scales favorably when the number of units to match is large. Entropic regularization plays a crucial role in both inference and computation; it helps control the width of the individual confidence intervals and design fast optimization algorithms.

econ.EM↗

arXiv2024

Learning When the Concept Shifts: Confounding, Invariance, and Dimension Reduction

Practitioners often face the challenge of deploying prediction models in new environments with shifted distributions of covariates and responses. With observational data, such shifts are often driven by unobserved confounding, and can in fact alter the concept of which model is best. This paper studies distribution shifts in the domain adaptation problem with unobserved confounding. We postulate a linear structural causal model to account for endogeneity and unobserved confounding, and we leverage exogenous invariant covariate representations to cure concept shifts and improve target prediction. We propose a data-driven representation learning method that optimizes for a lower-dimensional linear subspace and a prediction model confined to that subspace. This method operates on a non-convex objective -- that interpolates between predictability and stability -- constrained to the Stiefel manifold, using an analog of projected gradient descent. We analyze the optimization landscape and prove that, provided sufficient regularization, nearly all local optima align with an invariant linear subspace resilient to distribution shifts. This method achieves a nearly ideal gap between target and source risk. We validate the method and theory with real-world data sets to illustrate the tradeoffs between predictability and stability.

cs.LG↗

arXiv2023

Robust Point Matching with Distance Profiles

Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice, but its theoretical understanding is limited. By delving into the statistical complexity of the previously proposed method based on distance profiles, we show that it suffers from the curse of dimensionality unless we make certain assumptions on the underlying metric measure spaces. Building on this insight, we propose and analyze a modified matching procedure that can be used to robustly match points under a certain probabilistic setting. We demonstrate the performance of the proposed methods using simulations and real data applications to complement the theoretical findings. As a result, we contribute to the literature by providing theoretical underpinnings of the matching procedures based on distance invariants like distance profiles, which have been widely used in practice but rarely analyzed theoretically.

stat.ME↗

arXiv2023

Detecting Weak Distribution Shifts via Displacement Interpolation

Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical applications in social and economic sciences. Given two probability distributions $P$ (null) and $Q$ (alternative), we study the problem of detecting weak distribution shift deviating from the null $P$ toward the alternative $Q$, where the level of deviation vanishes as a function of $n$, the sample size. We propose a model for weak distribution shifts via displacement interpolation between $P$ and $Q$, drawing from the optimal transport theory. We study a hypothesis testing procedure based on the Wasserstein distance, derive sharp conditions under which detection is possible, and provide the exact characterization of the asymptotic Type I and Type II errors at the detection boundary using empirical processes. We demonstrate how the proposed testing procedure works in modeling and detecting weak distribution shifts in real data sets using two empirical examples: distribution shifts in consumer spending after COVID-19, and heterogeneity in the published p-values of statistical tests in journals across different disciplines.

math.ST↗

arXiv2022

Online Learning to Transport via the Minimal Selection Principle

Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw connections between online learning, optimal transport, and partial differential equations through an insight called the minimal selection principle, originally studied in the Wasserstein gradient flow setting by \citet{Ambrosio_2005}. This allows us to extend the standard online learning framework to the infinite-dimensional setting seamlessly. Based on our framework, we derive a novel method called the \textit{minimal selection or exploration (MSoE) algorithm} to solve OLT problems using mean-field approximation and discretization techniques. In the displacement convex setting, the main theoretical message underpinning our approach is that minimizing transport cost over time (via the minimal selection principle) ensures optimal cumulative regret upper bounds. On the algorithmic side, our MSoE algorithm applies beyond the displacement convex setting, making the mathematical theory of optimal transport practically relevant to non-convex settings common in dynamic resource allocation.

cs.LG↗

arXiv2021

Reversible Gromov-Monge Sampler for Simulation-Based Inference

This paper introduces a new simulation-based inference procedure to model and sample from multi-dimensional probability distributions given access to i.i.d.\ samples, circumventing the usual approaches of explicitly modeling the density function or designing Markov chain Monte Carlo. Motivated by the seminal work on distance and isomorphism between metric measure spaces, we propose a new notion called the Reversible Gromov-Monge (RGM) distance and study how RGM can be used to design new transform samplers to perform simulation-based inference. Our RGM sampler can also estimate optimal alignments between two heterogeneous metric measure spaces $(\cX, \mu, c_{\cX})$ and $(\cY, \nu, c_{\cY})$ from empirical data sets, with estimated maps that approximately push forward one measure $\mu$ to the other $\nu$, and vice versa. We study the analytic properties of the RGM distance and derive that under mild conditions, RGM equals the classic Gromov-Wasserstein distance. Curiously, drawing a connection to Brenier's polar factorization, we show that the RGM sampler induces bias towards strong isomorphism with proper choices of $c_{\cX}$ and $c_{\cY}$. Statistical rate of convergence, representation, and optimization questions regarding the induced sampler are studied. Synthetic and real-world examples showcasing the effectiveness of the RGM sampler are also demonstrated.

stat.ME↗