12 papers
Minimax Wasserstein Testing under Differential Privacy
Bonwoo Lee, Ilmun Kim, Cheolwoo Park
We study Wasserstein- goodness-of-fit and two-sample testing under differential privacy. For general compact metric spaces, we establish upper and lower bounds on the minimax se…
A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables
Seongchan Lee, Ilmun Kim
We prove a Hoeffding-type moment generating function bound for weighted sums of bounded exchangeable random variables centered by their finite-population average. The bound reduces…
Sharp Minimax Rates for Smooth Two-Sample Testing under Central Differential Privacy
Ilmun Kim
We establish sharp minimax limits for two-sample testing of Hölder-smooth densities under central differential privacy. Given two independent samples, the goal is to decide whether…
Aggregation of Statistical Evidence under Exchangeability
Antonin Schrab, Rajen Shah, Arthur Gretton +1
We study aggregation of statistical evidence under unknown and potentially complex dependence using group-invariance. Building on permutation-based constructions that treat transfo…
High-Confidence Minimax Testing with Prescribed Errors
Ilmun Kim
Classical minimax lower bounds for testing are typically derived for fixed error probabilities, while high-confidence results often impose a common failure probability. We study pr…
More Permutations Do Not Always Increase Power: Non-monotonicity in Monte Carlo Permutation Tests
Suman Cha, Seongchan Lee, Antonin Schrab +1
Monte Carlo permutation tests are a cornerstone of valid, model-free statistical inference. A widely held practical intuition is that increasing the number of sampled permutations…
Minimax Optimal Two-Sample Testing under Local Differential Privacy
Jongmin Mun, Seungwoo Kwak, Ilmun Kim
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 b…
General Frameworks for Conditional Two-Sample Testing
Seongchan Lee, Suman Cha, Ilmun Kim
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This pr…
Computational-Statistical Trade-off in Kernel Two-Sample Testing with Random Fourier Features
Ikjun Choi, Ilmun Kim
Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high…
Enhancing Sufficient Dimension Reduction via Hellinger Correlation
Seungbeom Hong, Ilmun Kim, Jun Song
In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based o…
Robust Kernel Hypothesis Testing under Data Corruption
Antonin Schrab, Ilmun Kim
We propose a general method for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corru…
Differentially Private Permutation Tests
Ilmun Kim, Antonin Schrab
Recent years have witnessed growing concerns about the privacy of sensitive data. In response to these concerns, differential privacy has emerged as a rigorous framework for privac…