1 code implementation • 30 May 2024 • Antonin Schrab, Ilmun Kim
We propose two general methods for constructing robust permutation tests under data corruption.
1 code implementation • 30 May 2024 • 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 on conditional independence.
no code implementations • 29 Feb 2024 • Ilmun Kim, Larry Wasserman, Sivaraman Balakrishnan, Matey Neykov
Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming.
3 code implementations • 29 Oct 2023 • Ilmun Kim, Antonin Schrab
The proposed framework extends classical non-private permutation tests to private settings, maintaining both finite-sample validity and differential privacy in a rigorous manner.
no code implementations • 18 Dec 2022 • Shubhanshu Shekhar, Ilmun Kim, Aaditya Ramdas
In nonparametric independence testing, we observe i. i. d.\ data $\{(X_i, Y_i)\}_{i=1}^n$, where $X \in \mathcal{X}, Y \in \mathcal{Y}$ lie in any general spaces, and we wish to test the null that $X$ is independent of $Y$.
no code implementations • 27 Nov 2022 • Shubhanshu Shekhar, Ilmun Kim, Aaditya Ramdas
The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus it has an intractable limiting distribution.
1 code implementation • 3 Nov 2022 • Anton Rask Lundborg, Ilmun Kim, Rajen D. Shah, Richard J. Samworth
In this work we study the problem of testing the model-free null of conditional mean independence, i. e. that the conditional mean of $Y$ given $X$ and $Z$ does not depend on $X$.
4 code implementations • 18 Jun 2022 • Antonin Schrab, Ilmun Kim, Benjamin Guedj, Arthur Gretton
We derive non-asymptotic uniform separation rates for MMDAggInc and HSICAggInc, and quantify exactly the trade-off between computational efficiency and the attainable rates: this result is novel for tests based on incomplete $U$-statistics, to our knowledge.
3 code implementations • NeurIPS 2023 • Antonin Schrab, Ilmun Kim, Mélisande Albert, Béatrice Laurent, Benjamin Guedj, Arthur Gretton
In practice, this parameter is unknown and, hence, the optimal MMD test with this particular kernel cannot be used.
no code implementations • NeurIPS 2020 • Yue Li, Ilmun Kim, Yuting Wei
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$.
no code implementations • 10 Nov 2020 • Ilmun Kim, Aaditya Ramdas
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity.
1 code implementation • 27 May 2019 • Niccolò Dalmasso, Ann B. Lee, Rafael Izbicki, Taylor Pospisil, Ilmun Kim, Chieh-An Lin
At the heart of our approach is a two-sample test that quantifies the quality of the fit at fixed parameter values, and a global test that assesses goodness-of-fit across simulation parameters.
no code implementations • 6 Feb 2016 • Ilmun Kim, Aaditya Ramdas, Aarti Singh, Larry Wasserman
We prove two results that hold for all classifiers in any dimensions: if its true error remains $\epsilon$-better than chance for some $\epsilon>0$ as $d, n \to \infty$, then (a) the permutation-based test is consistent (has power approaching to one), (b) a computationally efficient test based on a Gaussian approximation of the null distribution is also consistent.