Cheap Permutation Testing
- URL: http://arxiv.org/abs/2502.07672v1
- Date: Tue, 11 Feb 2025 16:19:07 GMT
- Title: Cheap Permutation Testing
- Authors: Carles Domingo-Enrich, Raaz Dwivedi, Lester Mackey,
- Abstract summary: Permutation tests are a popular choice for distinguishing distributions and testing independence.
Standard permutation tests are also expensive, requiring a test statistic to be computed hundreds or thousands of times.
In this work, we offer a simple approach to accelerate testing: group your datapoints into bins and permute only those bins.
- Score: 34.48696502346266
- License:
- Abstract: Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard permutation tests are also expensive, requiring a test statistic to be computed hundreds or thousands of times to detect a separation between distributions. In this work, we offer a simple approach to accelerate testing: group your datapoints into bins and permute only those bins. For U and V-statistics, we prove that these cheap permutation tests have two remarkable properties. First, by storing appropriate sufficient statistics, a cheap test can be run in time comparable to evaluating a single test statistic. Second, cheap permutation power closely approximates standard permutation power. As a result, cheap tests inherit the exact false positive control and minimax optimality of standard permutation tests while running in a fraction of the time. We complement these findings with improved power guarantees for standard permutation testing and experiments demonstrating the benefits of cheap permutations over standard maximum mean discrepancy (MMD), Hilbert-Schmidt independence criterion (HSIC), random Fourier feature, Wilcoxon-Mann-Whitney, cross-MMD, and cross-HSIC tests.
Related papers
- Precise Error Rates for Computationally Efficient Testing [75.63895690909241]
We revisit the question of simple-versus-simple hypothesis testing with an eye towards computational complexity.
An existing test based on linear spectral statistics achieves the best possible tradeoff curve between type I and type II error rates.
arXiv Detail & Related papers (2023-11-01T04:41:16Z) - Spectral Regularized Kernel Two-Sample Tests [7.915420897195129]
We show the popular MMD (maximum mean discrepancy) two-sample test to be not optimal in terms of the separation boundary measured in Hellinger distance.
We propose a modification to the MMD test based on spectral regularization and prove the proposed test to be minimax optimal with a smaller separation boundary than that achieved by the MMD test.
Our results hold for the permutation variant of the test where the test threshold is chosen elegantly through the permutation of the samples.
arXiv Detail & Related papers (2022-12-19T00:42:21Z) - A Permutation-Free Kernel Independence Test [36.50719125230106]
In nonparametric independence testing, we observe i.i.d. data $(X_i,Y_i)_i=1n$, where $X in mathcalX, Y in mathcalY$ lie in any general spaces.
Modern test statistics such as the kernel Hilbert-Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics.
This paper provides a simple but nontrivial modification of HSIC
arXiv Detail & Related papers (2022-12-18T15:28:16Z) - A Permutation-free Kernel Two-Sample Test [36.50719125230106]
We propose a new quadratic-time MMD test statistic based on sample-splitting and studentization.
For large sample sizes, our new cross-MMD provides a significant speedup over the MMD, for only a slight loss in power.
arXiv Detail & Related papers (2022-11-27T18:15:52Z) - Sequential Permutation Testing of Random Forest Variable Importance
Measures [68.8204255655161]
It is proposed here to use sequential permutation tests and sequential p-value estimation to reduce the high computational costs associated with conventional permutation tests.
The results of simulation studies confirm that the theoretical properties of the sequential tests apply.
The numerical stability of the methods is investigated in two additional application studies.
arXiv Detail & Related papers (2022-06-02T20:16:50Z) - Exact Paired-Permutation Testing for Structured Test Statistics [67.71280539312536]
We provide an efficient exact algorithm for the paired-permutation test for a family of structured test statistics.
Our exact algorithm was $10$x faster than the Monte Carlo approximation with $20000$ samples on a common dataset.
arXiv Detail & Related papers (2022-05-03T11:00:59Z) - Optimal Testing of Discrete Distributions with High Probability [49.19942805582874]
We study the problem of testing discrete distributions with a focus on the high probability regime.
We provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors.
arXiv Detail & Related papers (2020-09-14T16:09:17Z) - Noisy Adaptive Group Testing using Bayesian Sequential Experimental
Design [63.48989885374238]
When the infection prevalence of a disease is low, Dorfman showed 80 years ago that testing groups of people can prove more efficient than testing people individually.
Our goal in this paper is to propose new group testing algorithms that can operate in a noisy setting.
arXiv Detail & Related papers (2020-04-26T23:41:33Z) - The Chi-Square Test of Distance Correlation [7.748852202364896]
chi-square test is non-parametric, extremely fast, and applicable to bias-corrected distance correlation using any strong negative type metric or characteristic kernel.
We show that the underlying chi-square distribution well approximates and dominates the limiting null distribution in upper tail, prove the chi-square test can be valid and consistent for testing independence.
arXiv Detail & Related papers (2019-12-27T15:16:40Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.