• Corpus ID: 233301258

# Testing for Outliers with Conformal p-values

@inproceedings{Bates2021TestingFO,
title={Testing for Outliers with Conformal p-values},
author={Stephen Bates and Emmanuel J. Cand{\e}s and Lihua Lei and Yaniv Romano and Matteo Sesia},
year={2021}
}`
• Published 16 April 2021
• Computer Science, Mathematics
This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a broadly applicable framework which yields p-values that are marginally valid but mutually dependent for diﬀerent test points. We prove these p-values are positively dependent and enable exact…

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## References

SHOWING 1-10 OF 111 REFERENCES
Combining P-Values Via Averaging
• Mathematics
• 2012
This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of $p$-values without making any assumptions about their
Prediction and outlier detection in classification problems
• Computer Science
Journal of the Royal Statistical Society. Series B, Statistical Methodology
• 2022
This work considers the multi‐class classification problem when the training data and the out‐of‐sample test data may have different distributions and proposes a method called BCOPS (balanced and conformal optimized prediction sets), which tries to optimize the out-of-sample performance and estimates the outlier detection rate of a given procedure.
A comparison of some conformal quantile regression methods
• Mathematics
Stat
• 2020
We compare two recent methods that combine conformal inference with quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano,
Multivariate Outlier Detection With High-Breakdown Estimators
In this paper we develop multivariate outlier tests based on the high-breakdown Minimum Covariance Determinant estimator. The rules that we propose have good performance under the null hypothesis of
Classification Accuracy as a Proxy for Two Sample Testing
• Computer Science, Mathematics
The Annals of Statistics
• 2021
This work proves 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), and (b) a computationally efficient test based on a Gaussian approximation of the null distribution is also consistent.
Distribution-free conditional predictive bands using density estimators
• Computer Science, Mathematics
AISTATS
• 2020
Two conformal methods based on conditional density estimators that do not depend on this type of assumption to obtain asymptotic conditional coverage are introduced: Dist-split and CD-split.
On the evaluation of unsupervised outlier detection: measures, datasets, and an empirical study
• Computer Science
Data Mining and Knowledge Discovery
• 2015
An extensive experimental study on the performance of a representative set of standard k nearest neighborhood-based methods for unsupervised outlier detection, across a wide variety of datasets prepared for this purpose, and provides a characterization of the datasets themselves.
A Distribution-Free Test of Covariate Shift Using Conformal Prediction
• Computer Science
• 2020
This is the first successful attempt of using conformal prediction for testing statistical hypotheses and can be effectively combined with existing classification algorithms to find good conformity score functions.
Classification with Valid and Adaptive Coverage
• Computer Science
NeurIPS
• 2020
A novel conformity score is developed, which is explicitly demonstrate to be powerful and intuitive for classification problems, but whose underlying principle is potentially far more general.
Uncertainty Sets for Image Classifiers using Conformal Prediction
• Computer Science
ICLR
• 2021
An algorithm is presented that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90%, which provides a formal finite-sample coverage guarantee for every model and dataset.