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具有错误覆盖率控制的信息性共形预测集选择AI 解读

Abstract In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be ‘informative’ in a well-defined sense. We consider both the classification and regression settings where the analyst may…

具有错误发现率保证的自适应新异检测AI 解读

This paper studies the semisupervised novelty detection problem where a set of “typical” measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast…

未知零假设分布下的错误发现率控制：能否模拟理想程序？AI 解读

Classical multiple testing theory prescribes the null distribution, which is often too stringent an assumption for nowadays large scale experiments. This paper presents theoretical foundations to understand the limitations caused by ignoring the null distribution, and how it can be properly learned from the same data set, when possible. We explore this issue in the setting where the null distributions are Gaussian with unknown rescaling parameters (mean and variance) whereas…

伴随异常值筛选的最小效应估计AI 解读

We introduce one-sided versions of Huber’s contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of the uncorrupted samples (minimum effect) and selection of the corrupted samples (outliers). Regarding estimation of the minimum effect, we derive the minimax risks and introduce estimators that are adaptive with respect to the unknown number of contaminations. The optimal…

泊松过程强度的连续检验：扫描统计量的新视角AI 解读

We propose a continuous testing framework to test the intensities of Poisson processes that allows a rigorous definition of the complete testing procedure, from an infinite number of hypotheses to joint error rates. Our work extends procedures based on scanning windows by controlling the familywise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. We introduce the p-value process on which the decision rule is based. Our method is…

基于 Romano–Wolf 启发式控制错误发现比例的新程序AI 解读

The false discovery proportion (FDP) is a convenient way to account for false positives when a large number $m$ of tests are performed simultaneously. Romano and Wolf [ Ann. Statist. 35 (2007) 1378–1408] have proposed a general principle that builds FDP controlling procedures from $k$-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [ J. Statist. Plann. Inference 124 (2004) 379–398]; Romano and Wolf…

稀疏分类中的错误发现率阈值法AI 解读

We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The “$0$”-class (null) is assumed to have a known density while the “$1$”-class (alternative) is obtained from the “$0$”-class either by translation or by scaling. Furthermore, the “$1$”-class is assumed to have a small number of elements w.r.t. the “$0$”-class (sparsity). We focus on densities of the Subbotin family, including Gaussian and Laplace models. Nonasymptotic…

错误发现比例的精确计算及其最不利配置应用AI 解读

In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable, which leads to explicit computations of the c.d.f., the sth moment and the mean of the FDP, the latter corresponding to the false discovery rate (FDR). For step-down…

高维重抽样的若干非渐近结果（二）：多重检验AI 解读

In the context of correlated multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann.…

高维重抽样的若干非渐近结果（一）：置信区域AI 解读

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two…