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自适应采集数据的随机化检验AI 解读

Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and constructing (by inverting a permutation test) model-free prediction intervals via conformal prediction. Randomization tests are exactly valid for any sample size, but their use is generally confined to exchangeable data. Yet in many applications,…

条件于后验样本的灵活频率学派拟合优度检验AI 解读

Summary Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial datasets that are exchangeable with the real data under the null hypothesis (but not under the alternative), as this allows the analyst to conduct a valid test using any test statistic they desire. Such sampling is typically done by conditioning on either an exact or an approximate sufficient statistic, but existing methods…

通过贝叶斯线性规划控制信号发现与定位AI 解读

Scientists often must simultaneously localize and discover signals. For instance, in genetic fine-mapping, high correlations between nearby genetic variants make it hard to identify the exact locations of causal variants. So the statistical task is to output as many disjoint regions containing a signal as possible, each as small as possible, while controlling false positives. Similar problems arise in any application where signals cannot be perfectly localized, such as…

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使用近似共充分抽样检验拟合优度与条件独立性AI 解读

Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct ties to model selection, confidence interval construction, conditional independence testing, and multiple testing, just to name a few applications. While testing the GoF of a simple (point) null hypothesis provides an analyst great flexibility in the choice of test statistic while still ensuring validity, most GoF tests for composite null hypotheses are far more constrained, as the test statistic must…

条件随机化检验与knockoff的高维功效分析AI 解读

Summary In many scientific applications, researchers aim to relate a response variable $Y$ to a set of potential explanatory variables $X = (X_1,\dots,X_p)$, and start by trying to identify variables that contribute to this relationship. In statistical terms, this goal can be understood as trying to identify those $X_j$ on which $Y$ is conditionally dependent. Sometimes it is of value to simultaneously test for each $j$, which is more commonly known as variable selection.…

通过蒸馏实现快速且有力的条件随机化检验AI 解读

Summary We consider the problem of conditional independence testing: given a response $Y$ and covariates $(X,Z)$, we test the null hypothesis that $Y {\perp\!\!\!\perp} X \mid Z$. The conditional randomization test was recently proposed as a way to use distributional information about $X\mid Z$ to exactly and nonasymptotically control Type-I error using any test statistic in any dimensionality without assuming anything about $Y\mid (X,Z)$. This flexibility, in principle,…

基于 Metropolis–Hastings 的 Knockoff 采样AI 解读

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This article introduces techniques for…

Summary Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a non-linear fashion, such as when the response is binary. Although this modelling problem has been extensively studied, it remains unclear how to control the fraction of false discoveries effectively even in high dimensional logistic regression, not to mention general high dimensional non-linear models. To address such a…

EigenPrism：高维信噪比推断AI 解读

Summary Consider the following three important problems in statistical inference: constructing confidence intervals for the error of a high dimensional (p > n) regression estimator, the linear regression noise level and the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the l2-norm of the signal in high dimensional linear…

稳健多代理古气候重建与温度条件分位数建模AI 解读

Great strides have been made in the field of reconstructing past temperatures based on models relating temperature to temperature-sensitive paleoclimate proxies. One of the goals of such reconstructions is to assess if current climate is anomalous in a millennial context. These regression based approaches model the conditional mean of the temperature distribution as a function of paleoclimate proxies (or vice versa). Some of the recent focus in the area has considered…