论文检索

保形化生存分析AI 解读

Abstract In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically…

利用共形 p 值检验异常值AI 解读

This paper studies the construction of p-values for nonparametric outlier detection, from 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 general framework yielding p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact…

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…

深度 Knockoff 方法AI 解读

This article introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between…

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…

Lasso 路径上的错误发现会较早出现AI 解读

In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that in a regime of linear sparsity—meaning that the fraction of variables with a nonvanishing effect tends to a constant, however small—this cannot really be the case, even when the design variables are stochastically independent. We…

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…

SLOPE 对未知稀疏度的自适应性与渐近极小极大性AI 解读

We consider high-dimensional sparse regression problems in which we observe $\mathbf{y}=\mathbf{X}\boldsymbol{\beta} +\mathbf{z}$, where $\mathbf{X}$ is an $n\times p$ design matrix and $\mathbf{z}$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\sigma^{2}$. Our focus is on the recently introduced SLOPE estimator [Ann. Appl. Stat. 9 (2015) 1103–1140], which regularizes the least-squares estimates with the rank-dependent penalty $\sum_{1\le i\le p}\lambda_{i}|\widehat{\beta} |_{(i)}$…

回应讨论：当变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation.The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions.We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in the discussions.Of special interest is the diversity of perspectives, which include…