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选择有效工具变量的置信区间方法AI 解读

Abstract We propose a new method, the confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs…

借助置信分布拓展Fisher随机化检验：推断、组合与融合学习AI 解读

Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate…

高维模型中个体化处理效应的最优统计推断AI 解读

Abstract The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a hypothesis testing approach to choosing between two potential treatments for a given individual in the framework of high-dimensional linear models. The methodological novelty lies in the construction of a debiased estimator of the ITE and establishment of its asymptotic normality uniformly for an arbitrary future…

随机生长树的历史推断AI 解读

Abstract The spread of infectious disease in a human community or the proliferation of fake news on social media can be modelled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains important information such as the source of the infection. We consider the problem of statistical inference on aspects of the latent history using only a single snapshot of the final tree. Our approach is to apply random labels to the…

《高维普通最小二乘投影变量筛选》的引理修正说明AI 解读

The conclusion in Lemma 5 in the supplementary material (SM) of Wang and Leng (2016), on which Theorems 1–3 rely, is incorrect. Here we provide an additional condition under which the conclusion of this lemma holds. We assume that the rows of the matrix X follow a Gaussian distribution with precision matrix Ω = Σ−1 that satisfies c 4 - 1 n - τ / 2 ≤ λ min ( Ω ) ≤ λ max ( Ω ) ≤ c 4 n τ / 2 . This implies the assumption on the condition number of Σ in Assumption A3. We drop…

利用非凸融合惩罚建模高维分类数据AI 解读

Abstract We propose a method for estimation in high-dimensional linear models with nominal categorical data. Our estimator, called SCOPE, fuses levels together by making their corresponding coefficients exactly equal. This is achieved using the minimax concave penalty on differences between the order statistics of the coefficients for a categorical variable, thereby clustering the coefficients. We provide an algorithm for exact and efficient computation of the global minimum…

内生二元处理下适用于任意响应类型的工具残差估计AI 解读

Abstract Given an endogenous/confounded binary treatment D, a response Y with its potential versions (Y0, Y1) and covariates X, finding the treatment effect is difficult if Y is not continuous, even when a binary instrumental variable (IV) Z is available. We show that, for any form of Y (continuous, binary, mixed,…), there exists a decomposition Y = μ0(X) + μ1(X)D + error with E(error|Z,X) = 0, where μ1(X)≡E(Y1-Y0|complier,X) and ‘compliers’ are those who get treated if and…

二元工具变量与删失数据下的因果分位数效应估计AI 解读

Abstract The causal effect of a treatment is of fundamental interest in the social, biological and health sciences. Instrumental variable (IV) methods are commonly used to determine causal treatment effects in the presence of unmeasured confounding. In this work, we study a new binary IV framework with randomly censored outcomes where we propose to quantify the causal treatment effect by the concept of complier quantile causal effect (CQCE). The CQCE is identifiable under…

GGM Knockoff 筛选：高斯图模型的错误发现率控制AI 解读

Abstract We propose a new method to learn the structure of a Gaussian graphical model with finite sample false discovery rate control. Our method builds on the knockoff framework of Barber and Candès for linear models. We extend their approach to the graphical model setting by using a local (node-based) and a global (graph-based) step: we construct knockoffs and feature statistics for each node locally, and then solve a global optimization problem to determine a threshold…

AMF：用于在线学习的聚合 Mondrian 森林AI 解读

Abstract Random forest (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high-dimensional settings. The…

提高观察性研究中异常结局检验功效的自适应方法AI 解读

Abstract In many observational studies, the interest is in the effect of treatment on bad, aberrant outcomes rather than the average outcome. For such settings, the traditional approach is to define a dichotomous outcome indicating aberration from a continuous score and use the Mantel–Haenszel test with matched data. For example, studies of determinants of poor child growth use the World Health Organization’s definition of child stunting being height-for-age z-score ≤ − 2.…

用扩展先验样本量评估先验影响及先验—似然不协调AI 解读

Abstract This paper outlines a framework for quantifying the prior’s contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual purpose by extending the classic notion of prior sample size, M, in three directions: (I) estimating M beyond conjugate families; (II) formulating M as a relative notion that is as a function of the likelihood sample size k, M(k),…

利用 ABC 贝叶斯森林进行变量选择AI 解读

Abstract Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening…

现状数据的有效与近似有效置信区间AI 解读

Abstract We introduce a new approach for creating pointwise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our approach is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid that is guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches…

通过模型复杂度选择估计主流形AI 解读

Abstract We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve algorithm as special cases. We propose a novel method for model complexity selection to avoid overfitting, eliminate the effects of outliers and improve the computation speed. Additionally, we propose a method for identifying the…

实验设计中随机化的最优性：极小极大方差与基于设计的推断AI 解读

Abstract I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes vary in a given set and the objective is effect-estimation precision. When this set is permutation symmetric, the optimal design is shown to be complete randomization. Notably, even when the set has structure (i.e., is not permutation symmetric), being minimax-optimal for precision still requires randomization beyond a single partition of units, that is, beyond…

利用工具变量估计最优治疗规则：部分识别学习方法AI 解读

Abstract Individualized treatment rules (ITRs) are considered a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate the average treatment effect conditional on a subject’s covariate information, which is often challenging in observational studies due to the universal concern of unmeasured confounding. Instrumental variables (IVs) are widely used tools to infer the treatment effect when there is…

复杂区域上的非参数密度估计AI 解读

Abstract We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility.…

锚回归：异质数据与因果性AI 解读

Abstract We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution either many variables are affected by interventions or only some variables are affected, but the perturbations are strong. If the training and test distributions differ by a shift, causal parameters might be too conservative to…

利用迭代 α 扩展从线性测量中估计梯度稀疏信号AI 解读

Abstract We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the “ℓ0-norm” of the signal’s discrete graph gradient. The method uses a non-convex variant of proximal gradient descent, applying the alpha-expansion procedure to approximate the proximal mapping in each iteration, and…

高维均值向量变点的有限样本推断与定位AI 解读

Abstract Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence…

用于近似输运的 Gibbs 流及其贝叶斯计算应用AI 解读

Abstract Let π0 and π1 be two distributions on the Borel space (Rd,B(Rd)). Any measurable function T:Rd→Rd such that Y=T(X)∼π1 if X∼π0 is called a transport map from π0 to π1. For any π0 and π1, if one could obtain an analytical expression for a transport map from π0 to π1, then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distribution π0 to the target distribution π1 using this transport map. Although it…

近端 Robbins–Monro 方法AI 解读

Abstract The need for statistical estimation with large data sets has reinvigorated interest in iterative procedures and stochastic optimization. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general and fast. However, standard stochastic approximations are often numerically unstable. Deterministic optimization, in contrast, increasingly uses proximal updates to achieve numerical stability in a principled…

两组模型中错误发现准则的最优控制AI 解读

Abstract The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate…