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高维回归中的推断AI 解读

Abstract This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter, the remaining coefficients being nuisance parameters, and seeks an optimal interest-respecting transformation, inducing sparsity on the relevant blocks of the notional Fisher information matrix. The induced sparsity is exploited…

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…

多处理臂及可能包含析因结构的实验中的协变量调整AI 解读

Abstract Randomized experiments are the gold standard for causal inference and enable unbiased estimation of treatment effects. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multiarmed experiments. We start with the commonly used additive and fully interacted models for regression adjustment in estimating average…

缺失数据的偏样本经验似然加权：逆概率加权的替代方法AI 解读

Abstract Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable if some probabilities are very close to zero. To overcome this problem, at least three remedies have been developed in the literature: stabilizing, thresholding, and trimming. However, the final estimators are still IPW-type…

基于张量 CP 分解的矩阵时间序列建模AI 解读

Abstract We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further…

种子二元分割：快速且最优的变点检测通用方法AI 解读

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to…

倾向得分在观察性因果研究设计中的作用AI 解读

Summary The design of any study, whether experimental or observational, that is intended to estimate the causal effects of a treatment condition relative to a control condition refers to those activities that precede any examination of outcome variables. As defined in our 1983 article (Rosenbaum & Rubin, 1983), the propensity score is the unit-level conditional probability of assignment to treatment versus control given the observed covariates; so the propensity score…

高维响应多元回归的响应变量最优子集选择AI 解读

Summary This article investigates the statistical problem of response-variable selection with high-dimensional response variables and a diverging number of predictor variables with respect to the sample size in the framework of multivariate linear regression. A response best-subset selection model is proposed by introducing a 0-1 selection indicator for each response variable, and then a response best-subset selector is developed by introducing a separation parameter and a…

通过偏内积进行协方差估计的可分离展开AI 解读

Summary The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalizes…

具有有限样本保证的简明通用去偏机器学习定理AI 解读

Summary Debiased machine learning is a meta-algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e., scalar summaries, of machine learning algorithms. For example, an analyst may seek the confidence interval for a treatment effect estimated with a neural network. We present a non-asymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies…

高维高斯图模型的统一推断AI 解读

Summary Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters $d$ is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods…

线性化最大秩相关估计AI 解读

Summary We propose a linearized maximum rank correlation estimator for the single-index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be…

存在处理习惯化的时序实验中因果效应的极小极大设计AI 解读

Summary In many modern settings, such as an online marketplace, randomized experiments need to be executed over multiple time periods. In such temporal experiments, it has been observed that the effects of an intervention on an experimental unit may be large when the unit is first exposed to it, but then it attenuates after repeated exposures. This is typically due to units’ habituation to the intervention, or some other form of learning, such as when users gradually start…

数据整合：利用外部简化模型的参数估计比值AI 解读

Summary We consider the situation of estimating the parameters in a generalized linear prediction model, from an internal dataset, where the outcome variable $Y$ is binary and there are two sets of covariates, $X$ and $Z$. We have information from an external study that provides parameter estimates for a generalized linear model of $Y$ on $X$. We propose a method that makes limited assumptions about the similarity of the distributions in the two study populations. The method…

基于 F 建模的方差经验贝叶斯估计AI 解读

Summary We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an…

加权最小二乘估计的最优极小极大随机设计AI 解读

Summary This work studies an experimental design problem where the values of a predictor variable, denoted by $x$, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to $m(x)$, but it is not assumed that the model is correctly specified. It follows that the quantity of interest is the best linear approximation of $m(x)$, which is denoted by $\ell(x)$. It is shown that in this framework the ordinary least…

可交换关系数组的回归AI 解读

Summary Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression…

时变处理边际结构Cox模型的工具变量估计AI 解读

Summary Robins (1998) introduced marginal structural models, a general class of counterfactual models for the joint effects of time-varying treatments in complex longitudinal studies subject to time-varying confounding. Robins (1998) established the identification of marginal structural model parameters under a sequential randomization assumption, which rules out unmeasured confounding of treatment assignment over time. The marginal structural Cox model is one of the most…

一般均衡下的大规模教育改革：来自印度的断点回归证据AI 解读

The economic consequences of large-scale government investments in education depend on general equilibrium effects in both the labor market and the education sector. I develop a general equilibrium model capturing the consequences of massive countrywide schooling initiatives. I provide unbiased estimates of the model’s elasticities, using a regression discontinuity derived from Indian government policy. The earnings returns to a year of education are 13.4%, and the general…

非参数混合模型的一致相合性AI 解读

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to…

稳定算法的条件预测推断AI 解读

We investigate generically applicable and intuitively appealing prediction intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response…

含测量误差的高维泊松模型：非线性非凸优化中的假设检验AI 解读

We study estimation and testing in the Poisson regression model with noisy high-dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a nonconvex target function to minimize. Treating the high-dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target…

破解孟德尔随机化中的赢家诅咒：再随机化逆方差加权估计量AI 解读

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made the application of two-sample Mendelian Randomization (MR) with summary data increasingly popular. Conventional two-sample MR methods often employ the same sample for selecting relevant genetic variants and for constructing final causal estimates. Such a practice often leads to biased causal effect estimates due to the well-known “winner’s curse”…

随机数据下迭代非凸优化的精确全局收敛保证AI 解读

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms for this task from a random initialization. In particular, provided each iteration can be written as the solution to a convex optimization problem satisfying some natural conditions, we leverage Gaussian comparison theorems to derive a…