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具有时间序列与异方差误差的高维回归变量选择AI 解读

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitative finance, environmental science, and many other fields. The error term in our model is the product of two components: one time…

因子调整的正则化模型选择AI 解读

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric and financial studies, we consider the case where covariate dependence can be reduced through the factor model, and propose a consistency strategy named Factor-Adjusted…

梯度提升双重机器学习及其对大型审计机构质量效应的应用AI 解读

In this paper, we study the double machine learning (DML) approach of Chernozhukov et al. (2018) for estimating average treatment effect and apply this approach to examine the Big N audit quality effect in the accounting literature. This approach relies on machine learning methods and is suitable when a high dimensional nuisance function with many covariates is present in the model. This approach does not suffer from the “regularization bias” when a learning method with a…

半参数回归模型的集成估计与变量选择AI 解读

Summary We consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components, with an efficient estimator of the regression parameter available for each component. An optimal weighted combination of the component estimators, named an ensemble estimator, may be employed as an overall estimate of the regression parameter, and may be fully efficient under uncorrelatedness conditions. This approach is useful when the full…

MIMIX：用于设计实验微生物组数据的贝叶斯混合效应模型AI 解读

Recent advances in bioinformatics have made high-throughput microbiome data widely available, and new statistical tools are required to maximize the information gained from these data. For example, analysis of high-dimensional microbiome data from designed experiments remains an open area in microbiome research. Contemporary analyses work on metrics that summarize collective properties of the microbiome, but such reductions preclude inference on the fine-scale effects of…

通过原型分析进行非负矩阵分解AI 解读

Hamid Javadia* & Andrea Montanarib*a Department of Electrical and Computer Engineering, Rice University, Houston, TX; b Department of Electrical Engineering and Statistics, Stanford University, Stanford, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.CONTACT Hamid Javadi hrhakim@rice.edu Department of…

面向大规模多输入计算机实验的多分辨率函数型方差分析AI 解读

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multiresolution functional ANOVA (MRFA) model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input…

随机设计下稀疏惩罚回归的置信区间AI 解读

With the abundance of large data, sparse penalized regression techniques are commonly used in data analysis due to the advantage of simultaneous variable selection and estimation. A number of convex as well as non-convex penalties have been proposed in the literature to achieve sparse estimates. Despite intense work in this area, how to perform valid inference for sparse penalized regression with a general penalty remains to be an active research problem. In this paper, by…

右删失事件时间数据的 Copula 连接加性模型AI 解读

This article proposes an approach to estimate and make inference on the parameters of copula link-based survival models. The methodology allows for the margins to be specified using flexible parametric formulations for time-to-event data, the baseline survival functions to be modeled using monotonic splines, and each parameter of the assumed joint survival distribution to depend on an additive predictor incorporating several types of covariate effects. All the model’s…

广义地理加性模型的估计与推断AI 解读

In many application areas, data are collected on a count or binary response with spatial covariate information. In this article, we introduce a new class of generalized geoadditive models (GGAMs) for spatial data distributed over complex domains. Through a link function, the proposed GGAM assumes that the mean of the discrete response variable depends on additive univariate functions of explanatory variables and a bivariate function to adjust for the spatial effect. We…

高维数据下合并概率与非概率样本的双重稳健推断AI 解读

Summary We consider integrating a non-probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly…

β 混合厚尾时间序列中 Lasso 的理论保证AI 解读

Many theoretical results for lasso require the samples to be i.i.d. Recent work has provided guarantees for lasso assuming that the time series is generated by a sparse Vector Autoregressive (VAR) model with Gaussian innovations. Proofs of these results rely critically on the fact that the true data generating mechanism (DGM) is a finite-order Gaussian VAR. This assumption is quite brittle: linear transformations, including selecting a subset of variables, can lead to the…

高维数据下正则化校准估计的处理效应模型辅助推断AI 解读

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. We develop new methods and theory to obtain not only doubly robust point estimators for average treatment effects, which remain consistent if either the propensity score model or the outcome regression model is correctly specified, but also model-assisted confidence intervals, which…

模型搜索后的预测误差AI 解读

Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also uses data to select a set of variables and constructs the estimation rule using only the selected variables. In this work, we propose an asymptotically unbiased estimator for the prediction error after model search. Under some additional mild assumptions, we show that our estimator converges to the true prediction error in $L^{2}$ at the rate of $O(n^{-1/2})$, with $n$ being…

单调分段常数信号的估计AI 解读

Consider a sequence of real data points $X_{1},\ldots ,X_{n}$ with underlying means $\theta ^{*}_{1},\dots ,\theta ^{*}_{n}$. This paper starts from studying the setting that $\theta ^{*}_{i}$ is both piecewise constant and monotone as a function of the index $i$. For this, we establish the exact minimax rate of estimating such monotone functions, and thus give a nontrivial answer to an open problem in the shape-constrained analysis literature. The minimax rate under the…

基于均值中位数的稳健机器学习：理论与实践AI 解读

Median-of-means (MOM) based procedures have been recently introduced in learning theory (Lugosi and Mendelson (2019); Lecué and Lerasle (2017)). These estimators outperform classical least-squares estimators when data are heavy-tailed and/or are corrupted. None of these procedures can be implemented, which is the major issue of current MOM procedures (Ann. Statist. 47 (2019) 783–794). In this paper, we introduce minmax MOM estimators and show that they achieve the same…

宏基因组数据中细菌组成矩阵的多样本估计AI 解读

Summary Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where bacterial composition is estimated based on the sequencing read counts. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which tend to result in inaccurate…

模型误设与高维数据下倾向得分的正则化校准估计AI 解读

Summary Propensity scores are widely used with inverse probability weighting to estimate treatment effects in observational studies. We study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors…

同时实现降秩与变量选择的贝叶斯稀疏多响应回归AI 解读

Summary We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax…

基于重拟合交叉验证的超高维精度矩阵估计AI 解读

This paper develops a new estimation procedure for ultrahigh dimensional sparse precision matrix, the inverse of covariance matrix. Regularization methods have been proposed for sparse precision matrix estimation, but they may not perform well with ultrahigh dimensional data due to the spurious correlation. We propose a refitted cross validation (RCV) method for sparse precision matrix estimation based on its Cholesky decomposition, which does not require the Gaussian…

利用个性化PageRank对巨型分块模型图进行定向抽样AI 解读

Summary The paper provides statistical theory and intuition for personalized PageRank (called ‘PPR’): a popular technique that samples a small community from a massive network. We study a setting where the entire network is expensive to obtain thoroughly or to maintain, but we can start from a seed node of interest and ‘crawl’ the network to find other nodes through their connections. By crawling the graph in a designed way, the PPR vector can be approximated without…

删失数据下估计方程数量增长的惩罚广义经验似然AI 解读

This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored survival models where a parametric likelihood is not available. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood, where the general estimating equations are constructed based on the semiparametric efficiency bound of estimation with given moment conditions. The…

通过样本分割一致选择变点数量AI 解读

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and…

稀疏高维回归：可扩展精确算法与相变AI 解读

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes $n$ and number of regressors $p$ in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to…