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We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ0 in the presence of high‐dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η0, we consider the use of statistical or machine learning (ML) methods, which are particularly…

从次梯度优化及相关方法重新理解线性回归中的提升算法AI 解读

We analyze boosting algorithms [Ann. Statist. 29 (2001) 1189–1232; Ann. Statist. 28 (2000) 337–407; Ann. Statist. 32 (2004) 407–499] in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm ($\\text{FS}_{\\varepsilon}$) and least squares boosting [LS-BOOST$(\\varepsilon)$], can be viewed as subgradient descent to…

利用因子模型进行充分预测AI 解读

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive…

变分推断：面向统计学研究者的综述AI 解读

One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this article, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization. VI has been used in many applications and tends to be faster…

植入分区模型下谱超图划分的一致性AI 解读

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph…

用于估计个体化治疗规则的残差加权学习AI 解读

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has…

用于大型精度矩阵估计的偏相关筛选及其分类应用AI 解读

Given $n$ samples $X_{1},X_{2},\ldots,X_{n}$ from $N(0,\Sigma)$, we are interested in estimating the $p\times p$ precision matrix $\Omega=\Sigma^{-1}$; we assume $\Omega$ is sparse in that each row has relatively few nonzeros. We propose Partial Correlation Screening (PCS) as a new row-by-row approach. To estimate the $i$th row of $\Omega$, $1\leq i\leq p$, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a…

数字实验中异质性处理效应的非参数贝叶斯分析AI 解读

Randomized controlled trials play an important role in how Internet companies predict the impact of policy decisions and product changes. In these “digital experiments,” different units (people, devices, products) respond differently to the treatment. This article presents a fast and scalable Bayesian nonparametric analysis of such heterogenous treatment effects and their measurement in relation to observable covariates. New results and algorithms are provided for…

混合表示、包络表示与层级对偶AI 解读

Summary We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection by using the term ‘hierarchical duality’. Our results suggest an interesting and previously underexploited relationship between marginalization and profiling, or equivalently between the Fenchel–Moreau theorem for convex functions and the Bernstein–Widder theorem for Laplace transforms. We give several different…

评论：多阶段化疗方案的 Q-learning 与 O-learningAI 解读

Xu, Müller, Wahed, and Thall proposed a Bayesian model to analyze an acute leukemia study involving multi-stage chemotherapy regimes. We discuss two alternative methods, Q-learning and O-learning, to solve the same problem from the machine learning point of view. The numerical studies show that these methods can be flexible and have advantages in some situations to handle treatment heterogeneity while being robust to model misspecification.

跨转录组研究识别疾病亚型的稀疏 K 均值元分析框架AI 解读

Disease phenotyping by omics data has become a popular approach that potentially can lead to better personalized treatment. Identifying disease subtypes via unsupervised machine learning is the first step toward this goal. In this article, we extend a sparse K-means method toward a meta-analytic framework to identify novel disease subtypes when expression profiles of multiple cohorts are available. The lasso regularization and meta-analysis identify a unique set of gene…

潜在因子模型中的个性化预测与稀疏性追求AI 解读

Yunzhang Zhu, Xiaotong Shen & Changqing YeYunzhang Zhu (E-mail: zhuxx351@umn.edu), Xiaotong Shen (E-mail: shenx002@umn.edu), and Changqing Ye (E-mail: cqye@stat.umn.edu), School of Statistics, University of Minnesota, Minneapolis, MN 55455. Research supported in part by NSF grants DMS-1207771 and DMS-1415500, NIH grants R02GM08153 and R01HL105397. The authors would like to thank Professor Hui Jiang for technical help in OpenMP coding, and thank the editor, the associate…

In this paper, we introduce a new type of tree-based method, reinforcement learning trees (RLT), which exhibits significantly improved performance over traditional methods such as random forests (Breiman, 2001) under high-dimensional settings. The innovations are three-fold. First, the new method implements reinforcement learning at each selection of a splitting variable during the tree construction processes. By splitting on the variable that brings the greatest future…

随机森林的一致性AI 解读

Random forests are a learning algorithm proposed by Breiman [ Mach. Learn. 45 (2001) 5–32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice originates in the difficulty to simultaneously analyze both the randomization process and the highly data-dependent tree…

估计最优动态治疗方案的新统计学习方法AI 解读

Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. The goal is to accommodate heterogeneity among patients and find the DTR which will produce the best long-term outcome if implemented. We introduce two new statistical learning methods for estimating the optimal DTR, termed backward outcome weighted learning (BOWL), and simultaneous outcome weighted learning (SOWL). These approaches convert…

通过切片逆回归进行一般指标模型的变量选择AI 解读

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential variables under the general index model, in which the response is dependent of predictors through an unknown function of one or more linear combinations of them. Instead of building a predictive model of the response given combinations of…

采用平方根降温的模拟随机逼近退火全局优化AI 解读

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which…

正则化统计估计的通用路径算法AI 解读

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution toward prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints lead to the popular lasso, fused-lasso, and other generalized ℓ1 penalized…

利用数据降维方法预测金融与宏观变量：新的实证证据AI 解读

In this paper, we empirically assess the predictive accuracy of a large group of models that are specified using principle components and other shrinkage techniques, including Bayesian model averaging and various bagging, boosting, least angle regression and related methods. Our results suggest that model averaging does not dominate other well designed prediction model specification methods, and that using “hybrid” combination factor/shrinkage methods often yields superior…

假设检验中距离统计量与 RKHS 统计量的等价性AI 解读

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a…

用于文本分析的多项逆回归AI 解读

Text data, including speeches, stories, and other document forms, are often connected to sentiment variables that are of interest for research in marketing, economics, and elsewhere. It is also very high dimensional and difficult to incorporate into statistical analyses. This article introduces a straightforward framework of sentiment-sufficient dimension reduction for text data. Multinomial inverse regression is introduced as a general tool for simplifying predictor sets…

缺少类别标识时的辅助标记分类AI 解读

Constructing classification rules for accurate diagnosis of a disorder is an important goal in medical practice. In many clinical applications, there is no clinically significant anatomical or physiological deviation exists to identify the gold standard disease status to inform development of classification algorithms. Despite absence of perfect disease class identifiers, there are usually one or more disease-informative auxiliary markers along with feature variables…

大规模数据的高效高斯过程回归AI 解读

Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of…

作者答复：通过凸优化选择潜变量图模型AI 解读

Introduction.We thank all the discussants for their careful reading of our paper, and for their insightful critiques.We would also like to thank the editors for organizing this discussion.Our paper contributes to the area of high-dimensional statistics which has received much attention over the past several years across the statistics, machine learning and signal processing communities.In this rejoinder we clarify and comment on some of the points raised in the…