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条件平均处理效应及其他因果函数的去偏机器学习AI 解读

Summary This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning tools. We represent this structural function as a conditional expectation of an unbiased signal that depends on a nuisance parameter, which we estimate by modern machine learning techniques. We first adjust the signal to…

SuperMix：混合模型的稀疏正则化AI 解读

This paper investigates the statistical estimation of a discrete mixing measure μ0 involved in a kernel mixture model. Using some recent advances in ℓ1-regularization over the space of measures, we introduce a “data fitting and regularization” convex program for estimating μ0 in a grid-less manner from a sample of mixture law, this method is referred to as Beurling-LASSO. Our contribution is two-fold: we derive a lower bound on the bandwidth of our data fitting term…

时间与空间依赖下的 LASSO 推断AI 解读

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap…

稀疏高维加性模型中的统计推断AI 解读

In this paper, we discuss the estimation of a nonparametric component f1 of a nonparametric additive model Y=f1(X1)+⋯+fq(Xq)+ϵ. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f1 in the oracle model Z=f1(X1)+ϵ, for which the additive components f2,…,fq are known. We construct a two-step presmoothing-and-resmoothing…

白噪声回归中的框架约束总变差正则化AI 解读

Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for quite some time to be minimax optimal for denoising one-dimensional signals, for higher dimensions this remains elusive until today. In this paper, we consider frame-constrained TV estimators including many well-known (overcomplete)…

基于伪似然的贝叶斯向量自回归模型强选择一致性AI 解读

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for…

高维交叉验证Lasso的理论分析AI 解读

In this paper, we derive nonasymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using K-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, L2, and L1 norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation error of…

重尾数据的收缩原则：高维稳健低秩矩阵恢复AI 解读

This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from subexponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ∗ from the trace regression model Y=Tr(Θ∗⊤X)+ε. It encompasses four popular problems: sparse…

通过两阶段非参数惩罚样条求解欧拉方程AI 解读

This study proposes a novel estimation-based approach to solving asset pricing models for both stationary and time-varying observations. Our method is robust to misspecification errors while inheriting a closed-form solution. By representing the Euler equation into a well-posed integral equation of the second kind, we propose a penalized two-stage nonparametric estimation method and establish its optimal convergence under mild conditions. With the merit of penalized splines,…

异质性处理效应的准 Oracle 估计AI 解读

Summary Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical applications, such as personalized medicine and optimal resource allocation. In this article we develop a general class of two-step algorithms for heterogeneous treatment effect estimation in observational studies. First, we estimate marginal effects and treatment propensities to form an objective function that isolates the causal component of the signal. Then, we optimize…

稀疏广义线性模型中的后验收缩AI 解读

Summary We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior…

可能误设的高维模型中处理效应参数的推断AI 解读

Summary Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators, such as the lasso, or other regularization approaches. Naïve use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates…

广义线性混合模型的惩罚拟似然信息准则AI 解读

Summary Information criteria are commonly used for joint fixed and random effects selection in mixed models. While information criteria are straightforward to implement, a major difficulty in applying them is that they are typically based on maximum likelihood estimates, but calculating such estimates for one candidate mixed model, let alone multiple models, presents a major computational challenge. To overcome this hurdle, we study penalized quasilikelihood estimation and…

贝叶斯MIDAS惩罚回归：估计、选择与预测AI 解读

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian estimation and inference. In particular, to improve the prediction properties of the model and its sparse recovery ability, we consider a Group Lasso with a spike-and-slab prior. Penalty hyper-parameters governing the model shrinkage are automatically tuned via an adaptive MCMC algorithm. We establish good frequentist asymptotic…

带正则化的最大线性回归模型AI 解读

Motivated by the newly developed max-linear competing copula factor models and max-stable nonlinear time series models, we propose a new class of max-linear regression models to take advantages of easy interpretable features embedded in linear regression models. It can be seen that linear relation is a special case of max-linear relation. We develop an EM algorithm based maximum likelihood estimation procedure. The consistency and asymptotics of the estimators for parameters…

随机系数多项 Logit 模型中的惩罚似然参数选择AI 解读

This paper is about estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters, some of which may be zero. The paper gives conditions under which, with probability approaching 1 as the sample size increases, penalized maximum likelihood (PML) estimation with the adaptive LASSO (AL) penalty distinguishes correctly between zero and non-zero parameters. The paper also gives conditions under which PML…

多个时变关联群组的建模：动态层次贝叶斯方法及其在健康与退休研究中的应用AI 解读

As the population of the older individuals continues to grow, it is important to study the relationship among the variables measuring financial health and physical health of the older individuals to better understand the demand for healthcare, and health insurance. We propose a semiparametric approach to jointly model these variables. We use data from the Health and Retirement Study which includes a set of correlated longitudinal variables measuring financial and physical…

纵向数据分位数回归系数函数的参数化建模AI 解读

In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (qrcm), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this article, we describe how the qrcm paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used…

高维稀有特征选择AI 解读

It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such “rare features” has received little attention despite its prevalence in diverse areas, ranging from natural language processing (e.g., rare words) to biology (e.g., rare species). We show, both theoretically and empirically, that not explicitly accounting for the…

多个脑功能网络的贝叶斯联合建模AI 解读

Investigating the similarity and changes in brain networks under different mental conditions has become increasingly important in neuroscience research. A standard separate estimation strategy fails to pool information across networks and hence has reduced estimation accuracy and power to detect between-network differences. Motivated by a fMRI Stroop task experiment that involves multiple related tasks, we develop an integrative Bayesian approach for jointly modeling…

多层基因组网络中的贝叶斯结构学习AI 解读

Integrative network modeling of data arising from multiple genomic platforms provides insight into the holistic picture of the interactive system, as well as the flow of information across many disease domains including cancer. The basic data structure consists of a sequence of hierarchically ordered datasets for each individual subject, which facilitates integration of diverse inputs, such as genomic, transcriptomic, and proteomic data. A primary analytical task in such…

通过自适应 LASSO 推断非二叉系统发育树AI 解读

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including sampled ancestors in which we sequence a genotype along with its direct descendants, and polytomies in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches…

以无向网络为预测变量的贝叶斯回归：脑连接组应用AI 解读

This article focuses on the relationship between a measure of creativity and the human brain network for subjects in a brain connectome dataset obtained using a diffusion weighted magnetic resonance imaging procedure. We identify brain regions and interconnections that have a significant effect on creativity. Brain networks are often expressed in terms of symmetric adjacency matrices, with row and column indices of the matrix representing the regions of interest (ROI), and a…

多面体约束条件下模型选择后置信区间的长度AI 解读

Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee, et al. (2016), allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the length of these intervals. For one of these confidence…