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高维线性回归逐协变量多重检验变量选择法的狭义复现AI 解读

Summary Chudik, Kapetanios, & Pesaran (Econometrica 2018, 86, 1479‐1512) propose a one covariate at a time, multiple testing (OCMT) approach to variable selection in high‐dimensional linear regression models as an alternative approach to penalised regression. We offer a narrow replication of their key OCMT results based on the Stata software instead of the original MATLAB routines. Using the new user‐written Stata commands baing and ocmt , we find results that match closely…

刀切经验似然：小带宽、稀疏网络与高维渐近AI 解读

Summary This article aims to shed light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of the jackknife empirical likelihood. Examples include small-bandwidth asymptotics for semiparametric inference and goodness-of-fit testing, sparse-network asymptotics, many-covariates asymptotics for regression models, and many-weak-instruments asymptotics for instrumental variable regression. We first establish…

通过预测变量增广确定降维阶数AI 解读

Summary In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based…

Wilks 现象的相变AI 解读

Summary Wilks’ theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the conventional Wilks’ phenomenon of the likelihood ratio test statistic often fails. Although new approximations have been proposed in high-dimensional settings, there still lacks a clear statistical guideline regarding how to choose…

用于α散度最小化的无限维梯度下降AI 解读

This paper introduces the (α,Γ)-descent, an iterative algorithm which operates on measures and performs α-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions Γ, this algorithm leads at each step to a systematic decrease in the α-divergence and derive convergence results. Our…

含时变协变量的非参数风险函数提升估计AI 解读

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent…

二阶 Stein 公式：SURE 的风险估计及高维推断应用AI 解读

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf is the divergence of the function f and z is a standard normal vector. This paper aims to propose a second-order Stein formula to characterize the variance of such random variables for all functions f(z) with square integrable gradient, and to demonstrate the usefulness of this second-order Stein formula in various applications. In…

Lasso 的分布：稀疏球上的一致控制与自适应参数调节AI 解读

The Lasso is a popular regression method for high-dimensional problems in which the number of parameters θ1,…,θN, is larger than the number n of samples: N>n. A useful heuristics relates the statistical properties of the Lasso estimator to that of a simple soft-thresholding denoiser, in a denoising problem in which the parameters (θi)i≤N are observed in Gaussian noise, with a carefully tuned variance. Earlier work confirmed this picture in the limit n,N→∞, pointwise in the…

全连接深度神经网络回归估计的收敛速率AI 解读

Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results…

高维距离相关推断的渐近分布AI 解读

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in…

具有因子结构的多任务分位数回归AI 解读

A multivariate quantile regression model with a factor structure is proposed to study data with multivariate responses with covariates. The factor structure is allowed to vary with the quantile levels, which is more flexible than the classical factor models. Assuming the number of factors is small, and the number of responses and the input variables are growing with the sample size, the model is estimated with the nuclear norm regularization. The incurred optimization…

利用因果推断与机器学习评估1990年《清洁空气法》修正案的健康影响AI 解读

We develop a causal inference approach to estimate the number of adverse health events that were prevented due to changes in exposure to multiple pollutants attributable to a large-scale air quality intervention/regulation, with a focus on the 1990 Clean Air Act Amendments (CAAA). We introduce a causal estimand called the Total Events Avoided (TEA) by the regulation, defined as the difference in the number of health events expected under the no-regulation pollution exposures…

利用双重 Lasso 惩罚非参数估计星系团辐射率并检测点源AI 解读

Astrophysicists are interested in recovering the three-dimensional gas emissivity of a galaxy cluster from a two-dimensional telescope image. Blurring and point sources make this inverse problem harder to solve. The conventional approach requires in a first step to identify and mask the point sources. Instead we model all astrophysical components in a single Poisson generalized linear model. To enforce sparsity on the parameters, maximum likelihood estimation is regularized…

高维季节性天气预测的多元后处理方法AI 解读

–Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical postprocessing of the output to correct systematic biases and unrealistic uncertainty assessments. We propose a multivariate postprocessing approach using covariance tapering, combined with a dimension reduction step based on principal component…

神经网络训练作为数据自适应核学习：表示与逼近收益AI 解读

Consider the problem: given the data pair (x,y) drawn from a population with f*(x)=E[y|x=x], specify a neural network model and run gradient flow on the weights over time until reaching any stationarity. How does ft , the function computed by the neural network at time t, relate to f*, in terms of approximation and representation? What are the provable benefits of the adaptive representation by neural networks compared to the pre-specified fixed basis representation in the…

利用干扰参数惩罚回归对高维数据开展目标推断AI 解读

Analysis of high dimensional data has received considerable and increasing attention in statistics. In practice, we may not be interested in every variable that is observed. Instead, often some of the variables are of particular interest, and the remaining variables are nuisance. To this end, we propose the nuisance penalized regression which does not penalize the parameters of interest. When the coherence between interest parameters and nuisance parameters is negligible, we…

基于 Metropolis–Hastings 的 Knockoff 采样AI 解读

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This article introduces techniques for…

个体化多方向变量选择AI 解读

In this article, we propose a heterogeneous modeling framework which achieves individual-wise feature selection and heterogeneous covariates’ effects subgrouping simultaneously. In contrast to conventional model selection approaches, the new approach constructs a separation penalty with multidirectional shrinkages, which facilitates individualized modeling to distinguish strong signals from noisy ones and selects different relevant variables for different individuals.…

通过递归在线得分估计进行高维模型推断AI 解读

In this paper, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the…

函数型 Cox 模型的半参数推断AI 解读

This article studies penalized semiparametric maximum partial likelihood estimation and hypothesis testing for the functional Cox model in analyzing right-censored data with both functional and scalar predictors. Deriving the asymptotic joint distribution of finite-dimensional and infinite-dimensional estimators is a very challenging theoretical problem due to the complexity of semiparametric models. For the problem, we construct the Sobolev space equipped with a special…

树上 Wasserstein 距离的最优估计及微生物组应用AI 解读

The weighted UniFrac distance, a plug-in estimator of the Wasserstein distance of read counts on a tree, has been widely used to measure the microbial community difference in microbiome studies. Our investigation however shows that such a plug-in estimator, although intuitive and commonly used in practice, suffers from potential bias. Motivated by this finding, we study the problem of optimal estimation of the Wasserstein distance between two distributions on a tree from the…

ALMOND：基于神经网络与 Langevin 扩散的自适应潜变量建模和优化AI 解读

Latent variable models cover a broad range of statistical and machine learning models, such as Bayesian models, linear mixed models, and Gaussian mixture models. Existing methods often suffer from two major challenges in practice: (a) a proper latent variable distribution is difficult to be specified; (b) making an exact likelihood inference is formidable due to the intractable computation. We propose a novel framework for the inference of latent variable models that…

高维数据位置参数的逆范数符号检验AI 解读

We consider the one sample location testing problem for high-dimensional data, where the data dimension is potentially much larger than the sample size. We devise a novel inverse norm sign test (INST) that is consistent and has much improved power than many existing popular tests. We further construct a general class of weighted spatial sign tests which includes these existing tests, and show that INST is the optimal member within this class, in that it is consistent and is…

在稀疏分位数回归中纳入预测变量的图结构AI 解读

Quantile regression in high-dimensional settings is useful in analyzing high-dimensional heterogeneous data. In this article, different from existing methods in quantile regression which treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection, and prediction in sparse quantile regression. It is shown under mild conditions that the proposed method…