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生存数据的高维变量选择AI 解读

The minimal depth of a maximal subtree is a dimensionless order statistic measuring the predictiveness of a variable in a survival tree. We derive the distribution of the minimal depth and use it for high-dimensional variable selection using random survival forests. In big p and small n problems (where p is the dimension and n is the sample size), the distribution of the minimal depth reveals a “ceiling effect” in which a tree simply cannot be grown deep enough to properly…

通过广义信息准则选择正则化参数AI 解读

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice of regularization parameter, which controls the model complexity. In this paper, we propose employing the generalized information criterion (GIC), encompassing the commonly used Akaike information criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter. Our proposal makes a…

在高维分类器中纳入类别先验概率AI 解读

In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of high-dimensional classifiers, partly because there are no likelihoods to be constructed or Bayes risks to be estimated. Nevertheless, including information about prior probabilities…

贝叶斯检验与估计及其在小波阈值化中的应用AI 解读

We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various sparse lp-balls are extended to more general cases. We show that, for a properly chosen prior on the number of nonzero entries of…

向量自回归过程的加权最小二乘近似限制似然估计AI 解读

We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and…

局部加性估计AI 解读

Summary Additive models are popular in high dimensional regression problems owing to their flexibility in model building and optimality in additive function estimation. Moreover, they do not suffer from the so-called curse of dimensionality generally arising in non-parametric regression settings. Less known is the model bias that is incurred from the restriction to the additive class of models. We introduce a new class of estimators that reduces additive model bias, yet…

核学习中的正则化AI 解读

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm.

常微分方程参数广义剖面估计的渐近效率与有限样本性质AI 解读

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop efficient estimation procedures for these parameters. Among the proposed methods in the literature, the generalized profiling estimation method developed by Ramsay and colleagues is particularly promising for its computational efficiency and good…

核随机矩阵的谱AI 解读

We place ourselves in the setting of high-dimensional statistical inference where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n. We consider the spectrum of certain kernel random matrices, in particular n×n matrices whose (i, j)th entry is f(X'iXj/p) or f(‖Xi−Xj‖2/p) where p is the dimension of the data, and Xi are independent data vectors. Here f is assumed to be a locally smooth function. The study is…

加性系数模型的样条回拟核平滑AI 解读

Additive coefficient model (Xue and Yang, 2006a, 2006b) is a flexible regression and autoregression tool that circumvents the “curse of dimensionality.” We propose spline-backfitted kernel (SBK) and spline-backfitted local linear (SBLL) estimators for the component functions in the additive coefficient model that are both (i) computationally expedient so they are usable for analyzing high dimensional data, and (ii) theoretically reliable so inference can be made on the…

多元或函数型数据线性预测中的成分排序与选择AI 解读

Summary The problem of component choice in regression-based prediction has a long history. The main cases where important choices must be made are functional data analysis, and problems in which the explanatory variables are relatively high dimensional vectors. Indeed, principal component analysis has become the basis for methods for functional linear regression. In this context the number of components can also be interpreted as a smoothing parameter, and so the viewpoint…

同时降维与变量选择的稀疏偏最小二乘回归AI 解读

Summary Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate…

高斯与部分非高斯状态空间模型的随机设定搜索AI 解读

Model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time-varying. To this aim a new model space MCMC method is developed in this paper. It is based on extending the Bayesian variable selection approach which is usually applied to variable selection in regression models to state space models. For non-Gaussian state space models stochastic model search…

聚类失效时间线性回归的广义矩估计：引文更正AI 解读

Although Qu et al. (2000) was cited in § 1 of our paper, it should also have been mentioned as the source of the basis representation of the inverse correlation matrix following our equation (3). Moreover our Theorem 3 rests on arguments similar to those leading to Theorem 1 of Qu et al. (2000). We thank Dr Qu for pointing this out. ‘A group bridge approach for variable selection’ BY JIAN HUANG, SHUANGGE MA, HUILIANG XIE AND CUN-HUI ZHANG [email protected][email…

利用平滑阈值估计方程自动选择变量AI 解读

This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley--James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A bic -type criterion for tuning…

指数族非线性模型中的偏差缩减AI 解读

In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized…

贝叶斯 lasso 回归AI 解读

The lasso estimate for linear regression corresponds to a posterior mode when independent, double-exponential prior distributions are placed on the regression coefficients. This paper introduces new aspects of the broader Bayesian treatment of lasso regression. A direct characterization of the regression coefficients’ posterior distribution is provided, and computation and inference under this characterization is shown to be straightforward. Emphasis is placed on point…

高维加性建模AI 解读

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but…

状态空间模型中的趋势估计：渐近均方误差与收敛速度AI 解读

The focus of this paper is on trend estimation for a general state-space model Yt=μt+ɛt, where the dth difference of the trend {μt} is assumed to be i.i.d., and the error sequence {ɛt} is assumed to be a mean zero stationary process. A fairly precise asymptotic expression of the mean square error is derived for the estimator obtained by penalizing the dth order differences. Optimal rate of convergence is obtained, and it is shown to be “asymptotically equivalent” to a…

大型协方差矩阵估计的稀疏一致性与收敛速度AI 解读

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three…

从观测数据估计高维干预效应AI 解读

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the…

以正则化最小二乘统一模型选择与稀疏恢复AI 解读

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares estimator enjoys a nonasymptotic property, called the weak oracle property, where the dimensionality can grow exponentially…

高维数据分类的稳健最近邻方法AI 解读

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of heavy-tailed data. Empirical rules are suggested for choosing the threshold. They require the bare minimum of data; only one data vector is needed from each population. Theoretical and numerical aspects of performance are explored, paying…

用于分组与层级变量选择的复合绝对惩罚族AI 解读

Extracting useful information from high-dimensional data is an important focus of today’s statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including L1 to form an…