Investigating the Effect of Randomly Selected Feature Subsets on Bagging and Boosting

Bagging, boosting, and random subspace methods are three most commonly used approaches for constructing ensemble classifiers. In this article, the effect of randomly selected feature subsets (intersectant or disjoint) on bagging and boosting is investigated. The performance of the related ensemble methods are compared by conducting experiments on some UCI benchmark datasets. The results demonstrate that bagging can be generally improved using the randomly selected feature subsets whereas boosting can only be optimized in some cases. Furthermore, the diversity between classifiers in an ensemble is also discussed and related to the prediction accuracy of the ensemble classifier.     

Pitman closeness of record values from two sequences to population quantiles

Suppose upper records from two independent sequences from iid continuous random variables from the same distribution are observed. Pitman's measure of closeness of these statistics to population quantiles of the parent distribution is studied and various exact expressions are derived. For symmetric distributions, Pitman closeness probabilities of records to median are also obtained. Examples including exponential and uniform distributions are discussed. Numerical evaluations are presented to illustrate all the results developed here.     

On Exact K-optimal Designs Minimizing the Condition Number

A new design criterion based on the condition number of an information matrix is proposed to construct optimal designs for linear models, and the resulting designs are called K-optimal designs. The relationship between exact and asymptotic K-optimal designs is derived. Since it is usually hard to find exact optimal designs analytically, we apply a simulated annealing algorithm to compute K-optimal design points on continuous design spaces. Specific issues are addressed to make the algorithm effective. Through exact designs, we can examine some properties of the K-optimal designs such as symmetry and the number of support points. Examples and results are given for polynomial regression models and linear models for fractional factorial experiments. In addition, K-optimal designs are compared with A-optimal and D-optimal designs for polynomial regression models, showing that K-optimal designs are quite similar to A-optimal designs.     

关于线性变换的根子空间

本文系统论述了属于线性变换特征概念范围的根子空间的基本问题，主要的有两点：（１）根向量所属于的特征值的唯一性；（２）根子空间与特征子空间的结构关系，作为论述这两个问题的预备定理，文中还证明了根向量或根子空间的其它两个重要性质。     

麦克风阵列二维方向估计聚焦算法研究

聚焦算法是解决宽带信号方向(DOA)估计问题的重要算法。常规的宽带聚焦算法需要进行预估计和多次迭代,算法的计算复杂度较高。该文根据宽带聚焦算法的思想,结合语音信号的特点,以各频率点的频域相关矩阵和聚焦点的相关矩阵的均方误差最小为最优化准则,提出了一种不需要预估计和迭代的二维宽带聚焦算法。该算法实时性好、计算复杂度低。采用八元均匀圆环麦克风阵列,仿真验证了该算法的良好二维DOA估计性能。     

一致有界实值函数集上的最佳同时逼近

给出了最佳同时逼近的特征定理 ,并由此导出了最佳同时逼近的交错定理和强唯一性定理     

Dimension reduction for the conditional mean and variance functions in time series

This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current observation given the vector of past observations is the same as that of the current observation given a few linear combinations of the past observations without loss of inferential information. The directions of the mean and variance functions are estimated by maximizing the Kullback–Leibler distance function. The consistency of the proposed estimators is established. A computational procedure is introduced to detect lags of the conditional mean and variance functions in practice. Numerical examples and simulation studies are performed to illustrate and evaluate the performance of the proposed estimators.     

Concordance-based estimation approaches for the optimal sufficient dimension reduction score

To characterize the dependence of a response on covariates of interest, a monotonic structure is linked to a multivariate polynomial transformation of the central subspace (CS) directions with unknown structural degree and dimension. Under a very general semiparametric model formulation, such a sufficient dimension reduction (SDR) score is shown to enjoy the existence, optimality, and uniqueness up to scale and location in the defined concordance probability function. In light of these properties and its single-index representation, two types of concordance-based generalized Bayesian information criteria are constructed to estimate the optimal SDR score and the maximum concordance index. The estimation criteria are further carried out by effective computational procedures. Generally speaking, the outer product of gradients estimation in the first approach has an advantage in computational efficiency and the parameterization system in the second approach greatly reduces the number of parameters in estimation. Different from most existing SDR approaches, only one CS direction is required to be continuous in the proposals. Moreover, the consistency of structural degree and dimension estimators and the asymptotic normality of the optimal SDR score and maximum concordance index estimators are established under some suitable conditions. The performance and practicality of our methodology are also investigated through simulations and empirical illustrations.     

Random sliced inverse regression

Sliced Inverse Regression (SIR; 1991) is a dimension reduction method for reducing the dimension of the predictors without losing regression information. The implementation of SIR requires inverting the covariance matrix of the predictors—which has hindered its use to analyze high-dimensional data where the number of predictors exceed the sample size. We propose random sliced inverse regression (rSIR) by applying SIR to many bootstrap samples, each using a subset of randomly selected candidate predictors. The final rSIR estimate is obtained by aggregating these estimates. A simple variable selection procedure is also proposed using these bootstrap estimates. The performance of the proposed estimates is studied via extensive simulation. Application to a dataset concerning myocardial perfusion diagnosis from cardiac Single Proton Emission Computed Tomography (SPECT) images is presented.     

Coefficient of relationship for two symmetric alpha-stable variables when alpha is in the interval (1,2]

This article derives a new coefficient of relationship of two symmetric alpha-stable variables when alpha is in the interval (1,2] based on covariation. Its numerical value ranges from ?1 to +1. Simulation studies are used to evaluate the performance of the coefficient of relationship estimators.