General Sparse Boosting: Improving Feature Selection of L2 Boosting by Correlation-Based Penalty Family

In high-dimensional setting, componentwise L₂boosting has been used to construct sparse model that performs well, but it tends to select many ineffective variables. Several sparse boosting methods, such as, SparseL₂Boosting and Twin Boosting, have been proposed to improve the variable selection of L₂boosting algorithm. In this article, we propose a new general sparse boosting method (GSBoosting). The relations are established between GSBoosting and other well known regularized variable selection methods in the orthogonal linear model, such as adaptive Lasso, hard thresholds, etc. Simulation results show that GSBoosting has good performance in both prediction and variable selection.     

Splines for financial volatility

Summary.  We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B -splines of lagged observations and volatilities. Estimation of such a B -spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B -spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.     

Asymptotic convergence of dimension reduction based boosting in classification

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method–dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.     

一种新的空间权重矩阵选择方法

空间权重矩阵选择问题一直是空间计量经济学中的一个难题,权重矩阵的选择正确与否关系到模型的最终估计结果。本文在空间滞后模型框架下,把空间权重矩阵选择问题转化为变量选择问题,然后利用CWB方法进行变量选择。中国城市服务业集聚机理实证研究显示,利用本文所提出的方法所选取的空间权重矩阵较为合理,进而可以减少因为空间权重矩阵误设问题而引起的模型估计偏误。在大样本情形下,该方法可以非常有效地降低计算成本。     

A Comparative Study of Semiparametric Estimation in Partially Linear Single-index Models

We consider a semiparametric method based on partial splines for estimating the unknown function and partially linear regression parameters in partially linear single-index models. Three methods—project pursuit regression (PPR), average derivative estimation (ADE), and a boosting method—are considered for estimating the single-index parameters. Simulations revealed that PPR with partial splines was superior in estimating single-index parameters, while the boosting method with partial splines performed no better than PPR and ADE. All three methods performed similarly in estimating the partially linear regression parameters. The relative performances of the methods are also illustrated using a real-world data example.     

Modelling price paths in on-line auctions: smoothing sparse and unevenly sampled curves by using semiparametric mixed models

Summary.  On-line auctions pose many challenges for the empirical researcher, one of which is the effective and reliable modelling of price paths. We propose a novel way of modelling price paths in eBay's on-line auctions by using functional data analysis. One of the practical challenges is that the functional objects are sampled only very sparsely and unevenly. Most approaches rely on smoothing to recover the underlying functional object from the data, which can be difficult if the data are irregularly distributed. We present a new approach that can overcome this challenge. The approach is based on the ideas of mixed models. Specifically, we propose a semiparametric mixed model with boosting to recover the functional object. As well as being able to handle sparse and unevenly distributed data, the model also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's on-line auctions. On-line auctions produce monotonic increasing price curves that are often correlated across auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also manages to capture the underlying monotonic trend in the data without imposing model constraints. Our application shows that the resulting functional objects are conceptually more appealing. Moreover, when used to forecast the outcome of an on-line auction, our approach also results in more accurate price predictions compared with standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants.     

A comparison of methods for the fitting of generalized additive models

There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.     

Penalized regression with correlation-based penalty

A new regularization method for regression models is proposed. The criterion to be minimized contains a penalty term which explicitly links strength of penalization to the correlation between predictors. Like the elastic net, the method encourages a grouping effect where strongly correlated predictors tend to be in or out of the model together. A boosted version of the penalized estimator, which is based on a new boosting method, allows to select variables. Real world data and simulations show that the method compares well to competing regularization techniques. In settings where the number of predictors is smaller than the number of observations it frequently performs better than competitors, in high dimensional settings prediction measures favor the elastic net while accuracy of estimation and stability of variable selection favors the newly proposed method.     

New Bootstrap Applications in Supervised Learning

Some bootstrap and boosting methods for problems related to classification are introduced in this article. The first method chooses better boosting weights by using a bootstrap search algorithm. The second method is a good way to define a classification frontier. A new formulation for boosting in linear discriminant analysis is given. Since in this new formulation the uncertainty is represented by the weighted covariance matrix, it is more appropriate from the conceptual point of view. Simulation results show that the proposed methods perform well in data analysis.     

论科技对艺术发展的影响

文章就科学技术对艺术发展的多方面影响展开了论述。提出科学为艺术的创作提供了技术支持,科学技术拓展了艺术的发展空间,促进了艺术表现形式及风格的多样性及创新性。文章最后指出,随着科学技术的进一步发展,它必将对艺术的发展起到越来越深刻的影响。