基于Group Lasso的多重信号分类声源 定位优化算法*

多重信号分类算法因其抑制噪声能力强、计算速度快等优点,在声源定位领域得到广泛应用。但该算法在中低频段分辨率及聚焦性能较差。针对该问题,提出一种基于Group Lasso的多重信号分类优化算法。该算法将多重信号分类算法输出值作为初始值,并在Group Lasso算法组间计算时对目标信号进行稀疏、在组内计算时对该组信号进行平滑及阈值截断。仿真结果表明:该优化算法在中低频段可明显提高多重信号分类算法分辨率,同时改善因扫描位置与声源面位置不重合引起的聚焦性能下降问题。     

Sparse Multivariate Regression With Covariance Estimation

We propose a procedure for constructing a sparse estimator of a multivariate regression coefficient matrix that accounts for correlation of the response variables. This method, which we call multivariate regression with covariance estimation (MRCE), involves penalized likelihood with simultaneous estimation of the regression coefficients and the covariance structure. An efficient optimization algorithm and a fast approximation are developed for computing MRCE. Using simulation studies, we show that the proposed method outperforms relevant competitors when the responses are highly correlated. We also apply the new method to a finance example on predicting asset returns. An R-package containing this dataset and code for computing MRCE and its approximation are available online.     

Shrinkage estimation and variable selection in multiple regression models with random coefficient autoregressive errors

In this paper, we consider improved estimation strategies for the parameter vector in multiple regression models with first-order random coefficient autoregressive errors (RCAR(1)). We propose a shrinkage estimation strategy and implement variable selection methods such as lasso and adaptive lasso strategies. The simulation results reveal that the shrinkage estimators perform better than both lasso and adaptive lasso when and only when there are many nuisance variables in the model.     

Lasso变量选择的分布式算法

Lasso是机器学习中比较常用的一种变量选择方法,适用于具有稀疏性的回归问题.当样本量巨大或者海量的数据存储在不同的机器上时,分布式计算是减少计算时间提高效率的重要方式之一.本文在给出Lasso模型等价优化模型的基础上,将ADMM算法应用到此优化变量可分离的模型中,构造了一种适用于Lasso变量选择的分布式算法,证明了...     

基于Lasso-Lars的密井网水驱注水量影响因素分析

目前大部分油藏工程都需要合理的注水量调整方案,为了准确预测注水量则需要分析注水量的影响因素及其之间的关系。通过lasso方法可将模型的系数进行压缩使之变小趋于0,利用lars算法可有效解决lasso的求解问题并记录正则化参数λ所有可能取值下对应的lasso优化问题的解,求得lasso正则化路径.应用lasso-lars正则化路径,得到每一个注水井注水量影响因素对应的回归系数及回归系数变化走势图,确定不同影响因素对注水井注水量的敏感程度.同时证明该方法相对于其他方法的有效性及优越性,对注水量预测模型的建立具有重要意义.     

基于Lasso和支持向量机的组合预测及其应用

针对Lasso方法与支持向量机两者的联系与各自的优势,给出了基于Lasso与支持向量机的串联型、并联型和嵌入型三种组合预测,并将它们运用到我国粮食价格预测中.实证结果表明,与单一预测方法的预测结果相比,基于Lasso方法与支持向量机的串联型组合预测和嵌入型组合预测具有更高的预测精度.     

Lasso solution strategies for the vehicle routing problem with pickups and deliveries

This paper considers the vehicle routing problem with pickups and deliveries (VRPPD) where the same customer may require both a delivery and a pickup. This is the case, for instance, of breweries that deliver beer or mineral water bottles to a set of customers and collect empty bottles from the same customers. It is possible to relax the customary practice of performing a pickup when delivering at a customer, and postpone the pickup until the vehicle has sufficient free capacity. In the case of breweries, these solutions will often consist of routes in which bottles are first delivered until the vehicle is partly unloaded, then both pickup and delivery are performed at the remaining customers, and finally empty bottles are picked up from the first visited customers. These customers are revisited in reverse order, thus giving rise to lasso shaped solutions. Another possibility is to relax the traditional problem even more and allow customers to be visited twice either in two different routes or at different times on the same route, giving rise to a general solution. This article develops a tabu search algorithm capable of producing lasso solutions. A general solution can be reached by first duplicating each customer and generating a Hamiltonian solution on the extended set of customers. Test results show that while general solutions outperform other solution shapes in term of cost, their computation can be time consuming. The best lasso solution generated within a given time limit is generally better than the best general solution produced with the same computing effort.     

Semiparametric Estimation and Selection for Nonstationary Spatial Covariance Functions

We propose a method for estimating nonstationary spatial covariance functions by representing a spatial process as a linear combination of some local basis functions with uncorrelated random coefficients and some stationary processes, based on spatial data sampled in space with repeated measurements. By incorporating a large collection of local basis functions with various scales at various locations and stationary processes with various degrees of smoothness, the model is flexible enough to represent a wide variety of nonstationary spatial features. The covariance estimation and model selection are formulated as a regression problem with the sample covariances as the response and the covariances corresponding to the local basis functions and the stationary processes as the predictors. A constrained least squares approach is applied to select appropriate basis functions and stationary processes as well as estimate parameters simultaneously. In addition, a constrained generalized least squares approach is proposed to further account for the dependencies among the response variables. A simulation experiment shows that our method performs well in both covariance function estimation and spatial prediction. The methodology is applied to a U.S. precipitation dataset for illustration. Supplemental materials relating to the application are available online.     

基于多重共线性的处理方法

多重共线性简称共线性是多元线性回归分析中一个重要问题。消除共线性的危害一直是回归分析的一个重点。目前处理严重共线性的常用方法有以下几种:岭回归、主成分回归、逐步回归、偏最小二乘法、Lasso回归等。本文就这几种方法进行比较分析,介绍它们的优缺点,通过实例分析以便于选择合适的方法处理共线性。