This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt...This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.展开更多
Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear mode...Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.展开更多
在传统的组合预测模型中,利用的数据大多为结构化数据,然而在网络环境下,非结构化数据广泛存在,因此充分利用非结构化数据所提供的有效信息是预测中要解决的关键问题之一。针对上述问题,文章构建了基于非结构化数据的局部线性嵌入和鲸...在传统的组合预测模型中,利用的数据大多为结构化数据,然而在网络环境下,非结构化数据广泛存在,因此充分利用非结构化数据所提供的有效信息是预测中要解决的关键问题之一。针对上述问题,文章构建了基于非结构化数据的局部线性嵌入和鲸鱼优化算法的最小二乘支持向量回归(locally linear embedding-whale optimization algorithm-least squares support vector regression,LLE-WOA-LSSVR)碳价格组合预测模型,通过LLE算法对非结构化的高维数据进行降维处理,并利用LSSVR进行预测。考虑到LSSVR模型中参数的选取会对预测结果产生影响,引入WOA算法优化模型中的参数。碳价格预测的实例结果表明,LLE-WOA-LSSVR预测模型可行且有效。展开更多
A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the ...A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the high efficiency and stability of the algorithm.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of m...Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.展开更多
基金This project is supported by the National Natural Science Foundation of China
文摘This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.
文摘Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.
文摘在传统的组合预测模型中,利用的数据大多为结构化数据,然而在网络环境下,非结构化数据广泛存在,因此充分利用非结构化数据所提供的有效信息是预测中要解决的关键问题之一。针对上述问题,文章构建了基于非结构化数据的局部线性嵌入和鲸鱼优化算法的最小二乘支持向量回归(locally linear embedding-whale optimization algorithm-least squares support vector regression,LLE-WOA-LSSVR)碳价格组合预测模型,通过LLE算法对非结构化的高维数据进行降维处理,并利用LSSVR进行预测。考虑到LSSVR模型中参数的选取会对预测结果产生影响,引入WOA算法优化模型中的参数。碳价格预测的实例结果表明,LLE-WOA-LSSVR预测模型可行且有效。
文摘A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the high efficiency and stability of the algorithm.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
文摘Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.
基金Supported by the National Natural Science Foundation of China （No. 61001105）, the National Science and Technology Major Projects （No. 2011ZX03001- 007- 03） and Beijing Natural Science Foundation （No. 4102043）.
