大气中臭氧含量分析预测的支向量机模型

以俄亥俄州(O h io)的气象、臭氧监测数据为基础,对一个监测点数据进行了分析处理,运用支持向量机回归方法,对气象指标的多参数样本进行学习,获得精确的支持向量机映射关系,并对臭氧含量进行预测.预测结果的误差较小,符合实际情况,能够较好的解决实际问题,说明支持向量机回归在预测上具有小的结构风险与强的泛化能力.     

鲁棒半监督ν-支持向量分类机

支持向量机在近十年成为机器学习的主要学习技术,而且已经成功应用到有监督学习问题中。Fung和Mangasarian利用支持向量机对于既有已标类别样本又有未知类别样本的训练集进行训练,方法主要是利用少量已标明类别的样本进行训练得到一个分类器的同时对于未标明类别的样本进行分类,使得间隔最大化。此优化问题中假定样本是精确的,而在现实生活中,样本通常带有统计误差。因此,考虑样本带有扰动信息的半监督两类分类问题,给出鲁棒半监督v-支持向量分类算法。该算法的参数v易于选择,而数值试验也表明该算法具有良好的稳定性和较好的分类结果。     

支持向量机的关键问题和展望

作为机器学习的主要方法之一,支持向量机不仅有坚实的统计学习理论基础,而且在众多领域中表现出优秀的泛化性能,因此受到了广泛关注.然而近几年来,相比于深度学习的蓬勃发展,支持向量机的研究进展缓慢.本文从支持向量机的本质出发,探讨支持向量机的理论方法与深度学习等机器学习热点研究的交叉与融合,提出一些新的思路.具体地,包括3个方面:支持向量机的大间隔原则及其带来的低密度性、核映射的高维划分技巧及其统计学习理论,以及支持向量机的浅层学习模式向深度学习和广度学习的拓展.同时,从这3个方面分别提出支持向量机研究中可以进一步挖掘的优良性质,并展望未来可能诱导出的理论和方法.     

基于主成分分析的支持向量机模型对上海房价的预测研究

采用基于主成分分析的支持向量机方法对上海房价进行预测.首先利用主成分分析法对原始数据进行降维处理,然后利用具有高水平的小样本学习能力的支持向量机进行预测模型的建立,对上海房价进行预测.实证显示,经过主成分分析的支持向量机模型能够较好地处理复杂的房地产数据,具有较高的预测能力,为上海房地产业的发展提供参考.特别地,该模型可以普遍应用于影响因素众多,时效性较强的短期小样本数据问题的预测,具有较高的泛化能力和很好的预测精度.     

加权支持向量机在证券指数预测中的研究

支持向量机是基于统计学习理论的新一代学习机器.它使用结构风险最小化原则,运用核技巧,较好地解决了学习问题.本文提出了一种基于支持向量机的加权算法,并将其应用于证券,指数预测.与径向基神经网络相比较,加权支持向量机表现出了良好的性能.     

基于最近边界向量的SVM增量学习算法

为了减少求支持向量过程中二次规划的复杂度,利用训练样本集的几何信息,选出两类中离另一类最近的边界向量集合,它是样本中最有可能成为支持向量的一部分,用它代替原样本集进行训练.对新增样本,若存在违反KKT条件的样本,只对这部分新样本进行学习.同时找出原样本中可能转化为支持向量的非支持向量样本.基于分析结果,提出了一种新的基于最近边界向量的增量式支持向量机学习算法.对标准数据集的实验结果表明,算法是可行的,有效的.     

基于双重粗糙样本的统计学习理论的理论基础

本文介绍双重粗糙理论的基本内容;提出双重粗糙经验风险泛函,双重粗糙期望风险泛函,双重粗糙经验风险最小化原则等概念;最后证明基于双重粗糙样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界.为系统建立基于不确定样本的统计学习理论并构建相应的支持向量机奠定了理论基础.     

基于分形流形学习的支持向量机空气污染指数预测模型北大核心CSCD

针对目前北京、上海和广州地区较严重空气污染问题,建立了基于分形流形学习的支持向量机空气污染指数预测模型.首先采用分形理论计算出空气污染数据集分形维数;其次根据分形维数,采用流形学习将高维空气污染数据集通过非线性映射嵌入到低维空间中,对空气污染数据集进行降维;最后建立基于高斯核的支持向量机预测模型对三地区空气污染指数进行预测.北京、上海和广州三地空气污染指数预测结果表明,该模型较传统预测模型,预测性能更优,具有良好的稳定性和有效性.     

SVMs在微阵列表达数据分析中的应用

微阵列技术允许同时录制成百万的基因表达水平。但由于经费和工艺的限制,目前研究者获得的表达数据集往往包含少量的样本,而基因表达的测量值却有上万条。很多传统的统计方法无法分析这样的数据,本文结合数据挖掘中统计学习理论的相关知识,详细介绍了一种有监督分析方法———支持向量机(SVMs)在微阵列表达数据分析中的应用。     

基于分形流形学习的支持向量机空气污染指数预测模型

针对目前北京、上海和广州地区较严重空气污染问题,建立了基于分形流形学习的支持向量机空气污染指数预测模型.首先采用分形理论计算出空气污染数据集分形维数;其次根据分形维数,采用流形学习将高维空气污染数据集通过非线性映射嵌入到低维空间中,对空气污染数据集进行降维;最后建立基于高斯核的支持向量机预测模型对三地区空气污染指数进行预测.北京、上海和广州三地空气污染指数预测结果表明,该模型较传统预测模型,预测性能更优,具有良好的稳定性和有效性.     

Multi-objective algorithm for the design of prediction intervals for wind power forecasting model

A composite forecasting framework is designed and implemented successfully to estimate the prediction intervals of wind speed time series simultaneously through machine learning method embedding a newly proposed optimization method (multi-objective salp swarm algorithm). In this study, data pre-process strategy based on feature extraction is served for reducing the fluctuations of wind power generation and select appropriate input forms of wind speed datasets for the sake of improving the overall performance. Besides, fuzzy set theory selection technique is used to determine the best compromise solutions from Pareto front set deriving from the optimization phase. To test the effectiveness of the proposed composite forecasting framework, several case studies based on different time-scale wind speed datasets are conducted. The corresponding results present that the proposed framework significantly outperforms other benchmark methods, and it can provide very satisfactory results in both goals between high coverage and small width.     

An efficient random forests algorithm for high dimensional data classification

In this paper, we propose a new random forest (RF) algorithm to deal with high dimensional data for classification using subspace feature sampling method and feature value searching. The new subspace sampling method maintains the diversity and randomness of the forest and enables one to generate trees with a lower prediction error. A greedy technique is used to handle cardinal categorical features for efficient node splitting when building decision trees in the forest. This allows trees to handle very high cardinality meanwhile reducing computational time in building the RF model. Extensive experiments on high dimensional real data sets including standard machine learning data sets and image data sets have been conducted. The results demonstrated that the proposed approach for learning RFs significantly reduced prediction errors and outperformed most existing RFs when dealing with high-dimensional data.     

Numerical study of learning algorithms on Stiefel manifold

Convex optimization methods are used for many machine learning models such as support vector machine. However, the requirement of a convex formulation can place limitations on machine learning models. In recent years, a number of machine learning methods not requiring convexity have emerged. In this paper, we study non-convex optimization problems on the Stiefel manifold in which the feasible set consists of a set of rectangular matrices with orthonormal column vectors. We present examples of non-convex optimization problems in machine learning and apply three nonlinear optimization methods for finding a local optimal solution; geometric gradient descent method, augmented Lagrangian method of multipliers, and alternating direction method of multipliers. Although the geometric gradient method is often used to solve non-convex optimization problems on the Stiefel manifold, we show that the alternating direction method of multipliers generally produces higher quality numerical solutions within a reasonable computation time.     

On the robustness of regularized pairwise learning methods based on kernels

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is regularized minimization of the error entropy loss which has recently attracted quite some interest from the viewpoint of consistency and learning rates. This paper shows that such RPL methods and also their empirical bootstrap have additionally good statistical robustness properties, if the loss function and the kernel are chosen appropriately. We treat two cases of particular interest: (i) a bounded and non-convex loss function and (ii) an unbounded convex loss function satisfying a certain Lipschitz type condition.     

基于支持向量机的大豆产量预测研究

应用支持向量机(SVM)的算法进行中国大豆产量的预测研究,用1991-2008年中国大豆数据组成样本集,建立影响因素与大豆产量之间的SVM模型.利用SVM对输入和输出数据进行训练学习,逼近历史数据所隐含的函数关系,完成对新数据序列的映射关系,从而完成对未来年份大豆的预测,并与其它几种方法的预测效果进行比较.结果表明,SVM预测模型预测大豆产量的精度优于其它预测方法.     

An error estimate for matrix equations

This paper proposes a new method for estimating the error in the solution of matrix equations. The estimate is based on the adjoint method in combination with small sample statistical theory. It can be implemented simply and is inexpensive to compute. Numerical examples are presented which illustrate the power and effectiveness of the new method.     

基于灰色关联分析的支持向量机的铁路货运量预测研究

采用基于灰色关联分析的支持向量机对铁路货运量进行预测.首先利用灰色关联分析法对影响铁路货运量的因素进行分析处理,然后利用基于高斯核函数的支持向量回归机建立了铁路货运量预测模型.通过分析预测结果可以发现,经过灰色关联分析后的支持向量机模型对复杂的铁路货运量数据有较好地处理能力,且预测相对误差较小.特别地,由于支持向量机的适应性,该模型具有较高的泛化能力,对影响因素较为复杂,样本数量小的预测问题可以提供一定参考.     

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

COVID-19 Epidemic Prediction Based on Deep Learning

In this paper, a multi-layer gated recurrent unit neural network (multi-head GRU) model is proposed to predict the confirmed cases of the new crown epidemic (COVID-19). We extract the time series relationship in the data, and the rolling prediction method is adopted to ensure the simple structure of the model and achieve higher precision and interpretability. The prediction results of this model are compared with the LSTM model, the Transformer model and the infectious disease model (SIR). The results show that the proposed model has higher prediction accuracy. The mean absolute error (MAE) of epidemic prediction in most countries (the United States, Brazil, India, the United Kingdom and Russia) is respectively 197.52, 68.02, 200.67, 24.78 and 123.50, which is much smaller than the prediction error of the SIR model, LSTM model and Transformer model. For the spread of the COVID-19 epidemic, traditional infectious disease models and machine learning models cannot achieve more accurate predictions. In this paper, we use a GRU model to predict the real-time spread of COVID-19, which has fewer parameters and reduces the risk of overfitting to train faster. Meanwhile, it can make up for the shortcoming of the transformer model to capture local features.     

Generalization errors of Laplacian regularized least squares regression

Semi-supervised learning is an emerging computational paradigm for machine learning,that aims to make better use of large amounts of inexpensive unlabeled data to improve the learning performance.While various methods have been proposed based on different intuitions,the crucial issue of generalization performance is still poorly understood.In this paper,we investigate the convergence property of the Laplacian regularized least squares regression,a semi-supervised learning algorithm based on manifold regularization.Moreover,the improvement of error bounds in terms of the number of labeled and unlabeled data is presented for the first time as far as we know.The convergence rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers.Some new techniques are exploited for the analysis since an extra regularizer is introduced.