In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t...In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.展开更多
In this paper,we obtain a refined non-asymptotic tail bound for the largest singular value(the soft edge)of sub-Gaussian matrix.As an application,we use the obtained theorem to compute the tail bound of the Gaussian T...In this paper,we obtain a refined non-asymptotic tail bound for the largest singular value(the soft edge)of sub-Gaussian matrix.As an application,we use the obtained theorem to compute the tail bound of the Gaussian Toeplitz matrix.展开更多
When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires i...When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.展开更多
The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based o...The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.展开更多
提出了一种新的嵌入高斯混合模型(GMM,Gaussian Mixture Model)遥感影像朴素贝叶斯网络模型GMM-NBC(GMMbased Na ve Bayesian Classifier)。针对连续型朴素贝叶斯网络分类器中假设地物服从单一高斯分布的缺点,该方法将地物在特征空间的...提出了一种新的嵌入高斯混合模型(GMM,Gaussian Mixture Model)遥感影像朴素贝叶斯网络模型GMM-NBC(GMMbased Na ve Bayesian Classifier)。针对连续型朴素贝叶斯网络分类器中假设地物服从单一高斯分布的缺点,该方法将地物在特征空间的分布用高斯混合模型来模拟,用改进EM算法自动获取高斯混合模型的参数;高斯混合模型整体作为一个子节点嵌入朴素贝叶斯网络中,将其输出作为节点(特征)的中间类后验概率,在朴素贝叶斯网络的框架下进行融合获得最终的类后验概率。对多光谱和高光谱数据的分类实验结果表明,该方法较传统贝叶斯分类器分类效果要好,且有较强的鲁棒性。展开更多
基金supported by National Natural Science Foundation of China (10901054)
文摘In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.DUT20LK38)。
文摘In this paper,we obtain a refined non-asymptotic tail bound for the largest singular value(the soft edge)of sub-Gaussian matrix.As an application,we use the obtained theorem to compute the tail bound of the Gaussian Toeplitz matrix.
基金This work was supported by JSPS Grant-in-Aid for Young Scientists(Grant No.18K12873)Waseda University Grants for Special Research Projects(“Tokutei Kadai”)(Grant No.2019C-688).
文摘When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.
文摘The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.
文摘提出了一种新的嵌入高斯混合模型(GMM,Gaussian Mixture Model)遥感影像朴素贝叶斯网络模型GMM-NBC(GMMbased Na ve Bayesian Classifier)。针对连续型朴素贝叶斯网络分类器中假设地物服从单一高斯分布的缺点,该方法将地物在特征空间的分布用高斯混合模型来模拟,用改进EM算法自动获取高斯混合模型的参数;高斯混合模型整体作为一个子节点嵌入朴素贝叶斯网络中,将其输出作为节点(特征)的中间类后验概率,在朴素贝叶斯网络的框架下进行融合获得最终的类后验概率。对多光谱和高光谱数据的分类实验结果表明,该方法较传统贝叶斯分类器分类效果要好,且有较强的鲁棒性。
