When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot ...When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.展开更多
A generalization of supervised single-label learning based on the assumption that each sample in a dataset may belong to more than one class simultaneously is called multi-label learning.The main objective of this wor...A generalization of supervised single-label learning based on the assumption that each sample in a dataset may belong to more than one class simultaneously is called multi-label learning.The main objective of this work is to create a novel framework for learning and classifying imbalancedmulti-label data.This work proposes a framework of two phases.The imbalanced distribution of themulti-label dataset is addressed through the proposed Borderline MLSMOTE resampling method in phase 1.Later,an adaptive weighted l21 norm regularized(Elastic-net)multilabel logistic regression is used to predict unseen samples in phase 2.The proposed Borderline MLSMOTE resampling method focuses on samples with concurrent high labels in contrast to conventional MLSMOTE.The minority labels in these samples are called difficult minority labels and are more prone to penalize classification performance.The concurrentmeasure is considered borderline,and labels associated with samples are regarded as borderline labels in the decision boundary.In phase II,a novel adaptive l21 norm regularized weighted multi-label logistic regression is used to handle balanced data with different weighted synthetic samples.Experimentation on various benchmark datasets shows the outperformance of the proposed method and its powerful predictive performances over existing conventional state-of-the-art multi-label methods.展开更多
I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surpr...I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12271294,12171225 and 12071248.
文摘When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.
基金partly supported by the Technology Development Program of MSS(No.S3033853)by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2021R1A4A1031509).
文摘A generalization of supervised single-label learning based on the assumption that each sample in a dataset may belong to more than one class simultaneously is called multi-label learning.The main objective of this work is to create a novel framework for learning and classifying imbalancedmulti-label data.This work proposes a framework of two phases.The imbalanced distribution of themulti-label dataset is addressed through the proposed Borderline MLSMOTE resampling method in phase 1.Later,an adaptive weighted l21 norm regularized(Elastic-net)multilabel logistic regression is used to predict unseen samples in phase 2.The proposed Borderline MLSMOTE resampling method focuses on samples with concurrent high labels in contrast to conventional MLSMOTE.The minority labels in these samples are called difficult minority labels and are more prone to penalize classification performance.The concurrentmeasure is considered borderline,and labels associated with samples are regarded as borderline labels in the decision boundary.In phase II,a novel adaptive l21 norm regularized weighted multi-label logistic regression is used to handle balanced data with different weighted synthetic samples.Experimentation on various benchmark datasets shows the outperformance of the proposed method and its powerful predictive performances over existing conventional state-of-the-art multi-label methods.
文摘I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.
