For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observat...For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.展开更多
In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel functi...In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions.Based on the derivation process,a unified form for the robust Gaussian filters(RGF)based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement.The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals.Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust antijamming performance.展开更多
In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].
The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle li...The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.展开更多
Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manife...Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manifesting as insufficient convergence and low estimation accuracy.To address this issue,this study proposes a novel robust adaptive filtering algorithm,namely the M-estimation-based minimum error entropy with affine projection(APMMEE)algorithm.This algorithm inherits the joint multi-data-block update mechanism of the affine projection algorithm,enabling rapid adaptation to the dynamic characteristics of raw echoes and achieving fast convergence.Meanwhile,it incorporates the M-estimation-based minimum error entropy(MMEE)criterion,which weights error samples in raw echoes through M-estimation functions,effectively suppressing outlier interference during the algorithm update.Both the system identification simulations and practical multipath interference suppression experiments using raw echoes demonstrate that the proposed APMMEE algorithm exhibits superior filtering performance.展开更多
In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to comp...In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed.展开更多
Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS...Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.展开更多
This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very m...This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.展开更多
An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild assumptions....An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild assumptions.In this paper,the limiting distributions of the M-estimators are investigated.It is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001).In addition,a recursive algorithm for computing the M-estimators of frequencies is proposed,and the strong consistency of these estimators is established.Monte Carlo simulation studies using Huber’sρfunction are also provided.展开更多
This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over a...This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.展开更多
This paper studies an M-estimator of a proxy periodic GARCH （p, q） scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimato...This paper studies an M-estimator of a proxy periodic GARCH （p, q） scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.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
The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distanc...The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.展开更多
This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. ...This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A （FY-3A） simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.展开更多
In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate pr...In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.展开更多
As a production quality index of hematite grinding process,particle size(PS)is hard to be measured in real time.To achieve the PS estimation,this paper proposes a novel data driven model of PS using stochastic configu...As a production quality index of hematite grinding process,particle size(PS)is hard to be measured in real time.To achieve the PS estimation,this paper proposes a novel data driven model of PS using stochastic configuration network(SCN)with robust technique,namely,robust SCN(RSCN).Firstly,this paper proves the universal approximation property of RSCN with weighted least squares technique.Secondly,three robust algorithms are presented by employing M-estimation with Huber loss function,M-estimation with interquartile range(IQR)and nonparametric kernel density estimation(NKDE)function respectively to set the penalty weight.Comparison experiments are first carried out based on the UCI standard data sets to verify the effectiveness of these methods,and then the data-driven PS model based on the robust algorithms are established and verified.Experimental results show that the RSCN has an excellent performance for the PS estimation.展开更多
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods at...A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering, which is more effective than normal bilateral filter.展开更多
基金co-supported by the National Natural Science Foundation of China(No.62303246,No.62103204)the China Postdoctoral Science Foundation(No.2023M731788)。
文摘For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.
基金supported by the Basic Science Center Program of the National Natural Science Foundation of China(62388101)the National Natural Science Foundation of China(61873275).
文摘In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions.Based on the derivation process,a unified form for the robust Gaussian filters(RGF)based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement.The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals.Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust antijamming performance.
文摘In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].
文摘The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.
基金supported by Shandong Provincial Natural Science Foundation(No.ZR2022MF314).
文摘Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manifesting as insufficient convergence and low estimation accuracy.To address this issue,this study proposes a novel robust adaptive filtering algorithm,namely the M-estimation-based minimum error entropy with affine projection(APMMEE)algorithm.This algorithm inherits the joint multi-data-block update mechanism of the affine projection algorithm,enabling rapid adaptation to the dynamic characteristics of raw echoes and achieving fast convergence.Meanwhile,it incorporates the M-estimation-based minimum error entropy(MMEE)criterion,which weights error samples in raw echoes through M-estimation functions,effectively suppressing outlier interference during the algorithm update.Both the system identification simulations and practical multipath interference suppression experiments using raw echoes demonstrate that the proposed APMMEE algorithm exhibits superior filtering performance.
基金supported by the Natural Sciences and Engineering Research Council of Canada
文摘In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed.
文摘Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.
基金supported by the National Natural Science Foundation of China (Grant No. 10471006)
文摘This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.
文摘An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild assumptions.In this paper,the limiting distributions of the M-estimators are investigated.It is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001).In addition,a recursive algorithm for computing the M-estimators of frequencies is proposed,and the strong consistency of these estimators is established.Monte Carlo simulation studies using Huber’sρfunction are also provided.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province,China(No.2014J01010)
文摘This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.
基金Supported by the National Natural Science Foundation of China(No.71673315)Foundation of Beijing Technology and Business University(LKJJ2016-03)Capital Circulation Research Base(JD-YB-2017-016)
文摘This paper studies an M-estimator of a proxy periodic GARCH （p, q） scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.
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.
基金National Natural Science Foundation of China under Grant No.61379116，Natural Science Foundation of Hebei Province under Grant No.F2015203046 and No.F2013203124，Key Program of Research on Science and Technology of Higher Education Institutions of Hebei Province under Grant No.ZH2012028
文摘The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.
基金Supported by Special Scientific Research Fund of Meteorological Public Welfare Profession of China(GYHY201406028)Meteorological Open Research Fund for Huaihe River Basin(HRM201407)Anhui Meteorological Bureau Science and Technology Development Fund(RC201506)
文摘This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A （FY-3A） simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.
文摘In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
文摘In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.
基金Projects(61603393,61741318)supported in part by the National Natural Science Foundation of ChinaProject(BK20160275)supported by the Natural Science Foundation of Jiangsu Province,China+1 种基金Project(2015M581885)supported by the Postdoctoral Science Foundation of ChinaProject(PAL-N201706)supported by the Open Project Foundation of State Key Laboratory of Synthetical Automation for Process Industries of Northeastern University,China
文摘As a production quality index of hematite grinding process,particle size(PS)is hard to be measured in real time.To achieve the PS estimation,this paper proposes a novel data driven model of PS using stochastic configuration network(SCN)with robust technique,namely,robust SCN(RSCN).Firstly,this paper proves the universal approximation property of RSCN with weighted least squares technique.Secondly,three robust algorithms are presented by employing M-estimation with Huber loss function,M-estimation with interquartile range(IQR)and nonparametric kernel density estimation(NKDE)function respectively to set the penalty weight.Comparison experiments are first carried out based on the UCI standard data sets to verify the effectiveness of these methods,and then the data-driven PS model based on the robust algorithms are established and verified.Experimental results show that the RSCN has an excellent performance for the PS estimation.
文摘A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering, which is more effective than normal bilateral filter.
