In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hen...In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.展开更多
One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper ...One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper provides further insights from another perspective that a co-dimensional matrix pair(shortly co-dim matrix pair)forms a building unit and a hierarchy of such building units sets up the BYY system.The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair,which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning.Besides updating typical algorithms of factor analysis(FA),binary FA(BFA),binary matrix factorization(BMF),and nonnegative matrix factorization(NMF)to share such a mechanism,we are also led to(a)a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA(LFA);(b)an alternative formulation of graph Laplacian based linear manifold learning;(c)a codecomposition of data and covariance for learning regularization and data integration;and(d)a co-dim matrix pair based generalization of temporal FA and state space model.Moreover,with help of a co-dim matrix pair in Hadamard product,we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model.Furthermore,we address that these advances provide with new tools for network biology studies,including learning transcriptional regulatory,Protein-Protein Interaction network alignment,and network integration.展开更多
Conventional sparse representation based classification （SRC） represents a test sample with the coefficient solved by each training sample in all classes. As a special version and improvement to SRC, collaborative r...Conventional sparse representation based classification （SRC） represents a test sample with the coefficient solved by each training sample in all classes. As a special version and improvement to SRC, collaborative representation based classification （CRC） obtains representation with the contribution from all training samples and produces more promising results on facial image classification. In the solutions of representation coefficients, CRC considers original value of contributions from all samples. However, one prevalent practice in such kind of distance-based methods is to consider only absolute value of the distance rather than both positive and negative values. In this paper, we propose an novel method to improve collaborative representation based classification, which integrates an absolute distance vector into the residuals solved by collaborative representation. And we named it AbsCRC. The key step in AbsCRC method is to use factors a and b as weight to combine CRC residuals rescrc with absolute distance vector disabs and generate a new dviaetion r = a·rescrc b.disabs, which is in turn used to perform classification. Because the two residuals have opposite effect in classification, the method uses a subtraction operation to perform fusion. We conducted extensive experiments to evaluate our method for image classification with different instantiations. The experimental results indicated that it produced a more promising result of classification on both facial and non-facial images than original CRC method.展开更多
A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to t...A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.展开更多
基于transformer架构,提出一种面向学习轨迹的知识追踪预测模型(knowledge tracing prediction model for learning trajectories,LTKT),解决知识追踪领域使用transformer架构所存在的问题:网络中缺乏知识点信息、注意力被分散到众多关...基于transformer架构,提出一种面向学习轨迹的知识追踪预测模型(knowledge tracing prediction model for learning trajectories,LTKT),解决知识追踪领域使用transformer架构所存在的问题:网络中缺乏知识点信息、注意力被分散到众多关联较小的试题及忽略了学习能力在答题决策中的影响。LTKT在数据预处理阶段,采用教育领域的知识融通机制整合题目涉及的多个知识点,作为模型学习的一个信息维度。在编码器与解码器结构中,根据注意力呈现长尾分布的特点引入稀疏自注意力机制,并在其中嵌入包含绝对距离和相对距离的位置编码,使注意力集中在少数高度相似的试题上,同时加强模型对位置信息的感知。在预测策略上,使用双线性层融合学习能力特征与学生的知识状态,综合预测学生下一时刻的作答表现。在两个真实的大型公开数据集上进行实验,与其他优秀模型进行对比,结果显示LTKT的AUC有了明显提升。展开更多
In fMRI experiments on object representation in visual cortex, we designed two types of stimuli: one is the gray face image and its line drawing, and the other is the illusion and its corresponding completed illusion....In fMRI experiments on object representation in visual cortex, we designed two types of stimuli: one is the gray face image and its line drawing, and the other is the illusion and its corresponding completed illusion. Both of them have the same global features with different minute details so that the results of fMRI experiments can be compared with each other. The first kind of visual stimuli was used in a block design fMRI experiment, and the second was used in an event-related fMRI experiment. Comparing and analyzing interesting visual cortex activity patterns and blood oxygenation level dependent (BOLD)- fMRI signal, we obtained results to show some invariance of global features of visual images. A plau- sible explanation about the invariant mechanism is related with the cooperation of synchronized re- sponse to the global features of the visual image with a feedback of shape perception from higher cortex to cortex V1, namely the integration of global features and embodiment of sparse representation and distributed population code.展开更多
We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and e...We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.展开更多
基金the National Science Fund for Distinguished Young Scholars(Grant No.51725502)the major program of the National Natural Science Foundation of China(Grant No.51490662)the National Key Research and Development Project of China(Grant No.2016YFD0701105).
文摘In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.
基金supported by the General Research Fund from Research Grant Council of Hong Kong(Project No.CUHK4180/10E)the National Basic Research Program of China(973 Program)(No.2009CB825404).
文摘One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper provides further insights from another perspective that a co-dimensional matrix pair(shortly co-dim matrix pair)forms a building unit and a hierarchy of such building units sets up the BYY system.The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair,which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning.Besides updating typical algorithms of factor analysis(FA),binary FA(BFA),binary matrix factorization(BMF),and nonnegative matrix factorization(NMF)to share such a mechanism,we are also led to(a)a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA(LFA);(b)an alternative formulation of graph Laplacian based linear manifold learning;(c)a codecomposition of data and covariance for learning regularization and data integration;and(d)a co-dim matrix pair based generalization of temporal FA and state space model.Moreover,with help of a co-dim matrix pair in Hadamard product,we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model.Furthermore,we address that these advances provide with new tools for network biology studies,including learning transcriptional regulatory,Protein-Protein Interaction network alignment,and network integration.
文摘Conventional sparse representation based classification （SRC） represents a test sample with the coefficient solved by each training sample in all classes. As a special version and improvement to SRC, collaborative representation based classification （CRC） obtains representation with the contribution from all training samples and produces more promising results on facial image classification. In the solutions of representation coefficients, CRC considers original value of contributions from all samples. However, one prevalent practice in such kind of distance-based methods is to consider only absolute value of the distance rather than both positive and negative values. In this paper, we propose an novel method to improve collaborative representation based classification, which integrates an absolute distance vector into the residuals solved by collaborative representation. And we named it AbsCRC. The key step in AbsCRC method is to use factors a and b as weight to combine CRC residuals rescrc with absolute distance vector disabs and generate a new dviaetion r = a·rescrc b.disabs, which is in turn used to perform classification. Because the two residuals have opposite effect in classification, the method uses a subtraction operation to perform fusion. We conducted extensive experiments to evaluate our method for image classification with different instantiations. The experimental results indicated that it produced a more promising result of classification on both facial and non-facial images than original CRC method.
基金supported by the National Natural Science Foundation of China (Nos. 10902020 and 10721062)
文摘A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.
文摘基于transformer架构,提出一种面向学习轨迹的知识追踪预测模型(knowledge tracing prediction model for learning trajectories,LTKT),解决知识追踪领域使用transformer架构所存在的问题:网络中缺乏知识点信息、注意力被分散到众多关联较小的试题及忽略了学习能力在答题决策中的影响。LTKT在数据预处理阶段,采用教育领域的知识融通机制整合题目涉及的多个知识点,作为模型学习的一个信息维度。在编码器与解码器结构中,根据注意力呈现长尾分布的特点引入稀疏自注意力机制,并在其中嵌入包含绝对距离和相对距离的位置编码,使注意力集中在少数高度相似的试题上,同时加强模型对位置信息的感知。在预测策略上,使用双线性层融合学习能力特征与学生的知识状态,综合预测学生下一时刻的作答表现。在两个真实的大型公开数据集上进行实验,与其他优秀模型进行对比,结果显示LTKT的AUC有了明显提升。
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60371045 & 60628101)the National High Technology Research and Development Program of China (Grant No. 2006AA01Z132)
文摘In fMRI experiments on object representation in visual cortex, we designed two types of stimuli: one is the gray face image and its line drawing, and the other is the illusion and its corresponding completed illusion. Both of them have the same global features with different minute details so that the results of fMRI experiments can be compared with each other. The first kind of visual stimuli was used in a block design fMRI experiment, and the second was used in an event-related fMRI experiment. Comparing and analyzing interesting visual cortex activity patterns and blood oxygenation level dependent (BOLD)- fMRI signal, we obtained results to show some invariance of global features of visual images. A plau- sible explanation about the invariant mechanism is related with the cooperation of synchronized re- sponse to the global features of the visual image with a feedback of shape perception from higher cortex to cortex V1, namely the integration of global features and embodiment of sparse representation and distributed population code.
文摘We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.
