This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be infe...This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.展开更多
A nonparametric Bayesian method is presented to classify the MPSK （M-ary phase shift keying） signals. The MPSK signals with unknown signal noise ratios （SNRs） are modeled as a Gaussian mixture model with unknown m...A nonparametric Bayesian method is presented to classify the MPSK （M-ary phase shift keying） signals. The MPSK signals with unknown signal noise ratios （SNRs） are modeled as a Gaussian mixture model with unknown means and covariances in the constellation plane, and a clustering method is proposed to estimate the probability density of the MPSK signals. The method is based on the nonparametric Bayesian inference, which introduces the Dirichlet process as the prior probability of the mixture coefficient, and applies a normal inverse Wishart （NIW） distribution as the prior probability of the unknown mean and covariance. Then, according to the received signals, the parameters are adjusted by the Monte Carlo Markov chain （MCMC） random sampling algorithm. By iterations, the density estimation of the MPSK signals can be estimated. Simulation results show that the correct recognition ratio of 2/4/8PSK is greater than 95% under the condition that SNR 〉5 dB and 1 600 symbols are used in this method.展开更多
The problem of "rich topics get richer"(RTGR) is popular to the topic models,which will bring the wrong topic distribution if the distributing process has not been intervened.In standard LDA(Latent Dirichlet...The problem of "rich topics get richer"(RTGR) is popular to the topic models,which will bring the wrong topic distribution if the distributing process has not been intervened.In standard LDA(Latent Dirichlet Allocation) model,each word in all the documents has the same statistical ability.In fact,the words have different impact towards different topics.Under the guidance of this thought,we extend ILDA(Infinite LDA) by considering the bias role of words to divide the topics.We propose a self-adaptive topic model to overcome the RTGR problem specifically.The model proposed in this paper is adapted to three questions:(1) the topic number is changeable with the collection of the documents,which is suitable for the dynamic data;(2) the words have discriminating attributes to topic distribution;(3) a selfadaptive method is used to realize the automatic re-sampling.To verify our model,we design a topic evolution analysis system which can realize the following functions:the topic classification in each cycle,the topic correlation in the adjacent cycles and the strength calculation of the sub topics in the order.The experiment both on NIPS corpus and our self-built news collections showed that the system could meet the given demand,the result was feasible.展开更多
Interest in automated data classification and identification systems has increased over the past years in conjunction with the high demand for artificial intelligence and security applications.In particular,recognizin...Interest in automated data classification and identification systems has increased over the past years in conjunction with the high demand for artificial intelligence and security applications.In particular,recognizing human activities with accurate results have become a topic of high interest.Although the current tools have reached remarkable successes,it is still a challenging problem due to various uncontrolled environments and conditions.In this paper two statistical frameworks based on nonparametric hierarchical Bayesian models and Gamma distribution are proposed to solve some realworld applications.In particular,two nonparametric hierarchical Bayesian models based on Dirichlet process and Pitman-Yor process are developed.These models are then applied to address the problem of modelling grouped data where observations are organized into groups and these groups are statistically linked by sharing mixture components.The choice of the Gamma mixtures is motivated by its flexibility for modelling heavy-tailed distributions.In addition,deploying the Dirichlet process prior is justified by its advantage of automatically finding the right number of components and providing nice properties.Moreover,a learning step via variational Bayesian setting is presented in a flexible way.The priors over the parameters are selected appropriately and the posteriors are approximated effectively in a closed form.Experimental results based on a real-life applications that concerns texture classification and human actions recognition show the capabilities and effectiveness of the proposed framework.展开更多
Microarray gene expression data are analyzed by means of a Bayesian nonparametric model, with emphasis on prediction of future observables, yielding a method for selection of differentially expressed genes and the cor...Microarray gene expression data are analyzed by means of a Bayesian nonparametric model, with emphasis on prediction of future observables, yielding a method for selection of differentially expressed genes and the corresponding classifier.展开更多
In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mi...In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the ＂correct＂ number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture （DPM） models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model （DPGMM）. We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.展开更多
In this paper,a nonparametric Bayesian graph topic model(GTM)based on hierarchical Dirichlet process(HDP)is proposed.The HDP makes the number of topics selected flexibly,which breaks the limitation that the number of ...In this paper,a nonparametric Bayesian graph topic model(GTM)based on hierarchical Dirichlet process(HDP)is proposed.The HDP makes the number of topics selected flexibly,which breaks the limitation that the number of topics need to be given in advance.Moreover,theGTMreleases the assumption of‘bag of words’and considers the graph structure of the text.The combination of HDP and GTM takes advantage of both which is named as HDP–GTM.The variational inference algorithm is used for the posterior inference and the convergence of the algorithm is analysed.We apply the proposed model in text categorisation,comparing to three related topic models,latent Dirichlet allocation(LDA),GTM and HDP.展开更多
The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable p...The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.展开更多
The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of th...The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and展开更多
When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. Th...When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. This is particularly true when multiple signal frequency bands overlap. Message passing algorithms (MPA) with Dirichlet process (DP) prior can be employed in a sparse Bayesian learning (SBL) framework with high precision. However, existing methods suffer from either high complexity or low precision. To address this, we propose a low-complexity DOA estimation algorithm based on a factor graph. This approach introduces two strong constraints via a stretching transformation of the factor graph. The first constraint separates the observation from the DP prior, enabling the application of the unitary approximate message passing (UAMP) algorithm for simplified inference and mitigation of divergence issues. The second constraint compensates for the deviation in estimation angle caused by the grid mismatch problem. Compared to state-of-the-art algorithms, our proposed method offers higher estimation accuracy and lower complexity.展开更多
In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to...In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.展开更多
Given a Markov process satisfying certain general type conditions,whose paths are notassumed to be continuous. Let D by an open subset of the state space E. Any bounded function defined on thecomplement of D extends t...Given a Markov process satisfying certain general type conditions,whose paths are notassumed to be continuous. Let D by an open subset of the state space E. Any bounded function defined on thecomplement of D extends to be a function on E (?)uch that it is harmonic in D and satisfies the Dirichletboundary condition at any regular boundary point of D. The relation between harmonic functions and theebaracteristic operator of the given process is discussed.展开更多
Albeit with the notable benefits associated with Dirichlet crash frequency models and spatial ones,there is little research dedicated to exploring their combined advantages.Such ensemble approach could be a viable alt...Albeit with the notable benefits associated with Dirichlet crash frequency models and spatial ones,there is little research dedicated to exploring their combined advantages.Such ensemble approach could be a viable alternative to existing models as it accounts for the unobserved heterogeneity by relaxing the constraints of specific distribution placed on the intercept while addressing the spatial correlations among roadway entities.To fill this gap,the authors aimed to develop Dirichlet semi-parametric models over the overdispersed generalized linear model framework while also incorporating spatially structured random effects using a distance-based weight matrix.Five models were developed which include four semi-parametric with flexible intercept and one parametric base model for comparison purposes.The four semi-parametric models entailed two models with a popular specification of stick-breaking Dirichlet process(DP)and two models with an alternative approach of Dirichlet distribution(DD),which are first applied in the field of traffic safety.All four models were estimated for mixture of points(discrete)and mixture of normals(continuous).The posterior density plots for the precision parameter justified the employment of the flexible Dirichlet approach to fit the crash data and supported the assumed prior for the precision parameter.All four Dirichlet models demonstrated the presence of distinct subpopulations suggesting that the intercepts of the models were not generated from a common distribution.The DP model based on mixture of normals illustrated better performance indicating its potential superiority to fit both insample and out-of-sample crash data.This finding indicated that the approach of continuous densities,unlike discrete points,may lend more flexibility to fit the data.展开更多
To automate heavy-duty hydraulic manipulators in construction applications,trajectory learning from demonstration is increasingly in demand.However,it faces difficulties in motion noise owing to factors such as size s...To automate heavy-duty hydraulic manipulators in construction applications,trajectory learning from demonstration is increasingly in demand.However,it faces difficulties in motion noise owing to factors such as size scaling and oscillation tendency.A smooth trajectory learning method is established to overcome this problem by segmenting the demonstration and extracting the subgoals for motion noise cancellation.The imperfect demonstration trajectory is segmented by clustering the end-effector’s velocity in the task space with locally weighted noise cancellation to reduce the impact of velocity fluctuations.A sequentially hierarchical Dirichlet process algorithm with temporal encoding is designed to extract the intended subgoals and filter inefficient operations.Then,the learned trajectory is reconstructed,combined with dynamic motion primitives(DMP).The comparison test results indicate that the proposed method can learn a relevant trajectory that reflects the real intention of the user from an imperfect demonstration.Taking DMP and Sparse Sampling as comparisons,two cases of automatic trajectory tracking tasks are performed,which shows that the average position error with respect to the reference can be reduced because inefficient operations or movements are effectively filtered.展开更多
This paper proposes a Bayesian semiparametric accelerated failure time model for doubly censored data with errors-in-covariates. The authors model the distributions of the unobserved covariates and the regression erro...This paper proposes a Bayesian semiparametric accelerated failure time model for doubly censored data with errors-in-covariates. The authors model the distributions of the unobserved covariates and the regression errors via the Dirichlet processes. Moreover, the authors extend the Bayesian Lasso approach to our semiparametric model for variable selection. The authors develop the Markov chain Monte Carlo strategies for posterior calculation. Simulation studies are conducted to show the performance of the proposed method. The authors also demonstrate the implementation of the method using analysis of PBC data and ACTG 175 data.展开更多
In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion c...In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion coefficients and distributional drift coefficients.展开更多
In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors...In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.展开更多
This paper aims to study the deep clustering problem with heterogeneous features and unknown cluster number.To address this issue,a novel deep Bayesian clustering framework is proposed.In particular,a heterogeneous fe...This paper aims to study the deep clustering problem with heterogeneous features and unknown cluster number.To address this issue,a novel deep Bayesian clustering framework is proposed.In particular,a heterogeneous feature metric is first constructed to measure the similarity between different types of features.Then,a feature metric-restricted hierarchical sample generation process is established,in which sample with heterogeneous features is clustered by generating it from a similarity constraint hidden space.When estimating the model parameters and posterior probability,the corresponding variational inference algorithm is derived and implemented.To verify our model capability,we demonstrate our model on the synthetic dataset and show the superiority of the proposed method on some real datasets.Our source code is released on the website:Github.com/yexlwh/Heterogeneousclustering.展开更多
The Surveillance, Epidemiology and End Results (SEER) cancer database contains survival data forUS individuals diagnosed with cancer. Semiparametric Bayesian methods are computationallyexpensive to fit for such large ...The Surveillance, Epidemiology and End Results (SEER) cancer database contains survival data forUS individuals diagnosed with cancer. Semiparametric Bayesian methods are computationallyexpensive to fit for such large data-sets. This paper develops a cost-effective Markov chain MonteCarlo strategy for censored outcomes to fit a semiparametric bayesian analysis of SEER data ofNew Mexico. We use an accelerated failure time model, with Dirichlet process random effectsfor inter-subject variation, and intrinsic conditionally autoregressive random effects for spatialcorrelations. The results offer insights into differences in breast cancer mortality rates betweenethnic groups, tumor grade and spatial effect of counties.展开更多
This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealan...This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.展开更多
基金Project (No. 60773180) supported by the National Natural Science Foundation of China
文摘This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.
基金Cultivation Fund of the Key Scientific and Technical Innovation Project of Ministry of Education of China(No.3104001014)
文摘A nonparametric Bayesian method is presented to classify the MPSK （M-ary phase shift keying） signals. The MPSK signals with unknown signal noise ratios （SNRs） are modeled as a Gaussian mixture model with unknown means and covariances in the constellation plane, and a clustering method is proposed to estimate the probability density of the MPSK signals. The method is based on the nonparametric Bayesian inference, which introduces the Dirichlet process as the prior probability of the mixture coefficient, and applies a normal inverse Wishart （NIW） distribution as the prior probability of the unknown mean and covariance. Then, according to the received signals, the parameters are adjusted by the Monte Carlo Markov chain （MCMC） random sampling algorithm. By iterations, the density estimation of the MPSK signals can be estimated. Simulation results show that the correct recognition ratio of 2/4/8PSK is greater than 95% under the condition that SNR 〉5 dB and 1 600 symbols are used in this method.
基金ACKNOWLEDGMENTS This work is supported by grants National 973 project （No.2013CB29606）, Natural Science Foundation of China （No.61202244）, research fund of ShangQiu Normal Colledge （No. 2013GGJS013）. N1PS corpus is supported by SourceForge. We thank the anonymous reviewers for their helpful comments.
文摘The problem of "rich topics get richer"(RTGR) is popular to the topic models,which will bring the wrong topic distribution if the distributing process has not been intervened.In standard LDA(Latent Dirichlet Allocation) model,each word in all the documents has the same statistical ability.In fact,the words have different impact towards different topics.Under the guidance of this thought,we extend ILDA(Infinite LDA) by considering the bias role of words to divide the topics.We propose a self-adaptive topic model to overcome the RTGR problem specifically.The model proposed in this paper is adapted to three questions:(1) the topic number is changeable with the collection of the documents,which is suitable for the dynamic data;(2) the words have discriminating attributes to topic distribution;(3) a selfadaptive method is used to realize the automatic re-sampling.To verify our model,we design a topic evolution analysis system which can realize the following functions:the topic classification in each cycle,the topic correlation in the adjacent cycles and the strength calculation of the sub topics in the order.The experiment both on NIPS corpus and our self-built news collections showed that the system could meet the given demand,the result was feasible.
基金The authors would like to thank Taif University Researchers Supporting Project number(TURSP-2020/26),Taif University,Taif,Saudi ArabiaThey would like also to thank Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2022R40),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Interest in automated data classification and identification systems has increased over the past years in conjunction with the high demand for artificial intelligence and security applications.In particular,recognizing human activities with accurate results have become a topic of high interest.Although the current tools have reached remarkable successes,it is still a challenging problem due to various uncontrolled environments and conditions.In this paper two statistical frameworks based on nonparametric hierarchical Bayesian models and Gamma distribution are proposed to solve some realworld applications.In particular,two nonparametric hierarchical Bayesian models based on Dirichlet process and Pitman-Yor process are developed.These models are then applied to address the problem of modelling grouped data where observations are organized into groups and these groups are statistically linked by sharing mixture components.The choice of the Gamma mixtures is motivated by its flexibility for modelling heavy-tailed distributions.In addition,deploying the Dirichlet process prior is justified by its advantage of automatically finding the right number of components and providing nice properties.Moreover,a learning step via variational Bayesian setting is presented in a flexible way.The priors over the parameters are selected appropriately and the posteriors are approximated effectively in a closed form.Experimental results based on a real-life applications that concerns texture classification and human actions recognition show the capabilities and effectiveness of the proposed framework.
文摘Microarray gene expression data are analyzed by means of a Bayesian nonparametric model, with emphasis on prediction of future observables, yielding a method for selection of differentially expressed genes and the corresponding classifier.
基金supported by Gatsby Charitable Foundation and PASCAL2
文摘In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the ＂correct＂ number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture （DPM） models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model （DPGMM）. We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.
基金supported by NSFC under grant No.71371074the 111 Project under No.B14019.
文摘In this paper,a nonparametric Bayesian graph topic model(GTM)based on hierarchical Dirichlet process(HDP)is proposed.The HDP makes the number of topics selected flexibly,which breaks the limitation that the number of topics need to be given in advance.Moreover,theGTMreleases the assumption of‘bag of words’and considers the graph structure of the text.The combination of HDP and GTM takes advantage of both which is named as HDP–GTM.The variational inference algorithm is used for the posterior inference and the convergence of the algorithm is analysed.We apply the proposed model in text categorisation,comparing to three related topic models,latent Dirichlet allocation(LDA),GTM and HDP.
基金supported in part by the National Natural Science Foundation of China(Grant No.11471161)the Technological Innovation Item in Jiangsu Province(No.BK2008156).
文摘The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.
文摘The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and
基金supported in part by the National Natural Science Foundation of China(Nos.6202780103 and 62033001)the Innovation Key Project of Guangxi Province(No.AA22068059)+2 种基金the Key Research and Development Program of Guilin(No.2020010332)the Natural Science Foundation of Henan Province(No.222300420504)Academic Degrees and Graduate Education Reform Project of Henan Province(No.2021SJGLX262Y).
文摘When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. This is particularly true when multiple signal frequency bands overlap. Message passing algorithms (MPA) with Dirichlet process (DP) prior can be employed in a sparse Bayesian learning (SBL) framework with high precision. However, existing methods suffer from either high complexity or low precision. To address this, we propose a low-complexity DOA estimation algorithm based on a factor graph. This approach introduces two strong constraints via a stretching transformation of the factor graph. The first constraint separates the observation from the DP prior, enabling the application of the unitary approximate message passing (UAMP) algorithm for simplified inference and mitigation of divergence issues. The second constraint compensates for the deviation in estimation angle caused by the grid mismatch problem. Compared to state-of-the-art algorithms, our proposed method offers higher estimation accuracy and lower complexity.
基金This work was supported in part by NSF under Grant CPS-1739344,ARO under grant W911NF-16-1-0448the DTRA under Grant HDTRA1-13-1-0029Part of this work will appear in the Proceedings of 40th IEEE International Conference on Distributed Computing Systems(ICDCS),Singapore,July 8-10,2020。
文摘In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.
文摘Given a Markov process satisfying certain general type conditions,whose paths are notassumed to be continuous. Let D by an open subset of the state space E. Any bounded function defined on thecomplement of D extends to be a function on E (?)uch that it is harmonic in D and satisfies the Dirichletboundary condition at any regular boundary point of D. The relation between harmonic functions and theebaracteristic operator of the given process is discussed.
文摘Albeit with the notable benefits associated with Dirichlet crash frequency models and spatial ones,there is little research dedicated to exploring their combined advantages.Such ensemble approach could be a viable alternative to existing models as it accounts for the unobserved heterogeneity by relaxing the constraints of specific distribution placed on the intercept while addressing the spatial correlations among roadway entities.To fill this gap,the authors aimed to develop Dirichlet semi-parametric models over the overdispersed generalized linear model framework while also incorporating spatially structured random effects using a distance-based weight matrix.Five models were developed which include four semi-parametric with flexible intercept and one parametric base model for comparison purposes.The four semi-parametric models entailed two models with a popular specification of stick-breaking Dirichlet process(DP)and two models with an alternative approach of Dirichlet distribution(DD),which are first applied in the field of traffic safety.All four models were estimated for mixture of points(discrete)and mixture of normals(continuous).The posterior density plots for the precision parameter justified the employment of the flexible Dirichlet approach to fit the crash data and supported the assumed prior for the precision parameter.All four Dirichlet models demonstrated the presence of distinct subpopulations suggesting that the intercepts of the models were not generated from a common distribution.The DP model based on mixture of normals illustrated better performance indicating its potential superiority to fit both insample and out-of-sample crash data.This finding indicated that the approach of continuous densities,unlike discrete points,may lend more flexibility to fit the data.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.52322503 and 52075055)in part by the Natural Science Foundation of Chongqing,China(Grant No.2024NSCQ-JQX0123)+1 种基金in part by the Major Scientific and Technological Research and Development Project of Jiangxi Province,China(Grant No.20233AAE02001)in part by the Independent Research Project of State Key Laboratory of Mechanical Transmission for Advanced Equipment,China(Grant No.SKLMT-ZZKT-2024R02).
文摘To automate heavy-duty hydraulic manipulators in construction applications,trajectory learning from demonstration is increasingly in demand.However,it faces difficulties in motion noise owing to factors such as size scaling and oscillation tendency.A smooth trajectory learning method is established to overcome this problem by segmenting the demonstration and extracting the subgoals for motion noise cancellation.The imperfect demonstration trajectory is segmented by clustering the end-effector’s velocity in the task space with locally weighted noise cancellation to reduce the impact of velocity fluctuations.A sequentially hierarchical Dirichlet process algorithm with temporal encoding is designed to extract the intended subgoals and filter inefficient operations.Then,the learned trajectory is reconstructed,combined with dynamic motion primitives(DMP).The comparison test results indicate that the proposed method can learn a relevant trajectory that reflects the real intention of the user from an imperfect demonstration.Taking DMP and Sparse Sampling as comparisons,two cases of automatic trajectory tracking tasks are performed,which shows that the average position error with respect to the reference can be reduced because inefficient operations or movements are effectively filtered.
基金supported by the National Natural Science Foundation of China under Grant Nos.11171007/A011103,11171230,and 11471024
文摘This paper proposes a Bayesian semiparametric accelerated failure time model for doubly censored data with errors-in-covariates. The authors model the distributions of the unobserved covariates and the regression errors via the Dirichlet processes. Moreover, the authors extend the Bayesian Lasso approach to our semiparametric model for variable selection. The authors develop the Markov chain Monte Carlo strategies for posterior calculation. Simulation studies are conducted to show the performance of the proposed method. The authors also demonstrate the implementation of the method using analysis of PBC data and ACTG 175 data.
文摘In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion coefficients and distributional drift coefficients.
基金Supported by National Natural Science Foundation of China(Grant Nos.11171007/A011103,11171230 and11471024)
文摘In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.62006131,62071260)the National Natural Science Foundation of Zhejiang Province(LQ21F020009,LQ18F020001).
文摘This paper aims to study the deep clustering problem with heterogeneous features and unknown cluster number.To address this issue,a novel deep Bayesian clustering framework is proposed.In particular,a heterogeneous feature metric is first constructed to measure the similarity between different types of features.Then,a feature metric-restricted hierarchical sample generation process is established,in which sample with heterogeneous features is clustered by generating it from a similarity constraint hidden space.When estimating the model parameters and posterior probability,the corresponding variational inference algorithm is derived and implemented.To verify our model capability,we demonstrate our model on the synthetic dataset and show the superiority of the proposed method on some real datasets.Our source code is released on the website:Github.com/yexlwh/Heterogeneousclustering.
基金National Science Foundation[grant number DMS-1461948].
文摘The Surveillance, Epidemiology and End Results (SEER) cancer database contains survival data forUS individuals diagnosed with cancer. Semiparametric Bayesian methods are computationallyexpensive to fit for such large data-sets. This paper develops a cost-effective Markov chain MonteCarlo strategy for censored outcomes to fit a semiparametric bayesian analysis of SEER data ofNew Mexico. We use an accelerated failure time model, with Dirichlet process random effectsfor inter-subject variation, and intrinsic conditionally autoregressive random effects for spatialcorrelations. The results offer insights into differences in breast cancer mortality rates betweenethnic groups, tumor grade and spatial effect of counties.
基金The author acknowledges financial support from the National Natural Science Foundation of China(NSFC,No.71773069).
文摘This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.
