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
Although Relevance Vector Machine (RVM) is the most popular algorithms in machine learning and computer vision, outliers in the training data make the estimation unreliable. In the paper, a robust RVM model under non-...Although Relevance Vector Machine (RVM) is the most popular algorithms in machine learning and computer vision, outliers in the training data make the estimation unreliable. In the paper, a robust RVM model under non-parametric Bayesian framework is proposed. We decompose the noise term in the RVM model into two components, a Gaussian noise term and a spiky noise term. Therefore the observed data is assumed represented as: where is the relevance vector component, of which is the kernel function matrix and is the weight matrix, is the spiky term and is the Gaussian noise term. A spike-slab sparse prior is imposed on the weight vector which gives a more intuitive constraint on the sparsity than the Student's t-distribution described in the traditional RVM. For the spiky component a spike-slab sparse prior is also introduced to recognize outliers in the training data effectively. Several experiments demonstrate the better performance over the RVM regression.展开更多
提出一新的非参数贝叶斯推理算法来辨识任意复杂的多模噪声分布,采用无穷维推理技术,能够较为精确地逼近噪声的后验分布。算法主要引入一随机度量分布满足一预设的先验过程——混合Dirichlet过程(Dirichlet Process Mixture,简称DPM),由...提出一新的非参数贝叶斯推理算法来辨识任意复杂的多模噪声分布,采用无穷维推理技术,能够较为精确地逼近噪声的后验分布。算法主要引入一随机度量分布满足一预设的先验过程——混合Dirichlet过程(Dirichlet Process Mixture,简称DPM),由于DPM具有形似于Polya urn的采样特性,能够很方便地对噪声数据进行聚类,并导出噪声的后验分布。仿真结果显示,噪声数据似然的Metropolis-Hastings(M-H)的采样算法比点估计的系统分析算法精度高。展开更多
针对线性动态系统在复杂噪声环境中的不确定性的传递问题,提出了用块采样推理方法逼近状态和噪声的后验分布.该方法在时序采样中,样本在基于条件独立性准则下可一次性更新,这通常比单独更新来得简单和有效.通过引入Dirichlet过程混合模...针对线性动态系统在复杂噪声环境中的不确定性的传递问题,提出了用块采样推理方法逼近状态和噪声的后验分布.该方法在时序采样中,样本在基于条件独立性准则下可一次性更新,这通常比单独更新来得简单和有效.通过引入Dirichlet过程混合模型(Dirichlet Process Mixture,DPM),能够较方便地获得马尔科夫链式样本.结合卡尔曼平滑技术,使块采样算法能够在分布空间逼近基础上取得较高的精度.仿真结果显示,块采样平滑算法具有较好的效果.展开更多
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 the National Natural Science Foundation of China (No. 30900328, 61172179)the Fundamental Research Funds for the Central Universities (No. 201112-1051)the Natural Science Foundation of Fujian Province of China (No. 2012J05160)
文摘Although Relevance Vector Machine (RVM) is the most popular algorithms in machine learning and computer vision, outliers in the training data make the estimation unreliable. In the paper, a robust RVM model under non-parametric Bayesian framework is proposed. We decompose the noise term in the RVM model into two components, a Gaussian noise term and a spiky noise term. Therefore the observed data is assumed represented as: where is the relevance vector component, of which is the kernel function matrix and is the weight matrix, is the spiky term and is the Gaussian noise term. A spike-slab sparse prior is imposed on the weight vector which gives a more intuitive constraint on the sparsity than the Student's t-distribution described in the traditional RVM. For the spiky component a spike-slab sparse prior is also introduced to recognize outliers in the training data effectively. Several experiments demonstrate the better performance over the RVM regression.
文摘提出一新的非参数贝叶斯推理算法来辨识任意复杂的多模噪声分布,采用无穷维推理技术,能够较为精确地逼近噪声的后验分布。算法主要引入一随机度量分布满足一预设的先验过程——混合Dirichlet过程(Dirichlet Process Mixture,简称DPM),由于DPM具有形似于Polya urn的采样特性,能够很方便地对噪声数据进行聚类,并导出噪声的后验分布。仿真结果显示,噪声数据似然的Metropolis-Hastings(M-H)的采样算法比点估计的系统分析算法精度高。
文摘针对线性动态系统在复杂噪声环境中的不确定性的传递问题,提出了用块采样推理方法逼近状态和噪声的后验分布.该方法在时序采样中,样本在基于条件独立性准则下可一次性更新,这通常比单独更新来得简单和有效.通过引入Dirichlet过程混合模型(Dirichlet Process Mixture,DPM),能够较方便地获得马尔科夫链式样本.结合卡尔曼平滑技术,使块采样算法能够在分布空间逼近基础上取得较高的精度.仿真结果显示,块采样平滑算法具有较好的效果.
