基于动态Gibbs采样的RBM训练算法研究

目前大部分受限玻尔兹曼机(Restricted Boltzmann machines, RBMs)训练算法都是以多步Gibbs采样为基础的采样算法. 本文针对多步Gibbs采样过程中出现的采样发散和训练速度过慢的问题,首先, 对问题进行实验描述,给出了问题的具体形式; 然后, 从马尔科夫采样的角度对多步Gibbs采样的收敛性质进行了理论分析, 证明了多步Gibbs采样在受限玻尔兹曼机训练初期较差的收敛性质是造成采样发散和训练速度过慢的主要原因; 最后, 提出了动态Gibbs采样算法,给出了对比仿真实验.实验结果表明, 动态Gibbs采样算法可以有效地克服采样发散的问题,并且能够以微小的运行时间为代价获得更高的训练精度.     

一种基于吉布斯抽样的MUSIC多维参数联合估计算法

将马尔可夫蒙特卡罗(MCMC)方法与多重子空间分类(MUSIC)方法估计相结合,提出一种用于联合估计多个目标的频率、方位和俯仰,基于吉布斯抽样的MUSIC多维参数联合估计新方法。该方法将MUSIC方法的谱函数作为频率、方位和俯仰的联合概率密度函数,采用MCMC吉布斯抽样方法对该联合概率密度函数进行采样。理论分析和仿真实验表明:在目标个数较少时,该方法不仅保持了常规MUSIC方法的高分辨能力,而且减少了计算量和存储量     

贝叶斯推理与并行回火研究综述

贝叶斯推理是统计学中的主要问题之一，旨在根据观测数据更新概率分布模型的先验知识。对于真实情况下常遇到的无法观测或难以直接计算的后验概率，贝叶斯推理可以对其进行近似，它是一种以贝叶斯定理为基础的重要方法。在许多机器学习问题中都涉及对包含各类特征数据的真实分布进行模拟和近似的过程，如分类模型、主题建模和数据挖掘等，因此贝叶斯推理在当今机器学习领域里具有重要而独特的研究价值。随着大数据时代的开始，研究者经由实际信息采集到海量的实验数据，导致需要模拟和计算的目标分布也非常复杂，如何在复杂数据下对目标分布进行结果精确和时间高效的近似推理，成为了当今贝叶斯推理问题的重难点。针对这一复杂分布模型下的推理问题，文中对近年来解决贝叶斯推理问题的两大主要方法——变分推理和采样方法，进行系统性地介绍和综述。首先，给出变分推理的问题定义与理论知识，详细介绍以坐标上升为基础的变分推理算法，并给出这一方法的已有应用与未来展望。然后，对国内外现有的采样方法的研究成果进行综述，给出各类主要采样方法的具体算法流程，并总结和对比这些方法的特性与优缺点。最后，引入并行回火技术，对其基本理论和方法进行概述，探讨并行回火与采样...     

基于先验节点序学习贝叶斯网络结构的优化方法

针对小样本数据集下学习贝叶斯网络 (Bayesian networks, BN)结构的不足, 以及随着条件集的增大, 利用统计方法进行条件独立 (Conditional independence, CI) 测试不稳定等问题, 提出了一种基于先验节点序学习网络结构的优化方法. 新方法通过定义优化目标函数和可行域空间, 首次将贝叶斯网络结构学习问题转化为求解目标函数极值的数学规划问题, 并给出最优解的存在性及唯一性证明, 为贝叶斯网络的不断扩展研究提出了新的方案. 理论证明以及实验结果显示了新方法的正确性和有效性.     

病态盲分离情况下的混合矩阵估计研究

在盲信号分离技术中,当混合矩阵是病态情况时,基于信号稀疏性的两步法可用来解决这一问题,而如何估计混合矩阵则是两步法的关键。提出了一种估计混合矩阵的新方法,即通过搜索重构观测信号采样点,每次只需搜索出少数某源信号取值占优的采样点,就可以通过这些采样点处的重构观测信号数据,估计出混合矩阵的某一列。依次类推,可以估计出整个混合矩阵。该方法估计混合矩阵时对源信号的稀疏度要求较低,其实现算法不需优化过程,计算简单,因此其实用性较高。仿真结果表明了该方法有效,有很好的性能。通过大量的仿真试验给出了方法的定量性能分析。     

正则化路径上三步式SVM贝叶斯组合

模型组合旨在整合并利用假设空间中多个模型提高学习系统的稳定性和泛化性.针对支持向量机(support vector machine,SVM)模型组合多采用基于样本采样方法构造候选模型集的现状,研究基于正则化路径的SVM模型组合.首先证明SVM模型组合Lh-风险一致性,给出SVM模型组合基于样本的合理性解释.然后提出正则化路径上的三步式SVM贝叶斯组合方法.利用SVM正则化路径分段线性性质构建初始模型集,并应用平均广义近似交叉验证(generalized approximate cross-validation,GACV)模型集修剪策略获得候选模型集.测试或预测阶段,应用最小近邻法确定输入敏感的最终组合模型集,并实现贝叶斯组合预测.与基于样本采样方法不同,三步式SVM贝叶斯组合方法基于正则化路径在整个样本集上构造模型集,训练过程易于实现,计算效率较高.模型集修剪策略可减小模型集规模,提高计算效率和预测性能.实验结果验证了正则化路径上三步式SVM模型组合的有效性.     

一种强干扰环境下的离格稀疏贝叶斯DOA估计方法

强干扰的环境下,基于传感器阵列的波达方向(Direction of arrival,DOA)估计是阵列信号处理中的重要问题。虽然对于网格点目标现有方法的DOA估计精度较高,但对于离格点目标现有方法的DOA估计性能会严重下降。本文提出一种离格情况下的DOA估计方法,首先设计一种鲁棒的正交零陷矩阵滤波法(Robust orthogonal matrix filter with nulling,ROMFN),它结合了正交零陷滤波法(Orthogonal matrix filter with nulling,OMFN)和最差性能下的鲁棒自适应波束形成,在对离格点目标达到滤波效果的同时只需设计较少的网格点。此外,新的矩阵滤波法保留了高斯白噪声的特性,避免了噪声白化的预处理过程。其次基于离格点稀疏贝叶斯推断(Off-grid sparse Bayesian inference,OGSBI)和ROMFN,形成一种强干扰下DOA估计的新方法。与现有方法相比,仿真结果表明该方法可以在不同的网格间距、不同的信噪比和干噪比下获得更高的估计精度。     

一种贝叶斯对数正态分布的张量分解插补算法

从智能交通系统中收集到的交通数据集,往往会因为诸多因素不可避免地产生数据丢失的问题.针对此问题,提出一种贝叶斯对数正态分布张量分解插补算法.将一般的矩阵分解扩展到高阶的张量维度上,保存了数据的原本结构;利用贝叶斯推断,对一组服从对数正态分布的随机数进行循环迭代,逐一将参数的似然估计和先验项结合得到后验公式;通过马尔可夫链蒙特卡洛算法(MCMC)得到Gibbs采样模型.选用在中国广州收集的时空交通速度数据集,将其分别变成二阶、三阶和四阶张量进行对比处理,并评估该算法的性能.结果表明,该算法相较其他方法在处理三阶张量数据上可以表现出更优的数据插补性能.     

基于Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪

在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC（Markov chain Monte Carlo）算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.     

GIBBS仿真方法运用在大型因果图的推理过程

在信度网基础上发展起来的因果图模型,克服了信度网的一些不足,目前已发展成一个能够处理离散变量和连续变量的混合模型,特别适于运用在大型的工业故障诊断领域。但因果图在推理计算中,面临着与信度网的推理算法复杂度过高的同样问题。通过比较几种MarkovChainMonteCarlo(MCMC)方法,论文基于Gibbs仿真算法的思想,并对进入稳态条件、采样顺序判定准则、采样结束判据等进行深入分析,进而提出了一种改进的仿真推理新方法。利用该采样仿真算法能极大地提高故障诊断的速度和准确度,这对因果图模型在工业在线故障诊断领域中的应用具有重要意义。     

贝叶斯高分辨方位估计新方法

针对贝叶斯方位估计方法计算量大的问题,将马尔可夫蒙特卡罗方法与贝叶斯方位估计方法相结合,提出一种基于Metropolis-Hastings抽样的贝叶斯方位估计方法(Bayesian DOA Estimator Basedon Metropolis-Hasting Sampling,简称MHB)。MHB方法将贝叶斯算法的空间谱函数作为信号的概率分布函数,并利用Metropolis-Hastings抽样方法从该概率分布函数中抽样。研究结果表明,MHB方法不但保持了贝叶斯方位估计方法的优良性能,而且大大减小了计算量。     

Two-step reliability test based unitary root-MUSIC for direction-of-arrival estimation

A two-step reliability test (TSRT) based unitary root-MUSIC algorithm for direction-of-arrival (DOA) estimation is proposed in this paper. We combine the conventional beamforming and unitary root-MUSIC to compute the DOA estimates and employ the pseudo-noise resampling (PR) technique to construct a DOA estimator bank. Unlike the standard reliability test, we devise the TSRT which retains the successful DOA estimates of a given DOA estimator separately to construct a DOA estimate set that is used to determine the final DOA estimates. Compared to the existing PR based DOA estimation methods, our solution can achieve better threshold performance by using fewer PR runs. Furthermore, the TSRT can be easily applied to other DOA estimation methods. Simulations verify the effectiveness of the proposed scheme.     

Covariance sparsity-aware DOA estimation for nonuniform noise

This paper reformulates the problem of direction-of-arrival (DOA) estimation for unknown nonuniform noise by exploiting a sparse representation of the array covariance vectors. In the proposed covariance sparsity-aware DOA estimator, the unknown noise variances can be eliminated by a linear transformation, and DOA estimation is reduced to a sparse reconstruction problem with nonnegativity constraint. The proposed method not only obtains an extended-aperture array with increased degrees of freedom which enables us to handle more sources than sensors, but also provides superiority in performance and robustness against nonuniform noise. Numerical examples under different conditions demonstrate the effectiveness of the proposed method.     

Learning in Gibbsian fields: how accurate and how fast can it be?

Gibbsian fields or Markov random fields are widely used in Bayesian image analysis, but learning Gibbs models is computationally expensive. The computational complexity is pronounced by the recent minimax entropy (FRAME) models which use large neighborhoods and hundreds of parameters. In this paper, we present a common framework for learning Gibbs models. We identify two key factors that determine the accuracy and speed of learning Gibbs models: The efficiency of likelihood functions and the variance in approximating partition functions using Monte Carlo integration. We propose three new algorithms. In particular, we are interested in a maximum satellite likelihood estimator, which makes use of a set of precomputed Gibbs models called "satellites" to approximate likelihood functions. This algorithm can approximately estimate the minimax entropy model for textures in seconds in a HP workstation. The performances of various learning algorithms are compared in our experiments     

Direction of arrival estimation for smart antenna in multipath environment using convolutional neural network

This article aims to present a novel direction of arrival (DOA) estimation strategy for smart antenna in multipath environment. The smart antenna is composed of 2 main parts: the DOA estimator and the switched‐beam system. In the first part, a DOA estimation method based on convolutional neural network (CNN) has been implemented. The CNN is capable to select the desired radiation beams of the switched‐beam antenna without knowing the number of source signals coming from different directions, and in the case of noncoherent and coherent signals. Simulation results have been presented to show the effectiveness of the proposed intelligent approach.     

基于广义Gibbs先验的低剂量X-CT优质重建研究

为获取低剂量条件下X-CT的优质重建,提出基于广义Gibbs先验的低剂量X-CT重建算法。新算法首先对投影数据进行统计建模,其后采用Bayesian最大后验估计方法,将投影数据中非局部的先验信息加诸于该数据的恢复中,达到抑制噪声的效果,最后仍采用经典的滤波反投影方法对恢复后的投影数据进行解释CT重建。文中将非局部先验称为广义Gibbs先验,其原因在于该先验具有传统Gibbs先验形式的同时,可以通过选择较大邻域和自适应的加权方式充分利用投影数据的全局信息进行数据恢复。通过与已有算法的对比实验,表明该文提出的基于广义Gibbs先验的低剂量X-CT重建算法在降低噪声效果和保持边缘方面具有较好的表现。     

An effective localization method for mixed far-field and near-field strictly non-circular sources

In this paper, an effective direction-of-arrival (DOA) and range estimations method for mixed far-field and near-field non-circular sources is proposed based on a large centrosymmetric uniform linear array (ULA). By exploiting the non-circularity of the sources, an extended signal is generated by concatenating the received array data and its conjugate counterparts. Then the DOAs of far-field signals are estimated based on the extended covariance matrix with the traditional MUSIC algorithm. After eliminating the far-field components from the extended signal subspace, the extended covariance matrix of the near-field signals is obtained. Thus a near-field estimator is constructed based on symmetric property of the extended array manifold where the generalized ESPRIT method is adopted to estimate the DOAs of near-field sources. Finally, the range estimator is derived using the DOA estimations of near-field sources. Simulation results are provided to validate that the proposed method has achieved a better performance than existing ones and is quite suitable for massive MIMO (multiple-input multiple-out) system.     

Wavelet-based image denoising with the normal inverse Gaussian prior and linear MMSE estimator

A new spatially adaptive wavelet-based method is introduced for reducing noise in images corrupted by additive white Gaussian noise. It is shown that a symmetric normal inverse Gaussian distribution is highly suitable for modelling the wavelet coefficients. In order to estimate the parameters of the distribution, a maximumlikelihood- based technique is proposed, wherein the Gauss?Hermite quadrature approximation is exploited to perform the maximisation in a computationally efficient way. A Bayesian minimum mean-squared error (MMSE) estimator is developed utilising the proposed distribution. The variances corresponding to the noisefree coefficients are obtained from the Bayesian estimates using a local neighbourhood. A modified linear MMSE estimator that incorporates both intra-scale and inter-scale dependencies is proposed. The performance of the proposed method is studied using typical noise-free images corrupted with simulated noise and compared with that of the other state-of-the-art methods. It is shown that the proposed method gives higher values of the peak signal-to-noise ratio compared with most of the other denoising techniques and provides images of good visual quality. Also, the performance of the proposed method is quite close to that of the state-of-the-art Gaussian scale mixture (GSM) method, but with much less complexity.