期望最大算法及其应用(2)

EM算法是实现极大似然估计的一种有效方法,主要用于非完全数据的参数估计。文章的第一部分已经详细介绍了算法的基本原理,这部分内容着重介绍算法的各种应用,特别是高斯混合模型、隐马尔科夫模型和因子分析中的参数估计。     

基于EM算法的混合模型的参数估计

介绍了极大似然参数估计，然后介绍了混合模型极大似然参数估计的EM算法实现，最后利用计算机仿真实验验证了此算法的有效性和收敛性．     

动态模糊极大似然估计算法

在机器学习中,一个广泛的应用是对模型的参数进行估计,即极大似然估计(MLE),EM算法是根据点估计中的MLE改进的一种迭代算法,是求极大似然估计的一种强有力的工具,但它收敛速度较慢,于是引入α-EM算法,克服了EM算法的缺陷.由于学习的过程中可能存在着大量的缺失数据及其动态模糊性,给出基于不完全数据的动态模糊极大似然估计算法并给出实例验证.     

EM算法研究与应用

引入了可处理缺失数据的EM算法.EM算法是一种迭代算法,每一次迭代都能保证似然函数值增加,并且收敛到一个局部极大值.对EM算法的基本原理和实施步骤进行了分析.算法的命名,是因为算法的每一迭代包括两步:第一步求期望(Expectation Step),称为E步;第二步求极大值(Maximization Step),称为M步.EM算法主要用来计算基于不完全数据的极大似然估计.在此基础上,把EM算法融合到状态空间模型的参数估计问题.给出了基于Kalman平滑和算法的线性状态空问模型参数估计方法.     

一种对统计信号处理中缺失数据估计的算法

EM算法是一种有效的应对缺失数据的估计算法,它的应用非常广泛,比如人工智能、模式识别、数理统计、图像处理、信号检测等等。首先对最有效的估计算法极大似然估计进行简单阐述,接下来引出算法的主要内容,在原理上说明了基于迭代理论的似然估计期望最大化算法,讨论EM算法的收敛性,并提出了EM算法的应用,最后简单介绍了几种EM改进型算法。     

基于分裂EM算法的GMM参数估计

期望最大化(Expectation Maximization,EM)算法是一种求参数极大似然估计的迭代算法,常用来估计混合密度分布模型的参数。EM算法的主要问题是参数初始化依赖于先验知识且在迭代过程中容易收敛到局部极大值。提出一种新的基于分裂EM算法的GMM参数估计算法,该方法从一个确定的单高斯分布开始,在EM优化过程中逐渐分裂并估计混合分布的参数,解决了参数迭代收敛到局部极值问题。大量的实验表明,与现有的其他参数估计算法相比,算法具有较好的运算效率和估算准确性。     

一种半监督机器学习的EM算法改进方法

EM(Expectation Maximization)算法是含有隐变量(latent variable)的概率参数模型最大似然估计、极大后验概率估计最有效的算法,但很容易进入局部最优现象,对此提出基于半监督机器学习机制的EM算法.本文方法是在最大似然函数中加入惩罚最小二乘因子,同时引入非负约束作为先验信息,结合半监督机器学习方法,将EM算法改进转化为最小化求解问题,再采用最大似然方法求解EM模型,有效估计了混合矩阵和高斯混合模型参数,实现EM算法的改进.仿真结果表明,该方法能够很好地解决了EM算法容易局部最优化问题.     

EM算法在统计自然语言处理中的应用

在统计自然语言处理中会经常遇到一类参数估值问题,就是当观察数据为不完全数据时如何求解参数的最大似然估计,EM算法就是解决这类问题的经典算法.给出了EM算法的基本框架,结合HMM和PCFG模型给出如何应用EM算法求解参数的极大似然估计,讨论了EM算法的优点和不足之处.     

极大似然估计的递推计算灵敏度算法

极大似然估计的递推计算灵敏度算法崔平远，吴瑶华，黄文虎，李乃宏（哈尔滨工业大学航天工程与力学系１５０００１）关键词连续－离散系统，极大似然估计，灵敏度，正交试验玉引言采用极大似然法对连续一离散系统进行参数估计，实际上是一个似然函数的优化计算问题，而其...     

基于粒子滤波的非线性系统静态参数估计方法*

针对基于滤波方法的最大似然参数估计步长序列过于单一,算法收敛缓慢并很容易收敛于局部最优解的问题,提出了基于似然权值的在线EM参数估计算法(LWOEM)。通过粒子滤波方法实时估计系统的状态值变化,结合最大似然方法计算静态参数的点估计,然后通过计算更新参数的似然值来动态更新步长序列.与在线EM参数估计算法(OEM)的实验结果比较,表明该算法具有更好的适应性和收敛效果。     

基于最大后验估计的无监督聚类算法

传统的基于EM算法的聚类方法,当模型的某个高斯分量的协方差矩阵变为奇异矩阵时,会导致聚类失败。提出在聚类过程中用最大后验估计（MAP）来代替极大似然估计（MLE）;将一种改进的贝叶斯信息准则（BIC）与模型参数估计同时处理,扩大了模型选择的搜索范围。该算法有效地避免了协方差矩阵在迭代中陷入奇异,并将参数估计和模型选择同时进行。通过R软件进行仿真分析,结过表明改进的算法在减少计算量同时,提高了聚类的准确度,并具有鲁棒性。     

一种改进的期望最大图像分割方法

期望最大算法是进行极大似然估计的一种有效方法,它主要用于观测数据不完全或者似然函数不是解析时的参数估计。文中提出了一种期望最大化和贝叶斯信息准则相结合的图像分割方法。首先,运用K均值方法初始化图像分布;然后,运用期望最大算法估计输入图像参数数据,图像中类的数目由贝叶斯消息准则自动确定;最后,运用最大似然标准将像素归类于最相近的类中。实验中将此方法用于对葡萄叶部病害彩色图像的分割,其结果表明此方法有效。     

一种自底向上的推测链路延迟分布的快速算法*

网络层析技术用端到端的测量结果来推测网络中的链路延迟分布。这方面已有的大部分工作都基于最大似然估计式 (MLE)和期望最大化（EM）算法,它们在求解过程中需要不断迭代,对于大规模网络需要消耗很长的时间。为了克服这方面的不足,提出了一种快速算法FBA,该算法自底向上估计出每层链路的延迟分布。定性的分析和实验仿真结果表明FBA大大减小了计算的复杂度,而且在发包数目足够多的情况下,它的估计结果的精确度接近EM算法。     

GSA-based maximum likelihood estimation for threshold vector error correction model

The log-likelihood function of threshold vector error correction models is neither differentiable, nor smooth with respect to some parameters. Therefore, it is very difficult to implement maximum likelihood estimation (MLE) of the model. A new estimation method, which is based on a hybrid algorithm and MLE, is proposed to resolve this problem. The hybrid algorithm, referred to as genetic-simulated annealing, not only inherits aspects of genetic-algorithms (GAs), but also avoids premature convergence by incorporating elements of simulated annealing (SA). Simulation experiments demonstrate that the proposed method allows to estimate the parameters of larger cointegrating systems. Additionally, numerical results show that the hybrid algorithm does a better job than either SA or GA alone.     

一种快速放射CT重建算法的研究

ＥＭ算法用于求解重建问题，具有一些非常好的特性，几十年来一直为人们所重视。ＥＭ算法也存在着缺点，例如收敛速度较慢，使它的应用受到一定的限制。为此，人们提出了很多加快收敛速度的方法，取得了不少有价值的结果。     

Maximum likelihood estimation from interval censored recurrent event data

In this paper, we consider the recurrent failures of several repairable units, which can only be observed at periodic inspection times. A unit is not aging over the period between a failure and its detection. The failure times are interval censored by the periodic assessment times. The observed data consists of censoring intervals of failure times and the unobserved data are the actual ages of the units at the failure times. We formulate the likelihood function and use several iterative algorithms to find the maximum likelihood estimate (MLE) of the parameters. The complete Expectation–Maximization (EM) algorithm, the EM gradient, full Newton–Raphson (NR), and the Simplex method are used. We derive recursive equations to calculate the expected values required in the algorithms. We estimate the parameters for four failure datasets, assuming that the failures follow a non-homogeneous Poisson process (NHPP). Three datasets are obtained from a hospital for the components of general infusion pump, and the fourth dataset is simulated. Since the estimation could take a long time, we compare the performance of the algorithms in terms of the required number of iterations to converge, the total execution time, and the precision of the estimated parameters. We also use Monte Carlo and Quasi-Monte Carlo simulation as the substitutes for the recursive procedures in the Expectation step of the EM gradient and compare the results.     

基于SMC-PHDF的部分可分辨的群目标跟踪算法

提出一种基于粒子概率假设密度滤波器(Sequential Monte Carlo probability hypothesis density filter, SMC-PHDF)的部分可分辨的群目标跟踪算法. 该算法可直接获得群而非个体的个数和状态估计. 这里群的状态包括群的质心状态和形状. 为了估计群的个数和状态, 该算法利用高斯混合模型(Gaussian mixture models, GMM)拟合SMC-PHDF中经重采样后的粒子分布, 这里混合模型的元素个数和参数分别对应于群的个数和状态. 期望最大化(Expectation maximum, EM)算法和马尔科夫链蒙特卡洛(Markov chain Monte Carlo, MCMC)算法分别被用于估计混合模型的参数. 混合模型的元素个数可通过删除、合并及分裂算法得到. 100次蒙特卡洛(Monte Carlo, MC)仿真实验表明该算法可有效跟踪部分可分辨的群目标. 相比EM算法, MCMC算法能够更好地提取群的个数和状态, 但它的计算量要大于EM算法.     

Nonlinear multiscale Maximal Lyapunov Exponent for accurate myoelectric signal classification

Surface Electromyography (sEMG) is a non-invasive, easy to record signal of superficial muscles from the skin surface. The sEMG is widely used in evaluating the functional status of the hand to assist in hand gesture recognition, prosthetics and rehabilitation applications. Considering the nonlinear and non-stationary characteristics of sEMG, hand gesture recognition using sEMG signals necessitate designers to use Maximal Lyapunov Exponent (MLE) or ensemble Empirical Mode Decomposition (EMD) based MLEs. In this research, we propose a hand gesture recognition method of sEMG based on nonlinear multiscale MLE. The aim is to increase the classification accuracy of sEMG features while reducing the complexity of EMD. The nonlinear MLE features are classified using Flexible Neural Tree (FNT), which can solve highly structured dependent problems of the Artificial Neural Network (ANN). The testing has been conducted using several experiments with five participants. The classification performance of nonlinear multiscale MLE method is compared with MLE and EMD-based MLE through simulations. Experimental results demonstrate that the former algorithm outperforms the two latter algorithms and can classify six different hand gestures up to 97.6% accuracy.     

Identification of chemical processes with irregular output sampling

In many chemical processes, variables which indicate product quality are infrequently and irregularly sampled. Often, the inter-sample behavior of these quality variables can be inferred from manipulated variables and other process variables which are measured frequently. When the quality variables are irregularly sampled, maximum likelihood estimation (MLE) of the model parameters can be performed using the expectation maximization (EM) approach. A state-space model identification procedure based on the EM algorithm yields a Kalman filter-based prediction–correction mechanism which can be used for optimal prediction of the quality variables. In this paper, we describe such a state-space model identification and estimation method and present the results of its application on simulation, laboratory-scale and industrial case studies.