基于EM算法的因子分析中隐变量的条件概率密度函数

因子分析是一种重要的多元统计分析技术,可以采用EM算法迭代得到模型的未知参数,其中一个关键的问题就是在已知观测数据和前一次迭代得到的参数估计值的条件下,如何得到隐变量的条件概率密度函数.国内外的有关文献都不加说明地直接给出了这个函数,本文给出了详细的推导过程.     

Online EM Algorithm for Hidden Markov Models

Online (also called “recursive” or “adaptive”) estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modeling. In this work, we propose an online parameter estimation algorithm that combines two key ideas. The first one, which is deeply rooted in the Expectation-Maximization (EM) methodology, consists in reparameterizing the problem using complete-data sufficient statistics. The second ingredient consists in exploiting a purely recursive form of smoothing in HMMs based on an auxiliary recursion. Although the proposed online EM algorithm resembles a classical stochastic approximation (or Robbins–Monro) algorithm, it is sufficiently different to resist conventional analysis of convergence. We thus provide limited results which identify the potential limiting points of the recursion as well as the large-sample behavior of the quantities involved in the algorithm. The performance of the proposed algorithm is numerically evaluated through simulations in the case of a noisily observed Markov chain. In this case, the algorithm reaches estimation results that are comparable to those of the maximum likelihood estimator for large sample sizes. The supplemental material for this article available online includes an appendix with the proofs of Theorem 1 and Corollary 1 stated in Section 4 as well as the MATLAB/OCTAVE code used to implement the algorithm in the case of a noisily observed Markov chain considered in Section 5.     

非线性混合模式的语音盲分离算法

本文针对FIR非线性混合模型，基于最大熵算法，提出了一种以高斯混合模式概率密度函数估计替代传统对数化概率密度估计的盲分离算法，以偶函数为非线性激活函数，采用最大期望（EM）迭代算法推导了分离算法的权向量迭代公式，通过模拟仿真实验结果与传统的最大熵和高阶累积量方法比较，新算法提高了收敛速度，并有效地完成了非线性语音分离任务，抑制了干扰语音信号的影响，提高了输出信噪比。