scholarly journals Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

Entropy ◽  
2018 ◽  
Vol 20 (1) ◽  
pp. 76 ◽  
Author(s):  
Saïd Maanan ◽  
Bogdan Dumitrescu ◽  
Ciprian Giurcăneanu
Keyword(s):  
Time Series ◽  
Maximum Entropy ◽  
Graphical Models ◽  
Expectation Maximization ◽  
Latent Variable ◽  
Multivariate Time Series ◽  
Expectation Maximization Algorithm

scholarly journals On the curved exponential family in the Stochatic Approximation Expectation Maximization Algorithm

2021 ◽  
Author(s):  
Vianney Debavelaere ◽  
Stéphanie Allassonnière
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Latent Variables ◽  
Latent Variable ◽  
Exponential Family ◽  
Expectation Maximization Algorithm ◽  
Computation Time ◽  
Initial Model ◽  
Joint Likelihood ◽  
Curved Exponential Family

The Expectation-Maximization Algorithm (EM) is a widely used method allowing to estimate the maximum likelihood of  models involving latent variables. When the Expectation step cannot be computed easily, one can use stochastic versions of the EM such as the Stochastic Approximation EM. This algorithm, however, has the drawback to require the joint likelihood to belong to the curved exponential family. To overcome this problem, \cite{kuhn2005maximum} introduced a rewriting of the model which ``exponentializes'' it by considering the parameter as an additional latent variable following a Normal distribution centered on the newly defined parameters and with fixed variance. The likelihood of this new exponentialized model now belongs to the curved exponential family. Although often used, there is no guarantee that the estimated mean is close to the  maximum likelihood estimate of the initial model. In this paper, we quantify the error done in this estimation while considering the exponentialized model instead of the initial one. By verifying those results on an example, we see that a trade-off must be made between the speed of convergence and the tolerated error. Finally, we propose a new algorithm allowing a better estimation of the parameter in a reasonable computation time to reduce the bias.

Blind source separation with time series variational Bayes expectation maximization algorithm

2012 ◽  
Vol 22 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Shijun Sun ◽  
Chenglin Peng ◽  
Wensheng Hou ◽  
Jun Zheng ◽  
Yingtao Jiang ◽  
...  
Keyword(s):  
Time Series ◽  
Blind Source Separation ◽  
Expectation Maximization ◽  
Source Separation ◽  
Expectation Maximization Algorithm ◽  
Variational Bayes
Sign in / Sign up

Export Citation Format

Share Document