# Questions tagged [expectation-maximization]

An optimization algorithm often used for maximum-likelihood estimation in the presence of missing data.

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### Expectation Maximization on Multivariate Gaussian Mixture Model for clustering

I have a dataset with 1000 observations and two features that define those N=1000 data points. Hence it is 1000*2 input matrix. I need to cluster them into k clusters. I am not understanding the E-M ...
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### Q function in Baum-Welch algorithm

Assume there's a hidden Markov Model $\lambda=(\pi, \mathbf{A}, \mathbf{B})$, where $\pi$ is an initial distribution, $\mathbf{A}$ is a transition matrix and $\mathbf{B}$ is an emission matrix. Also, ...
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### Observation from each cluster from EM algorithm manually implemented

I am interesting in implementing the EM algorithm manually. And I did it. However, I am still do not know how to get the observation from each cluster? For example, after run the EM algorithm, the ...
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### Need help understanding why the original proof of the EM algorithm had a flaw in it

I understand that in the original paper on the EM algorithm by Dempster, the proof of convergence in Theorem 2 had a flaw, and that a full proof wasn't given until CF Jeff Wu published it years later. ...
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### Continuously running the M step while approximating the E step

Let us assume we need to maximize the likelihood $p(x|\theta)$ of an observed variable $x$ given a set of parameters $\theta$. However, this likelihood also depends on a set of hidden variables $z$, ...
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### details of stochastic Expectation Maximization (EM) algorithm

I went into a paper, Online EM Algorithm for Latent Data Models (Olivier Cappé & Eric Moulines, 2009). I got confused by the first equation the authors wrote, the Q function: Here the authors ...
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### Can overlap impact the EM algorithm?

I am using EM algorithm for clustering. I see that if there is an overlap, the accuracy is reduced. However, it is improvesd if no overlap exists. My question is, can overlap affect the performance of ...
I have problem distinguishing between the latent variables $z_i$ and the parameters $\theta_i$ in EM algorithm. Suppose we have the hierarchical priors \begin{aligned} \beta|\tau,\omega &\sim \...