# Questions tagged [expectation-maximization]

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

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### Numerical example to understand Expectation-Maximization

I am trying to get a good grasp on the EM algorithm, to be able to implement and use it. I spent a full day reading the theory and a paper where EM is used to track an aircraft using the position ...
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### Clustering with K-Means and EM: how are they related?

I have studied algorithms for clustering data (unsupervised learning): EM, and k-means. I keep reading the following : k-means is a variant of EM, with the assumptions that clusters are ...
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### What is the difference between EM and Gradient Ascent?

What is the difference between the algorithms EM (Expectation Maximization) and Gradient Ascent (or descent)? Is there any condition under which they are equivalent?
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### Relation between variational Bayes and EM

I read somewhere that Variational Bayes method is a generalization of the EM algorithm. Indeed, the iterative parts of the algorithms are very similar. In order to test whether the EM algorithm is a ...
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### Why is the Expectation Maximization algorithm guaranteed to converge to a local optimum?

I have read a couple of explanations of EM algorithm (e.g. from Bishop's Pattern Recognition and Machine Learning and from Roger and Gerolami First Course on Machine Learning). The derivation of EM is ...
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### How to make a matrix positive definite?

I'm trying to implement an EM algorithm for the following factor analysis model; $$W_j = \mu+B a_j+e_j \quad\text{for}\quad j=1,\ldots,n$$ where $W_j$ is p-dimensional random vector, $a_j$ is a q-...
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### MCMC/EM limitations? MCMC over EM?

I am currently learning hierarchical Bayesian models using JAGS from R, and also pymc using Python ("Bayesian Methods for Hackers"). I can get some intuition from this post: "you will end up with a ...
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### EM algorithm Practice Problem

This is a practice problem for a midterm exam. The problem is an EM algorithm example. I am having trouble with part (f). I list parts (a)-(e) for completion and in case I made a mistake earlier. Let ...
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### Convergence from the EM Algorithm with bivariate mixture distribution

I have a mixture model which I want to find the maximum likelihood estimator of given a set of data $x$ and a set of partially observed data $z$. I have implemented both the E-step (calculating the ...
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### Why does the EM algorithm have to be iterative?

Suppose that you have a population with $N$ units, each with a random variable $X_i \sim \text{Poisson}(\lambda)$. You observe $n = N-n_0$ values for any unit for which $X_i > 0$. We want an ...
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### Help in Expectation Maximization from paper :how to include prior distribution?

The Question is based on the paper titled : Image reconstruction in diffuse optical tomography using the coupled radiative transportādiffusion model Download link The Authors apply EM algorithm with ...
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### Using EM algorithm for record linking

I am interested in linking records across 2 datasets by first name, last name, and birth year. Might this be doable with the EM algorithm, and if so, how? Consider the following record in the 1st as ...
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### Difference between MLE and Baum Welch on HMM fitting

In this popular question, high upvoted answer makes MLE and Baum Welch separate in HMM fitting. For training problem we can use the following 3 algorithms: MLE (maximum likelihood estimation), ...
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### Does EM algorithm consistently estimate the parameters in Gaussian Mixture model?

I am studying the Gaussian Mixture model and come up with this question myself. Suppose the underlying data is generated from a mixture of $K$ Gaussian distribution and each of them has a mean vector ...
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### Determine an unknown number of real world locations from GPS-based reports

I'm working on some software which should determine real world locations (f.e. speed cams) from several GPS-based reports. An user will be driving when reporting a location, thus the reports a very ...
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### Why is there a E in the name EM algorithm?

I understand where the E step happens in the algorithm (as explicated in the math section below). In my mind, the key ingenuity of the algorithm is the use of the Jensen's inequality to create a lower ...
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