# Questions tagged [expectation-maximization]

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

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### Hierarchical Expectation Maximization

Let us assume we have a generative model $y = g(\theta,x)$, where $\theta$ is a set of parameters, and $x$ is a set of latent variables. Given a datapoint $y$, I need to update the parameters $\theta$ ...
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### Kinds of Expectation-Maximization [closed]

I'm starting to dig into the variational inference literature, as I need to solve a learning problem where the latent variables form an hierarchical structure (an hierarchical Gaussian generative ...
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### Expectation-Maximization high missing rates and multiple variables

I know MICE can be used for imputation of multiple variables simultaneously. The expectation maximization approach (EM) can be used to impute missing data. Typically, one should only be using ...
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### Labeling unlabeled data (expectation maximization)

Say I have a database (Excel) consisting of 10k different dresses and accompanying attributes (column names) for each dress (sleeve length, color, pattern, ...). I would like to label each of these ...
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### How does expectation maximization compute missing data?

I have been searching for a simple example of how expectation-maximization (EM) computes missing data. All the examples I have found are based on multivariate normal models. I have seen that EM can be ...
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### Problems with convergence of the EM algorithm for a gaussian mixture regression

I have been implementing a EM-algorithm for a latent-class regression model, where every individual has a vector of observations. Currenly, I have the problem that the model does not converge. The log ...
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### EM derivation for mixture of t distributions

(Notation is at the bottom.) I'm currently self-studying the Expectation-Maximization algorithm and has learned to derive it for various mixture models including Gaussian mixture models, mixture of ...
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### Model choice with expectation maximization: which likelihood?

When deciding about the number of mixture components using Akaike or bayesian information criteria, should one use the full likelihood or the likelihood marginalized over the latent variables? Both ...
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### Benefits of Expectation Maximization for Mixture Models

What are the benefits of using expectation maximization for mixture models vs. direct maximization of the marginal likelihoods? Analytic maximization step In case of Gaussian mixtures the benefit is ...
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### Computing a prior from two components in Naive Bayes

Given a model parameter $\theta$ that is composed of two distributions in a Naive Bayes classifier, how is $P(\theta)$ typically computed in practice? More specifically, from the article of Nigam et ...
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### Expectation maximization: does the likelihood always increase monotonically?

When working with (gaussian) mixture models, I always took it for a mathematical fact that the marginal likelihood increases with every iteration step. If it were not the case, it always meant an ...
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### Practical considerations for EM clustering

EM algorithm guarantees finding a local rather then global minimum of the likelihood. As a consequence, the results are dependent on the initial conditions (e.g., if randomly choosing the initial ...
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### How can I derive the EM algorithm for a mixture of two Bernoulli distributions?

How can I derive the E-step and M-step in the EM algorithm for a mixture of two Bernoulli distributions? Note that I am aware that there are several notes online that explain how to do this for the ...
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### Finding category with maximum likelihood method

Let's say that we had an information for men and women heights. R code: ...
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