# Tagged Questions

EM stands for "expectation-maximization"; the algorithm is an iterative method for finding maximum likelihood estimates.

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### Normal Data with missing values (EM Algorithm)

Suppose we have multivariate normal data (some missing entries, at random), with known covariance matrix. We would like to estimate the mean vector by the EM algorithm. How would one approach this? ...
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### EM algorithm with a component for outliers

i have a vector of measurements from one to three classes, which can be modeled by gaussian distributions. There are some outliers in the data. I use the EM algorithm to learn the parameters of the ...
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### EM algorithm for mixture of Negative Binomial distributions

I am trying to derive the EM-algorithm of mixtures of negative binomial distribution $Neg\;Bin(r,p)$. I have the updating equations for updating the E-step as well as $p$ and the mixing coefficients ...
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### How is the Gaussian mixture model used in a hidden Markov model for speech recognition?

How is the Gaussian mixture model used in a hidden Markov model for speech recognition? How do you apply the EM algorithm to estimate the parameters of each Gaussian? How to utilized the transcription ...
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### Can the EM algorithm be applied to my problem? Input data set is based on a function of parameter

I understand EM algorithm is often used for missing data/mixture problem. But can it be used to optimize a particular type of likelihood based on jointly fitting variables and transformations of those ...
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### Distinguishing events from different periodic sources

I have records of the time stamps of events coming from a small number of independent sources. Each source $S$ issues events at a given period $Ts$. Due to some jitter the time intervals between two ...
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### EM algorithm manually implemented?

I want to implement the EM algorithm manually and then compare it to the results of the normalmixEM of mixtools package. Of ...
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### Formulas for fitting the parameters of a linear dynamical system

Using the expectation-maximization algorithm one can fit all the parameters of a linear dynamical system. I know the theory behind it, and I know how to derive the updated parameters from the Kalman ...
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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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### EM algorithm for fitting GMM in multivariate case in R

I am currently playing around with Gaussian Mixture Models in order to model stock returns. Part of all this is using the EM algorithm to obtain MLE of parameters. I have found a package in R ...
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### The relationship between expectation-maximization and majorization-minimization

I wonder about the relationship between two methods called expectation-maximization (EM) and majorization-minimization. One of them, the EM algorithm can be used for finding the mode of the likelihood ...
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### Does the EM algorithm require i.i.d?

The EM algorithm roughly has two steps. E-Step: Calculate the conditional expectation of the likelihood function given the data $x_1, . . . , x_n$ and the current estimates of parameters ...
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### Time dependant weights in hidden Markov models

I'm trying to modify a standard implementation of a continuous HMM with Gaussian Mixtures so that it internally gives more weight to newer observations in a time series. Essentially, I'm trying to ...
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### Maximum likelihood estimation in a Poisson model for football (soccer) scores

I've got a set of football results and I want to make a probabilty model of football scores as described in Dixon, Coles (1997, http://www.math.ku.dk/~rolf/teaching/thesis/DixonColes.pdf). They ...
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### Hidden Markov models and expectation maximization algorithm

Can somebody clarify how hidden Markov models are related to expectation maximization? I have gone through many links but couldn't come up with a clear view. Thanks!
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### Significance of initial transition probabilites in a hidden markov model

What are the benefits of giving certain initial values to transition probabilities in a Hidden Markov Model? Eventually system will learn them, so what is the point of giving values other than random ...
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### Averaged estimators in stochastic versions of EM

Recently I've been working EM algorithms for MAP estimation in a problem where the expectation is intractable, but the maximization is easy. Further, draws from the distribution in the E-step are ...
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### What is a “tempered EM algorithm”?

In the paper of Probabilistic Latent Semantic Analysis by Hofmann, the author fits the model for document $\times$ word matrix through EM Algorithm in section 3. I was able to follow the derivation ...
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### Soft and Hard EM (Expectation Maximization)

What is the difference between soft and hard expectation maximization? EDIT: ok, i've found out this paper: http://ttic.uchicago.edu/~dmcallester/ttic101-07/lectures/em/em.pdf that explain quite well ...
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### Using the EM Algorithm for unimodal distributions?

I've really only seen EM used for mixtures where one can point out multiple modes visually - e.g, the classic mixture of gaussians example. I would like to use EM for a mixture of an empirically ...
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### Optimization of MLE for mixture problems

I have about 1000 data points from some thick tailed distribution that I would like to fit a parametrized distribution to. From my data, I've made some adjustments and constructed an empirical ...