# Questions tagged [expectation-maximization]

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

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### Probabilty estimation for Bernoulli with number of trials as random variable

Problem description Suppose we have fixed number of people that are the test population, let's say $t=200$ persons. For each one of them $\mathbf{r}_j$ we know about $m=300$ features that describes ...
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### EM algorithm for normal mixtures with constraints

I have $G$ groups, each with $N_g$ data points $y_{ig}$, $g=1,\dots,G$ and $i = 1, \dots, N_g$. The group for each data point in observable. I want to estimate the normal mixtures model with $K$ ...
1answer
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### Why would split observed $x$ into two unobserved r.v $z_1,z_2$ consider a way to augmenting data in EM algorithm?

I am reading the materials on the EM algorithm, and I am a bit confused about the example provided on the material I am currently reading. The example is considered a classical missing data problem ...
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### normal mean variance mixture garch with OBSERVED mixing variable

I need to estimate this univariate garch model with the following discription My model (regression): Yt=mu + gamma * Gt + et Gt is GIVEN Where the crucial part is that: et= sqrt(Gt) * sqrt(ht) * Zt ...
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### Log-likelihood decrease in EM - two regressions

I am facing a problem with an EM algorithm where, in some iterations, the log-likelihood decreases. I have a two dimensional dataset $\{\vec{x}, \vec{y}\}$ and each data point belongs to one of these ...
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### Major discrepancy of latent variable in the Gaussian Mixture Model/Expectation and Maximization literature

I have read a couple of references on the interpretation of a latent variable in the GMM/EM literature and I found a massive discrepancy between the authors so much so I now have no idea how GMM/EM ...
1answer
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### About the derivation of EM for mixture of Gaussians

I'm reading Andrew Ng's note about Mixtures of Gaussians and the EM algorithm He writes the likelihood of data as where random variables $z^{(i)}$'s indicate which of the $k$ Gaussians each $x^{(i)}$ ...
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### Finding the Q function for the EM algorithm

I have a situation where $X_1,...X_n$ come from $N(\mu,1)$ and there is a realization of 10 $x$ values. I want to use the EM algorithm to work out the MLE. So, I am trying to compute the expected ...
1answer
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### Why maximizing the expected value of log likelihood under the posterior distribution of latent variables maximize the observed data log-likelihood?

I am trying to understand the Expectation-Maximization algorithm and I am not able to get the intuition of a particular step. I am able to verify the mathematical derivation but I want to understand ...
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### Fixing the parameters of the variational distribution in Expectation-Maximization

Consider directed graphical model $z \to x$ (with $z$ unobserved and $x$ observed). The evidence lower bound on the log-likelihood $\log p(x) = \log \sum_z p(x, z; \theta)$ for parameters $\theta$ (...
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### How to get number of iterations in EM-algorithm using R mclust gaussian mixture model

I am clustering data using the mclust function from the R mclust package. I am struggling to get the number of iterations the EM ...
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### derivation of E step in EM algorithm for pLSA via Lagrangian

I have trouble deriving the EM algorithm for the Probabilistic latent semantic analysis (pLSA) model via Lagrange multipliers. I model the missing data $Q_{zij} \in \{0,1\}$ for word $w_j$ in document ...