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

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Likelihood maximization: MCEM algorithm versus MCMC algorithm

Hello Everyone this is my first question. I am a particle physicist and I am doing some empirical studiues on parameters estimation using different methods (this might give me some handle to study on ...
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22 views

why is the incomplete log-likelihood difficult to optimize

I am trying to teach myself the expectation-maximization algorithm and the texts say the EM is particularly useful when the incomplete log-likelihood i.e. $P(X|\theta)$ where $\theta$ are the ...
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13 views

survival mixture model of gamma distribution via EM algorithm

I generated survival data for a three component survival mixture of gamma distribution with random right censored observations in R with the code; ...
4
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1answer
66 views

Question on how to use EM to estimate parameters of this model

I am trying to understand EM and trying to infer parameters of this model using this technique but am having trouble understanding how to begin: So, I have a weighted linear regression model as ...
3
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1answer
26 views

Deriving K-means algorithm as a limit of Expectation Maximization for Gaussian Mixtures

Christopher Bishop defines the expected value of the complete-data log likelihood function (i.e. assuming that we are given both the observable data X as well as the latent data Z) as follows: $$ ...
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1answer
37 views

Update Rules in Expectation Maximization

I am emulating a certain PDF behaviour using a function. However, due to divergent improper integral, I don't have a closed form expression for the normalization constant. To get the PDF, I just ...
0
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1answer
44 views

“The EM algorithm failed to converge in 25 iterations”

When I Replace Missing Values - Expectation-Maximization in SPSS, I receive the following message: The EM algorithm failed to converge in 25 iterations. Should the algorithm be able to converge? Can ...
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0answers
18 views

Contribution to the components of a Gaussian mixture by data features

My question is about modelling data with a GMM using EM. One can split the mean and variance of each component into parts as well when working with data with multiple features. My question is what ...
3
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2answers
82 views

Self-study: Finding the maximum likelihood estimates of the parameters of a density function

Consider a random sample $x_1,x_2,...,x_n$ from a newly-generated distribution, whose probability density function is given below \begin{equation} f(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( ...
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8 views

Clusteriod questions

I would like to clear some things up because I'm confusing everything. A $clusteriod$ is a coordinate for the mean value of a cluster? So if I have a 2-d .csv file I wish to perform kmeans, the ...
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54 views

Help with an exponential function with an indicator and using the EM Algorithm

Two bulbs, Brand A and Brand B, in which their lifetimes are distributed exponentially with expectations $\lambda$ and $\mu$ respectively. They pair $X_i$ and $Y_i$. In the ith experiment, instead ...
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1answer
23 views

Questions revolving GMM & EM

I am currently reading about the guassian mixture model and the expectation–maximization algorithm. From what I am reading the two differences between the two here is what I've come up with so far, ...
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20 views

Convergence Time of the EM Algorithm Depending on the Inital Parameter Values

I try to get an intuitive understanding of the convergence properties of the EM-Algorithm. I wrote a code that does the following experiment. We are given three coins: $H$, $A$ and $B$; with ...
2
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44 views

Unable to understand joint pdf and EM

I am unable to understand how the density function is derived in this paper Semiblind System Identification with Symbolic Chaotic Sequences The Authors have ...
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1answer
28 views

Unnatural clustering with known clusters shapes and optimization criteria

My question is similar to this question Clustering with shape prior, but with additional information. The second answer suggests a mixture model approach to this problem, which is something like ...
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0answers
6 views

EM convergence when using em.hmm from PLIS

I use em.hmm function from PLIS package. I tried it on dimensions in range from 2 to 6. In every case of provided data (z-values) EM algorithm does not converge for dimensions 2, 5, 6. So, I wonder ...
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49 views

Expectation Maximisation Algorithm: Understand through numeric example

I am trying to learn machine learning concepts through online materials. I just studied tutorial on Expectation Maximisation algorithm. I thought one numerical example can make better understanding. ...
0
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1answer
27 views

What is the values of the $P(a)$ and $P(b)$ here?

I am watching a video on EM algorithm here. It gives an example of how EM algorithm works. At first two Gaussian distributions are randomly given, and then by iterative calculations their parameters ...
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1answer
32 views

Does EM algorithm increase the lower bound as well as true likelihood

I am using a variational bayes method (without a M step since no parameters) to infer my model. My question is, if it is working correctly will it increase the log likelihood of the data, ...
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0answers
18 views

Expectation maximisation for right-censored iid data from Normal

This is the data (which are length of ropes), $\textrm{Data}=\{99, 70, o ,89, 88, o, 88,70, o ,o\}$, where $o$ are censored data with value above $100$. Assume that data are from $\textrm{iid} \sim ...
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0answers
15 views

r package for ecpectation maximization with probabilitis for each cluster

In r package i'm using EM algorythm.once it is completed i get latent variable z that assigns each observation a distinct cluster. i'd like to know what are the probabilities for each cluster in a ...
0
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2answers
97 views

Single EM imputation with R (using Amelia or other packages)

I am trying to impute missing values with R. I would like to use the EM algorithm for that. As it seems this algorithm is implemented in the ...
2
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0answers
76 views

Expectation-Maximization with dependent latent variables

Deriving the equations for a Expectation Maximization over my model, I end up with a posterior for the latent variables (E-step) that prevents me from going on. Generative model I assume my data is ...
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36 views

Baum Welch and a 1 state Markov model?

I'm using the Baum-Welch algorithm to determine the parameters of a 2 state Hidden Markov Model. It determines fairly well. When I increase the sample size, the estimations get more concentrated, and ...
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15 views

best theory on fitting mixture of gaussians

What are the current best results on fitting mixtures of Gaussians with any algorithm (EM or something fancier)? Specifically, if I know only the number of components, what are the sharpest sample ...
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21 views

Number of components in EM

How to find number of components that I need to use in expectation-maximization? The only thing that I can think of is to do a cross validation for each number of components. Is there a better way? ...
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17 views

plsa using maximum a posteriori

I have performed topic modeling by PLSA using maximum likelihood estimation. Now I need to perform using maximum a posteriori by using some prior distribution. The prior distribution consists of word ...
3
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1answer
132 views

K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going to $0$

My goal is to see that K-means algorithm is in fact Expectation-Maximization algorithm for Gaussian mixtures in which all components have covariance $\sigma^2 I$ in the limit as $\lim_{\sigma \to 0}$. ...
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90 views

Choosing initial transition and emission probabilities while training HMM

A Hidden Markov Model (HMM) is defined by the following parameters: $HMM =(prior, transmat, obsmat)$ Using K Murphy's HMM toolbox [1], I ran a small experiment where I define a set of true ...
3
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56 views

Is this problem Bayesian? And can I use variational approximation?

Suppose there are $N$ samples of observations $\mathbf X(n)$ ($n=1,\cdots,N$), which are given by probability distribution $p(\mathbf X(n)|\mathbf Z(n))$ with their conditions are given by hidden ...
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62 views

Record Linkage Using Fellegi-Sunter Model

I am trying to create a record linkage system using the fellegi-sunter model.I am following this paper http://digital.library.okstate.edu/etd/SHIN_okstate_0664M_10668.pdf. I am not understanding ...
5
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1answer
85 views

Hidden Markov Models with multiple emissions per state

I want to use Hidden Markov Models for an unsupervised sequence tagging problem. Due to the peculiarities of my application domain (recognition of dialogue acts in conversations), I would like to use ...
0
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1answer
42 views

Mixing probabilities in mixture models using EM

Assume we want to estimate the mixing probabilities ($\pi_{k}$) for each member distribution in the mixture model. We know that $\sum_{m}^{K}\pi_{m}=1$, so we can formulate the optimization problem ...
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11 views

unbiased sampling of expecation over maximization operator

My problem setting is as follows, I have a set of M random variable X = \{ {X_1},{X_2},...{X_M}\} where each variable X_i is estimated via stochastic sequence ...
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23 views

Expectation Maximization (EM) Method - All Constructs or One Construct at a time?

I want to ask whether I can run Expectation Maximization (EM) method in SPSS to replace ALL missing values of ALL constructs at one run, or I have to do for each construct separately? Thank you
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1answer
60 views

MAP estimate of posterior parameters

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
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1answer
137 views

EM for Mixtures of Bernoulli (M-step)

When applying the M-step for a mixture of Bernoulli distributions, one of the parameters in our maximization is the Bernoulli parameter $\mu_{k}$, where $k$ is the index of the "mixture component", ...
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168 views

Expectation Maximization, dice example, always converging in second iteration

I am simulating two loaded dice and trying to estimate individual die prior probabilities and probability mass functions for each of them using the EM algorithm. Below is my Matlab code. Likelihood ...
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30 views

High dimensional model estimation with outliers

I have a set H of k m-dimensional hyperplanes in n dimensional space, where ...
0
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1answer
37 views

non-EM algorithm approach to mixture model?

I have a mixture model and the components are further parameterized by ~200 variables. Originally I use EM-algorithm to get a MLE estimation of the parameters. The algorithm works quite well and ...
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52 views

How to separate distributions from weighted dataset?

I’m trying to separate two component distributions of an apparent finite mixture from a weighted dataset (determined by a weighted.histogram). I've a set of data and weights only for a part of the ...
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147 views

How to normalize bimodal (or multimodal) distributions?

If I have multiple data series, a = [a1, a2, ... a100] ~ bimodal with mu_a1, mu_a2, sigma_a1, sigma_a2, b = [b1, b2, ... b100] ~ bimodal with mu_b1, mu_b2, sigma_b1, sigma_b2, c = [c1, c2, ... ...
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37 views

How to treat “Missing Value Analysis” test results (problems)

I have a problem with Missing Value Analysis. I am using SPSS version 20. I am trying to test whether missing values are at complete random. As I know in order to ensure missing values are completely ...
6
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1answer
119 views

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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22 views

A framework for comparing the performance of Expectation Maximization

I have my own implementation of the Expectation Maximization (EM) algorithm based on the following paper http://pdf.aminer.org/000/221/588/fuzzy_k_means_clustering_with_crisp_regions.pdf I would like ...
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60 views

Estimation parameters for latent (unobserved) variable

Here is my problem: I have 3 variables $X,Y,Z$ : $X$ is the number of clicks we observed on an web advertisement; $Y$ is the number of time a customer do a sign-up on the website after clicking ...
4
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1answer
127 views

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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1answer
72 views

Relation between Gaussian mixture models and maximum likelihood?

I need some help understanding the relation between the maximum likelihood and Gaussian mixture models. I have seen that there is a relationship between the expectation maximization algorithms and ...
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33 views

Expectation maximization with variant length at observing data

Imagine one loaded dice. Based on EM algorithm, how could we compute how much it loaded if we introduced: Variant length on each rolling attempt (look at first and second attempt below 1st one has 6 ...
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31 views

Principled approach for PCA on correlated variables?

Related to Should one remove highly correlated variables before doing PCA?, PCA is used a lot in population genetics to essentially cluster individuals into ethnic group based on their genetic markers ...