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

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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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13 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 ...
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46 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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37 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 ...
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42 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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1answer
90 views

Unable to understand derivation of Expectation Maximizaton

In Paper, System Identification using Symbolic Chaotic Sequence, Authored by A. Kurian and H. Leung download link under section II B, can somebody please explain ...
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23 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 ...
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1answer
49 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 ...
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1answer
32 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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8 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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16 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
49 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
37 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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68 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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28 views

High dimensional model estimation with outliers

I have a set H of k m-dimensional hyperplanes in n dimensional space, where ...
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1answer
31 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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40 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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79 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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23 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 ...
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1answer
108 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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17 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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55 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 ...
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1answer
77 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
58 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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31 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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30 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 ...
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1answer
33 views

Gaussian clusters and original distributions

In Gaussian clustering (i.e. General Mixture Models) we model the data with some clusters. For example, in the below figure, we have two clusters $C_1, C_2$, each of which are modeled with a Gaussian ...
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30 views

EM Algorithm - Expectation w.r.t. a subset of current parameters

Suppose I want to make inference on a parameter vector $\theta $=$(\theta_{1},\theta_{2},\theta_{3})$ and I have some missing data $Y_{mis}$. I would like to use the EM algorithm to find the mode of ...
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49 views

Concavity of log likelihood for hidden markov models

Could you give me a good link where the concept of concavity of the log likelihood related to hidden markov model EM algorithm is clarified? Thank you in advance.
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27 views

What is delta in the maximization step in this EM algorithm?

The algorithm is used to classify english vs non-english tweets from unlabeled data. Given n observed tweets (x1 ... xn) where each tweet xi is a collection of d words (xi1 ... xid). y is the class ...
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30 views

peak detection - points / sigma ratio

I would like to ask you (statistics experts) if the following approach is kosher or a nonsense. Problem My EM based detection algorithm ends up (for some data) with a result that looks like attached ...
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1answer
66 views

Bayes' theorem in 1-d EM algorithm

I'm watching a video on the EM algorithm, When we use Bayes' Theorem to calculate $b_i$, how do I find $P(b)$ and $P(a)$ initially? It says we can estimate the priors $P(b)$ and $P(a)$ but that's ...
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110 views

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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1answer
54 views

EM algorithm decreases!

I have used the Bayes Net Toolbox to build a small network, which consists of 3 nodes and is shown below. Node 1 is a Bernoulli random variable, node 2 is a Gaussian random variable and node 3 is a ...
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1answer
45 views

Why Baum-Welch algorithm is an instantiation of EM algorithm?

$\newcommand{\E}{\mathrm{E}}$ I don't understand why Baum-Welch algorithm is an instantiation of EM algorithm. Indeed, why computing $\alpha_t(i)$ and $\beta_t(i)$ corresponds to Expectation step. ...
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24 views

Mode of Joint Posterior - Maximization Problems

I have a problem whereby I get two different answers if I try to maximize a function. let $ \begin{bmatrix} Y_{o}\\ Y_{a} \end{bmatrix}|\phi\sim N (0,\phi^{-1}A^{-1}) $ $\pi(\phi)=\frac{1}{\phi}$, ...
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135 views

Why is optimizing a mixture of Gaussian directly computationally hard?

Consider the log likelihood of a mixture of guassians: $$l(S_n; \theta) = \sum^n_{t=1}logP(x^{(t)}|\theta) = \sum^n_{t=1}log\sum^k_{i=1}p_iP(x^{(t)}|\mu^{(i)}, \sigma^2_i)$$ I was wondering why it ...
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19 views

Maximum likelihood hypothesis vs Expectation maximization

Maximum Likelihood is given by the formula $h_{ML}=arg\space max_{h \in H } \space\space p(D/h)$ I want to transform it in terms of mechanism involved in Expectation maximization. $h_{ML}=arg\space ...
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21 views

Possibilities of accelerating EM algortihm

I'm trying to use the EM to estimate some parameters. I've programmed and it delivers. The problem however is that for each run of my programme, it can take either 5 seconds, 1min, 3min or more to ...
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1answer
90 views

In EM derivation why can I sum over the iid variables in the conditional expectation?

In EM when you take the expectation: $E[\log P(y,x \mid \theta)\mid x, \theta']$ $= \sum\limits_yP(y\mid x, \theta') \log P(y,x\mid \theta)$ I understand this but the following part I don't ...
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57 views

Proper likelihood function in acceptance probability of Gibbs Sampler

I have a question about the acceptance ratio used when implementing a random walk M-H in a gibbs sampler to generate sample paths of an unobservable process. When computing the likelihood of a set of ...
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31 views

Simulating EM versus listwise deletion--unexpected results

I'm preparing a presentation on missing data strategies and conducted a simulation to compare listwise deletion (LD) to the EM. Here's what I expected based on the literature: Standard errors will ...
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1answer
51 views

Efficience of Expectation-Maximization algorithm in function of learning dataset size

I have datasets of increasing sizes identically distributed. I have tried to fit a gaussian mixture to these datasets using Expectation-Maximization algorithm. To check the quality of this fit, I ...
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57 views

Computing Standard Errors in EM algorithm

I'm applying the EM to a hidden markov chain (the $\mathbf{Z}=\{Z_1,...,Z_n\}$ variable), with observations(the $\mathbf{Y}=\{Y_0,...,Y_n\}$ variable) dependent not only on the hidden markov chain, ...
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62 views

Too good results from EM for gaussian mixture

My task is to identify parameters (mean, standard deviation, height) of gaussian peaks in given histogram data with as lowest CV as possible. Number of peaks and approximate means are known (pointed ...
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54 views

Learning Conditional Random Fields using EM Algorithm (from unaligned data)

I am trying to learn CRF from the unaligned data in Natural Language Understanding application. There is one paper in this field which does exactly the same, Learning conditional random fields from ...
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1answer
179 views

Estimating parameters for univariate skew t

How can I solve the MLE for the skew-t distribution via EM? I am comfortable with the EM methods for t, so could someone show it for the skew-t?
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1answer
133 views

t-distribution parameter estimation

I know there are already several threads on this, but none seem to explicitly cover what I want. I have a set of financial data (pulled straight from Bloomberg) and am trying to fit a t-distribution ...
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1answer
96 views

Variance of EM mean estimates in a simple mixture of two normals

Consider a mixture of two normal distributions: $ f(x) = p N(x|u_1, S_1) + (1-p) N(x|u_2, S_2) $ where N() is the normal pdf. $p$, $S_2$, and $S_2$ are known. The means are not. You can get the MLE ...
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1answer
91 views

Expectation maximization and Gaussian mixtures - bad results

I am supposed to find parameters of individual gaussians in a 1D mixture with a known number of components. I use my own implementation of EM algorithm; however, I am not able to find the right ...