# Tagged Questions

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

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### Does constrained EM algorithm work with bad initial inputs?

When trying to perform constrained optimization using EM algorithm, does EM work if the initial solution (x0) violates the constraints?
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### Finding a Scalable Approach to a modified coin-flip problem using MLE model

and thank you in advance for your help! I am interested in applying MLE to estimate parameters in a "modified" coin flip model, but have been having difficulties scaling the solution. The problem ...
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### mixed noise and gaussian

I have a large number of data sets. Each data set has something 200K data points lying in a square times a circle. The square is solid $I\times I$. The circle $S^1$ is hollow (dim 1). By reasoning ...
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### Training HMM for classifying a DNA region as telomeric or non-telomeric

This is the problem setting: I have a large set of strings (sequences of characters A,T,G,C) of length 100. These sequences are either from a telomeric region of a chromosome or non-telomeric. For ...
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### Learn a HMM with fixed emission probabilities constraint

Suppose we want to learn a HMM with the emission matrix is fixed. Can I use the Baum-Welch to estimate the transition probabilities $a_{ij}$ by skipping the $b_{ik}$ values update step at each ...
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### Baum-Welch algorithm variation for Hidden Markov model with reward

Following my previous question on the subject I would like to get your feedback on the following alternative solution. (The original solution to this question is the usage of the POMDP model proposed ...
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### Clustering groups of observations

I am having a situation where my data points consist of $r$ groups, that we want to force the observations within a group to be in the same cluster, with $n_r$ observations in each group. So the idea ...
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### Expectation Maximization Gaussian Mixture Example

I am a biologist trying to understand expectation maximization for a mixture of two Gaussian distributions. I think I understand how to deal with the means of the two distributions, but I don't know ...
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### Using the logLikelihood in the EM algorithm

I was obtaining parameter estimates via a EM like algorithm, but taking the expectation of the posterior distribution rather than the logPosterior distribution. I know that this now does not guarantee ...
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### Can expectation maximization be used to optimize a quadratic function? [duplicate]

My knowledge about Expectation Maximization (EM) is limited, from my understanding, EM is just an algorithm to do optimization. It works well when we have some hidden / latent variables, such as ...
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### How to identify parameters of distributions of a mixture when many samples are sum of the samples?

I have a list of values which are samples from 4 different normal distributions. The list also contains sum of two or three sample values. I would like to identify parameters of the distributions. An ...
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### Advantages and disadvantages of EM algorithm vs trust region methods for nonlinear optimization

I have a set of observations X that I believe were generated by a mixture of several probability distributions (specifically, two von mises and one uniform). I'd like to find the maximum likelihood ...
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### Soft Expectation Maximization + final hard assignments = Hard Expectation Maximization?

I am studying a given model $\mathcal{M}$ where the authors infer some parameters $\boldsymbol{\theta}$ that are common to all individuals in a population. The parameters are estimated by MLE, but ...
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### Expectation Maximization-Log Likehood interpretation

I am using EM algorithm in weka for genomic data, get the results in the images, but a don't know how interpret the log likehood index. Is better when is higher or lower, negative or positive. How ...
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### EM versus other methods of optimization

What are some good examples of likelihoods which are easily maximized by EM but not by other methods of optimization (e.g., gradient ascent) and vice versa?
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### Indirect solution for maximum entropy through sampling?

Is there a way to sample from a finite set $\{A,B,C,D\}$ such that the limiting empirical proportions converges to the maximum entropy solution of their probabilities consistent with known constraints?...
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### EM algorithm help - Plot of expectation

Can someone plot an expectation of a function and show me how maximizing it = maximizing the lower bound of its likelihood in the EM algorithm ? I don't know how to plot the expectation of a function ...
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### Interpreting Cluster Analysis from SAS Enterprise Miner

I am currently doing a text mining project and I conducted a clustering analysis in SAS enterprise miner. I am using the following settings: Anyway, The results look like this, showing me ...
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### Is it possible to see the slow decreasing in test negative-log-likelihood as overfitting?

We have developed a model for some real data and we use EM algorithm for optimization of the model (parameters). In first phase we generate synthetic data according to the model (with some known ...
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### Does the EM algorithm converge exactly where a grid search on the marginalized likelihood converges?

I have successfully implemented a grid search algorithm to estimate two parameters of a likelihood. I computed the likelihood $l(X;\theta)$ of observed data $X$ by integrating out the discrete ...
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### Iterative Maximization issue in Truncated Negative Binomial Regression in Stata

I was running truncated negative binomial regression in Stata and got a problem. During the iteration process, my results show " backed up" at the end of final iteration which means Stata could not ...
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### Cross validation or EM for selecting strength of the prior?

Often when I'm looking at bayesian analyses, the influence of the prior is chosen via cross validation. For example, suppose $X$ and $Y$ represent some real valued data that I want perform a bayesian ...
Assuming $A$ a set of vectors from a normal distribution, and $X$ a projection matrix and $B$ a set of projected vectors of $A$ using $X$: $B=A*X$ Using an EM approach and by initializing X from ...