Questions tagged [expectation-maximization]

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

473 questions
Filter by
Sorted by
Tagged with
1answer
13 views

In expectation maximization, why do we have a latent variable distribution for every sample of the data

I am reading this blog on expectation maximization - http://krasserm.github.io/2019/11/21/latent-variable-models-part-1/ Starting the section where the author starts explaining how EM is done in the ...
0answers
69 views
+250

Does EM algorithm require us to know the joint (predictive) distribution of the latent variables $Z$ when $Z$ is two-dimensional?

In its general form the E-step of the EM algorithm finds the expectation $$Q(\theta|\theta') =\int \log[ p(Y,Z | \theta)] p(Z|Y,\theta') d Z$$ where $Y$ the data, $Z$ the latent variables, $\theta'$...
1answer
131 views

ELBO maximization with SGD

In cases such as Gaussian mixture models, there's is no closed-term solution for the original likelihood maximization. Maximizing the ELBO, however, does have analytical update formulas (i.e. formulas ...
0answers
29 views

Compound distribution

I'm trying to compute a maximum likelihood of compound Poisson exponential distribution in R by using EM-algorithm method. The distribution is defined by $∑N_j=1 Y_j$ where $Y_n$ is i.i.d sequence ...
2answers
65 views

interpretation of the estimated parameters of a gaussian mixture model

I need to find/fit a model for the color of an object. Suppose its color is generally yellow and we have 10000-by-3 data which are pixel values for R, G, B channels. Firstly I choose a Multivariate ...
1answer
17 views

Gaussian Mixture model - Penalized log-likelihood in EM algorithm not monotone increasing

I am working on a multivariate Gaussian Mixture Model in R. The goal is to do regularized clustering on the data, where each component represents a cluster. I wrote an EM algorithm to maximize a ...
0answers
17 views

How to calculate weights in EM-algorithm?

Assume that we have 2 clusters with some initial model: Can you please explain how weights are calculated?
3answers
533 views

GMM EM algorithm complexity per iteration

I was fitting GMM clusters with diagonal covariance on my data using EM with $n$ (=5e6) points, each having $m$ (=160) ...
1answer
219 views

The ways to normalize the likelihood in EM algorithm

In Wikepedia it states that: In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. And ...
0answers
31 views

assessing the stability of importance (sampling) weights

I have read that when importance weights are used, the stability (variability) of the weights should be assessed (Levine and Casella, 2001) -- however, I wonder how this might be accomplished. For ...
1answer
11 views

Fitting mixture model on data with duplicate values

What is the correct procedure to fit finite mixture models on data with many duplicate values using EM? Let's say I have N(0,1) distributed data and try to fit a 2 component mixture using EM. There ...
0answers
20 views

Confusion in Sampling using the IP algorithm (Bishop PRML)

I'm reading Bishop's PRML p. 537 and I don't understand one piece of the IP (data augmentation) algorithm. Namely, the part that says "we use the samples $\{\mathbf{Z}^{(l)}\}$ obtained in the I step ...
0answers
26 views

Expectation Maximisation vs Expectation Propagation in the context of Bayesian Networks

I am confused about Expectation Maximisation and Expectation Propagation algorithms in the context of Bayesian Networks, especially whether one comprise another. What is the difference between ...
0answers
14 views

Newton-Raphson method to solve for dof when performing MLE of a multivariate Student-t distribution using EM

I am reading the derivation of EM algorithm to estimate the maximum likelihood of a multivariate Student-t distribution $\mathcal{T}(\mathbf{x} \vert \pmb{\mu}, \pmb{\Sigma}, \nu)$ in Kevin Murphy's ...
1answer
243 views

EM Derivation for Dawid-Skene Model

I am trying to derive the EM update equations for the Dawid-Skene model. Following the notation in Bayesian Classifier Combination by Kim and Ghahramani, $i$ is the index of the data point, $t_i$ is ...
0answers
42 views

Why Expectation and Maximization algorithm not used in Machine Learning while Gradient Descent algorithm used in Machine Learning?

I know that Newton Raphson, Expectation & Maximization, and Gradient Descent are all known to be optimization methods. Somehow, I wonder why Gradient Descent is chosen to be used in most of ...
0answers
18 views

Do I impute missing values with the response?

I have a dataset with missing values in both predictors and the response. As far as I know, the data are missing not at random, so I cannot simply use listwise deletion. Instead, I employed the EM ...
2answers
4k views

Simple Explanation of Baum Welch/Viterbi

I'm looking for a very simple explanation as possible for Baum Welch and Viterbi for HMMs with a straightforward well annotated example. Almost all of the explanations I find on the net invariably ...
0answers
18 views

Can someone verify if the following Bayesian Information Criterion (BIC) model selection algorithm is correct for Gaussian mixture models?

I am trying to find an automated way of picking the number of clusters $K \in \mathbb{N}$ for unsupervised learning scenarios, specifically for GMM. I was suggested to use something called the "...
0answers
39 views

Expectation Maximisation (EM) Algorithm

Some of my parameters do not have a closed form solution. Thus, for these parameters the M-step is implemented via a one-step Newton-Raphson update, i.e., \theta^{t+1} = \theta^t - \...
0answers
12 views

Outlier detection with EM

I am interested in using expectation maximization for outlier detection. In the literature this is usually done assuming that the data of interest are normally distributed while the outliers are ...
0answers
12 views

Using expectation maximization for robust regression

What are the advantages/disadvantages of using EM for robust estimation vs. the robust estimation with Huber or Tukey loss functions?
2answers
49 views

EM-algorithm for two clusters (when one of the distributions is uniform)

I am having a hard time with the EM-algorithm. Here's the problem that I am trying to solve. Dealing with noisy annotations is a common problem in computer vision, especially when using ...
2answers
77 views

Accounting for uncertain information (few observations) in a prior (empirial Bayes)

I did not really know how to choose an adequate title for this question, so please feel free to change it. I have a weird case wherein frequentist and Bayesian philosophies come together. I am ...
0answers
8 views

Consistency of EM for missing data in non-parametric setting

When we have missing data, a parametric model, and an expectation-maximization procedure, and we want to show that our procedure leads to consistent estimators, we can sometimes set up score functions ...
1answer
38 views

Calculation of AIC in finite mixture modeling

I have a question about calculation the AIC to find my optimal amount of clusters. I am applying mixture modeling with the EM algorithm. I know the formula AIC = -2ln(log-lik) + 2k. These are my log-...
0answers
13 views

Analysing faithful dataset in R using GMM

I have got a project on analysing the faithful data in R found in the package "datasets" and called using data(faithful) which is the data set off eruption time and waiting time of the Old Faithful ...
1answer
187 views

0answers
14 views

Convergence of Modified Expectation-Maximisation Algorithm - interpreting language of question

We're going to consider a modified E-M algorithm and its convergence properties. To do so, we will first need to review the convergence of the standard E-M algorithm as I'll need to refer back to it. ...