Sage-Tips

Is expectation maximization maximum likelihood?

The expectation-maximization algorithm is an approach for performing maximum likelihood estimation in the presence of latent variables. It does this by first estimating the values for the latent variables, then optimizing the model, then repeating these two steps until convergence.

What is the advantage of expectation step?

It can be used to fill the missing data in a sample. It can be used as the basis of unsupervised learning of clusters. It can be used for the purpose of estimating the parameters of Hidden Markov Model (HMM). It can be used for discovering the values of latent variables.

What is maximum likelihood estimation in machine learning?

Maximum Likelihood Estimation (MLE) is a frequentist approach for estimating the parameters of a model given some observed data. The general approach for using MLE is: Observe some data. Set the parameters of our model to values which maximize the likelihood of the parameters given the data.

Why do we use maximum likelihood estimation?

MLE is the technique which helps us in determining the parameters of the distribution that best describe the given data. These values are a good representation of the given data but may not best describe the population. We can use MLE in order to get more robust parameter estimates.

What is the significance of the term maximum likelihood?

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.

What is expectation maximization in statistics?

From Wikipedia, the free encyclopedia In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables.

Is the MLE of GMMs done using Expectation-maximization algorithms?

The MLE of GMMs is not done using those methods for a number of reasons that I will explain. But I leave that for the end of the article because I want to get to the most relevant materials first. The MLE of GMMs is done using the expectation-maximization algorithm.

What is Gaussian mixture model in statistics?

Gaussian Mixture Model This model is a soft probabilistic clustering model that allows us to describe the membership of points to a set of clusters using a mixture of Gaussian densities. It is a soft classification (in contrast to a hard one) because it assigns probabilities of belonging to a specific class instead of a definitive choice.

Is the expectation-maximization algorithm the same as the EM algorithm?

As you can see, as soon as we reach step 4 we are already at the best possible fit. The Expectation-Maximization algorithm is performed exactly the same way. In fact, the optimization procedure we describe above for GMMs is a specific implementation of the EM algorithm.