Why EM algorithm is required to optimize a Gaussian mixture model?

Why EM algorithm is required to optimize a Gaussian mixture model?

One benefit of EM is that it naturally produces valid parameters for the mixture distribution on every iteration. In contrast, standard optimization algorithms would need constraints to be imposed. For example, say you’re fitting a Gaussian mixture model.

What is expectation and maximization step in EM algorithm?

The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step.

Why can’t we just use the maximum likelihood approach for a mixture of Gaussians model?

A way to find the maximum likelihood estimate is to set the partial derivatives of the log-likelihood with respect to the parameters to 0 and solve the equations. As you can see, this approach is impractical because the sum over the Gaussian components appears inside the log making all the parameters tied together.

How does Gaussian mixture model works?

Gaussian Mixture Models (GMMs) assume that there are a certain number of Gaussian distributions, and each of these distributions represent a cluster. Hence, a Gaussian Mixture Model tends to group the data points belonging to a single distribution together.

What is the purpose of Gaussian mixture model?

Gaussian Mixture models are used for representing Normally Distributed subpopulations within an overall population. The advantage of Mixture models is that they do not require which subpopulation a data point belongs to. It allows the model to learn the subpopulations automatically.

How is Gaussian mixture model and expectation maximization algorithm used?

2.Gaussian Mixture Model (GMM) and Expectation-Maximization(EM) Algorithm 2.1 GMM For a complex data set in the real-world, it normally consists of a mixture of multiple stochastic processes. Therefore a single Gaussian distribution cannot fit such data set.

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

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. The EM algorithm is just more generally and formally defined (as it can be applied to many other optimization problems).

Is the MLE of GMMs done using Expectation maximization?

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.

Which is the best algorithm for Gaussian parameter estimation?

To estimate K set of Gaussian parameters directly and explicitly is difficult. The EM algorithm simplifies the likelihood function of GMM, and provides an iterative way to optimize the estimation.Here we try to briefly describe the EM algorithm for GMM parameter estimation.