How is expectation maximization used in data science?

How is expectation maximization used in data science?

Expectation Maximization (EM) is a classic algorithm developed in the 60s and 70s with diverse applications. It can be used as an unsupervised clustering algorithm and extends to NLP applications like Latent Dirichlet Allocation ¹, the Baum–Welch algorithm for Hidden Markov Models, and medical imaging.

How is the expectation maximization algorithm used in regression?

The expectation-maximization (EM) algorithm is an elegant algorithmic tool to maximize the likelihood (evidence) function for problems with latent/hidden variables. We will state the problem in a general formulation, and then we will apply it to different tasks, including regression.

Which is the first term in expectation maximization?

The first term on the left is the probability of observing the data and a specified latent variable assignment. The first term on the right hand side is the probability of the specified assignment of the latent variables given the observed data. The last term is the probability of observing the data.

How does the expectation maximization algorithm ( Saem ) work?

SAEM (as well as other EM-type algorithms) performs maximum likelihood estimation without any approximation of the statistical model. Near-“optimal” statistical properties (consistency and minimum variance of the estimate) are expected with SAEM.

How is expectation maximization in k-means clustering?

( Maximization) Update the parameters for each cluster (weighted mean location and variance-covariance matrix) based on the points in the cluster (weighted by their probability assigned in the first step). Note that unlike in k-means clustering, our model is generative: it purports to tell us the process by which the data was generated.

How are latent variables used in unsupervised learning?

This is the basis of unsupervised learning. If you think of an image (ex. human face) as the observed variable x then, the latent variable z could encode the features of the face (which are not seen during training), like it can encode whether the face is happy or sad, male or female etc. LVMs can also help us to deal with missing data.

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.

How to calculate the expectation maximizatio ( EM ) algorithm?

By taking derivatives with respect to ( w, μ, Σ) respectively and solving (remember to use Lagrange multipliers for the constraint that ∑ j = 1 k w j = 1 ), we get

Is there a closed form of expectation maximizatio?

There is no closed form for maximizing the parameters of this log-likelihood, and it is hard to maximize directly. Suppose we augment with the latent variable z that indicates which of the k Gaussians our observation y came from. The derivation of the E and M steps are the same as for the toy example, only with more algebra.

How is expectation maximization used in structural engineering?

In structural engineering, the Structural Identification using Expectation Maximization (STRIDE) algorithm is an output-only method for identifying natural vibration properties of a structural system using sensor data (see Operational Modal Analysis ). EM is also used for data clustering.