use words to specify the EM framework

The Expectation-Maximization (EM) algorithm is a statistical technique used for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. It is particularly useful for dealing with data that is missing or unobserved.

Here is a step-by-step explanation of the EM framework:

1. Initialization: Choose initial values for the parameters. This can be done randomly or based on some informed guess.

2. Expectation (E) Step: Given the current parameters, estimate the probability distribution of the latent variables. This is also known as the "E-step". The goal here is to compute the expected value of the log-likelihood function, with respect to the conditional distribution of the latent variables given the observed data and current parameter estimates.

3. Maximization (M) Step: Update the parameters to maximize the expected log-likelihood found on the E step. This is also known as the "M-step". The parameters are updated in a way that maximizes the expectation computed in the E-step.

4. Check for Convergence: Evaluate the log-likelihood and check if it has converged, i.e., if the increase in the log-likelihood is smaller than a small positive constant. If it has not converged, return to step 2.

5. Termination: The algorithm stops when the log-likelihood converges, or after a fixed number of iterations.

The EM algorithm guarantees that the log-likelihood will increase with each iteration, making it a popular method for maximum likelihood estimation. However, it only finds a local maximum rather than a global maximum, and the final estimates can be sensitive to the choice of initial values.