What is EM optimization?

What is EM optimization?

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 relationship between EM and alternating minimization?

The EM algorithm is an alternating minimization algorithm that iterates be- tween finding a greatest lower bound to the log-likelihood function and maxi- mizing this bound. The EM algorithm converges when the observed and hidden variable joint density form a convex set over the allowable parameters.

How to find the estimator of log likelihood?

The estimator is obtained by solving that is, by finding the parameter that maximizes the log-likelihood of the observed sample . This is the same as maximizing the likelihood function because the natural logarithm is a strictly increasing function. One may wonder why the log of the likelihood function is taken.

Can an EM algorithm converge to a maximum likelihood estimator?

Although an EM iteration does increase the observed data (i.e., marginal) likelihood function, no guarantee exists that the sequence converges to a maximum likelihood estimator. For multimodal distributions, this means that an EM algorithm may converge to a local maximum of the observed data likelihood function,…

Which is the first derivative of the log likelihood function?

The first derivative of the log-likelihood function is called Fisher’s score function, and is denoted by u(θ) = ∂logL(θ;y) ∂θ. (A.7) Note that the score is a vector of first partial derivatives, one for each element of θ. If the log-likelihood is concave, one can find the maximum likelihood

How is the likelihood function related to the parametric family?

In turn, given a sample and a parametric family of distributions (i.e., a set of distributions indexed by a parameter) that could have generated the sample, the likelihood is a function that associates to each parameter the probability (or probability density) of observing the given sample.