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Why does expectation Maximisation em converge to a local optimum?
EM is not guaranteed to converge to a local minimum. It is only guaranteed to converge to a point with zero gradient with respect to the parameters. So it can indeed get stuck at saddle points. First of all, it is possible that EM converges to a local min, a local max, or a saddle point of the likelihood function.
What is Expectation-Maximization used for?
The Expectation-Maximization (EM) algorithm is a way to find maximum-likelihood estimates for model parameters when your data is incomplete, has missing data points, or has unobserved (hidden) latent variables. It is an iterative way to approximate the maximum likelihood function.
What is meant by expectation-maximization?
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.
Why is em a local optimization?
Various constraints can be made on the parameters of the mixture model. The EM algorithm guarantees convergence to a solution which is locally optimal, meaning it is optimal given the initial parameter estimates, but may not be globally optimal, i.e., the best likelihood possible.
Will expectation maximization always converge?
EM is not guaranteed to converge to a local minimum. It is only guaranteed to converge to a point with zero gradient with respect to the parameters. So it can indeed get stuck at saddle points.
How is the expectation maximization algorithm used in statistics?
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.
When to use ordered subset expectation maximization ( EM )?
The EM algorithm (and its faster variant ordered subset expectation maximization) is also widely used in medical image reconstruction, especially in positron emission tomography, single-photon emission computed tomography, and x-ray computed tomography. See below for other faster variants of EM.
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.
Which is the maximization step in the EM iteration?
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.