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. [1]

Feb 4, 2025 · The Expectation-Maximization (EM) algorithm is an iterative method used in unsupervised machine learning to estimate unknown parameters in statistical models. It helps find the best values for unknown parameters, especially when some data is missing or hidden.

We will focus on the Expectation Maximization (EM) algorithm. Y , y observations. Y = random variable; y = realization of Y . X, x complete data. Z, z, missing data. Note that X = (Y , Z). f(y|θ) is the distribution of Y given θ. tth estimate of the θ in the EM iteration.

To apply the EM algorithm, we will start with some initial guesses (k= 0) for the parameters: b(k) = (pb(k) 1;pb (k) 2;:::;pb (k) N; b(k) 1; b(k) 2;:::; b(k) N): Then, we compute f(y ijx i; b(k)) = f(x ijy i; b(k)) f(y ij b(k)) f(x i j b(k)) = p(k) y i f y(x ij b y(k) i) P N j=1 pb (k) j f j(xj(k)) for y i= 1;2;:::;N. The EM algorithm \Q ...

Feb 7, 2019 · The Expectation-Maximization algorithm (or EM, for short) is probably one of the most influential and widely used machine learning algorithms in the field. When I first came to learn about...

ically rigorous understanding of EM and why it works. We explain the standard applications of EM to learning Gaussian mixture models (GMMs) and hidden Markov model. (HMMs), and prepare you to apply EM to new problems. This tutorial assumes you have an advanced unde. timator of a parameter of a pr.

try to maximize l( ; x) over directly using standard non-linear optimization algorithms. . owever, in this example we will perform the optimization instead using the EM algorithm. To do this we assume that the complete. r, instead of obs. rving y we only observe (y1 + y2; y3; y4; . y5 . common application of the EM algorithm is to estimate the.

Aug 28, 2020 · The Expectation-Maximization Algorithm, or EM algorithm for short, is an approach for maximum likelihood estimation in the presence of latent variables. A general technique for finding maximum likelihood estimators in latent variable models is the expectation-maximization (EM) algorithm.

At an intermediate level, EM for any mixture model involves an E-step that computes degrees of mem-bership, and an M-step that does weighted maximum likelihood; this level is the topic of Section 3 below. More abstractly, EM is an iterative method for maximiz-ing likelihood; this level is explained in Section 1.

The expectation-maximization algorithm is an iterative method for nding the maximum likelihood estimate for a latent variable model. It consists of iterating between two steps (\Expectation step" and \Maximization step", or \E-step" and \M-step" for short) until convergence. Both steps involve maximizing a lower bound on the likelihood.