Estimates of Parameters of GMM: The Expectation Maximization (EM) Algorithm We observe n data points x1,…,xn in Rd . We wish to maximize the GMM likelihood with respect to the parameter set θ={p1,…,pK,μ(1),…,μ(K),σ21,…,σ2K} . Maximizing the log-likelihood log(∏ni=1p(x(i)|θ)) is not tractable in the setting of GMMs. There is no closed-form solution to finding the parameter set θ that maximizes the likelihood. The EM algorithm is an iterative algorithm that finds a locally optimal solution θ^ to the GMM likelihood maximization problem.