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The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: . N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
For example, one of the solutions that may be found by EM in a mixture model involves setting one of the components to have zero variance and the mean parameter for the same component to be equal to one of the data points. The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function ...
Copula, for the definition of the Gaussian or normal copula model. Multivariate t-distribution , which is another widely used spherically symmetric multivariate distribution. Multivariate stable distribution extension of the multivariate normal distribution, when the index (exponent in the characteristic function) is between zero and two.
Histograms for one-dimensional datapoints belonging to clusters detected by an infinite Gaussian mixture model. During the parameter estimation based on Gibbs sampling , new clusters are created and grow on the data. The legend shows the cluster colours and the number of datapoints assigned to each cluster.
Subspace Gaussian mixture model (SGMM) is an acoustic modeling approach in which all phonetic states share a common Gaussian mixture model structure, and the means and mixture weights vary in a subspace of the total parameter space.
In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.