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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
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 ...
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.
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.
k-NN – Classification happens by locating the object in the feature space, and comparing it with the k nearest neighbors (training examples). The majority vote decides on the classification. GMM – is a probabilistic model used for representing the existence of subpopulations within the overall population. Each sub-population is described ...
To estimate parameters of a conditional moment model, the statistician can derive an expectation function (defining "moment conditions") and use the generalized method of moments (GMM). However, there are infinitely many moment conditions that can be generated from a single model; optimal instruments provide the most efficient moment conditions.
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.