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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
A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models (Technical Report TR-97-021). International Computer Science Institute. includes a simplified derivation of the EM equations for Gaussian Mixtures and Gaussian Mixture Hidden Markov Models.
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.
Types of generative models are: Gaussian mixture model (and other types of mixture model) Hidden Markov model; Probabilistic context-free grammar; Bayesian network (e.g. Naive bayes, Autoregressive model) Averaged one-dependence estimators; Latent Dirichlet allocation; Boltzmann machine (e.g. Restricted Boltzmann machine, Deep belief network)
Trump will probably make a show of eviscerating Biden’s climate plans while rebranding some of them as his own. Markets, in the end, may move in more or less the same direction.
A method better suited for multidimensional probability density functions (pdf) is to first make a pdf estimate with some method, and then, from the pdf estimate, compute the entropy. A useful pdf estimate method is e.g. Gaussian mixture modeling (GMM), where the expectation maximization (EM) algorithm is used to find an ML estimate of a ...