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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
Model-based clustering [1] based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not ...
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.
Fuzzy C-Means Clustering is a soft version of k-means, where each data point has a fuzzy degree of belonging to each cluster. Gaussian mixture models trained with expectation–maximization algorithm (EM algorithm) maintains probabilistic assignments to clusters, instead of deterministic assignments, and multivariate Gaussian distributions ...
A well-written short book on EM, including detailed derivation of EM for GMMs, HMMs, and Dirichlet. Bilmes, Jeff (1997). 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).
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.
Density of a mixture of three normal distributions (μ = 5, 10, 15, σ = 2) with equal weights.Each component is shown as a weighted density (each integrating to 1/3) Given a finite set of probability density functions p 1 (x), ..., p n (x), or corresponding cumulative distribution functions P 1 (x),..., P n (x) and weights w 1, ..., w n such that w i ≥ 0 and ∑w i = 1, the mixture ...