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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
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 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.
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)
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 ...
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 ...
Gaussian processes can also be used in the context of mixture of experts models, for example. [29] [30] The underlying rationale of such a learning framework consists in the assumption that a given mapping cannot be well captured by a single Gaussian process model. Instead, the observation space is divided into subsets, each of which is ...
ML; JMLR; Related articles ... Although this type of model was initially designed for unsupervised learning, [3] [4] ... is a mixture of Gaussian distributions. It is ...