Search results
Results from the WOW.Com Content 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 ...
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.
Standard model-based clustering methods include more parsimonious models based on the eigenvalue decomposition of the covariance matrices, that provide a balance between overfitting and fidelity to the data. One prominent method is known as Gaussian mixture models (using the expectation-maximization algorithm).
A more general class of regression-based multi-fidelity methods are Bayesian approaches, e.g. Bayesian linear regression, [3] Gaussian mixture models, [10] [11] Gaussian processes, [12] auto-regressive Gaussian processes, [2] or Bayesian polynomial chaos expansions.
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. [1] The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the ...
Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model.. In, for example, a two-stage hierarchical Bayes model, observed data = {,, …,} are assumed to be generated from an unobserved set of parameters = {,, …,} according to a probability distribution ().
It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. [2] EM clustering of Old Faithful eruption data. The random initial model (which, due to the different scales of the axes, appears to be two very flat and wide ellipses) is fit to the observed data.