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Jump to navigation Jump to search Not to be confused with mixed model. In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. However, not all inference procedures involve such steps. Mixture models should not be confused with models for compositional data, i. However, compositional models can be thought of as mixture models, where members of the population are sampled at random. A set of K mixture weights, which are probabilities that sum to 1. A set of K parameters, each specifying the parameter of the corresponding mixture component.
In many cases, each “parameter” is actually a set of parameters. For example, if the mixture components are Gaussian distributions, there will be a mean and variance for each component. In addition, in a Bayesian setting, the mixture weights and parameters will themselves be random variables, and prior distributions will be placed over the variables. This characterization uses F and H to describe arbitrary distributions over observations and parameters, respectively. Typically H will be the conjugate prior of F. A vector of Bernoulli-distributed values, corresponding, e.
Non-Bayesian Gaussian mixture model using plate notation. The indication means a vector of size K. Bayesian Gaussian mixture model using plate notation. Animation of the clustering process for one-dimensional data using a Bayesian Gaussian mixture model where normal distributions are drawn from a Dirichlet process. The histograms of the clusters are shown in different colours. During the parameter estimation process, new clusters are created and grow on the data. The legend shows the cluster colours and the number of datapoints assigned to each cluster.
Although EM-based parameter updates are well-established, providing the initial estimates for these parameters is currently an area of active research. Note that this formulation yields a closed-form solution to the complete posterior distribution. Such distributions are useful for assuming patch-wise shapes of images and clusters, for example. 20 components are needed to accurately model a given image distribution or cluster of data. Non-Bayesian categorical mixture model using plate notation.