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Hierarchical classification tackles the multi-class classification problem by dividing the output space i.e. into a tree. Each parent node is divided into multiple child nodes and the process is continued until each child node represents only one class. Several methods have been proposed based on hierarchical classification.
In statistics and machine learning, the hierarchical Dirichlet process (HDP) is a nonparametric Bayesian approach to clustering grouped data. [ 1 ] [ 2 ] It uses a Dirichlet process for each group of data, with the Dirichlet processes for all groups sharing a base distribution which is itself drawn from a Dirichlet process.
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 ().
Another way to analyze hierarchical data would be through a random-coefficients model. This model assumes that each group has a different regression model—with its own intercept and slope. [ 5 ] Because groups are sampled, the model assumes that the intercepts and slopes are also randomly sampled from a population of group intercepts and slopes.
The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM. HHMMs and HMMs are useful in many fields, including pattern recognition. [1] [2]
Bayesian model averaging (BMA) makes predictions by averaging the predictions of models weighted by their posterior probabilities given the data. [22] BMA is known to generally give better answers than a single model, obtained, e.g., via stepwise regression , especially where very different models have nearly identical performance in the ...
Hierarchical mixtures of experts [7] [8] uses multiple levels of gating in a tree. Each gating is a probability distribution over the next level of gatings, and the ...