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Bayesian probability; Bayes' theorem ... that is often claimed to be part of Bayesian statistics is the maximum a ... of an expectation-maximization algorithm. This ...
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. [1]
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model , the observed data is most probable.
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let be a discrete hidden random variable with possible values (i.e. We assume there are states in total).
where p(r | x) denotes the conditional joint probability density function of the observed series {r(t)} given that the underlying series has the values {x(t)}. In contrast, the related method of maximum a posteriori estimation is formally the application of the maximum a posteriori (MAP) estimation approach.
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).
The following algorithm using that relaxation is an expected (1-1/e)-approximation: [10] Solve the linear program L and obtain a solution O; Set variable x to be true with probability y x where y x is the value given in O. This algorithm can also be derandomized using the method of conditional probabilities.