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The maximum likelihood estimator selects the parameter value which gives the observed data the largest possible probability (or probability density, in the continuous case). If the parameter consists of a number of components, then we define their separate maximum likelihood estimators, as the corresponding component of the MLE of the complete ...
Thus, the α-EM algorithm by Yasuo Matsuyama is an exact generalization of the log-EM algorithm. No computation of gradient or Hessian matrix is needed. The α-EM shows faster convergence than the log-EM algorithm by choosing an appropriate α. The α-EM algorithm leads to a faster version of the Hidden Markov model estimation algorithm α-HMM ...
One algorithm takes ( /) rounds with high probability on any graph (directed or undirected), where n is the network size and is the reset probability (, which is called the damping factor) used in the PageRank computation.
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.
For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. [8]
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.
Group size measures; ... Maximum entropy probability distribution; Maximum entropy spectral estimation; ... Nested sampling algorithm; Network probability matrix;
The density of the maximum entropy distribution for this class is constant on each of the intervals [a j-1,a j). The uniform distribution on the finite set {x 1,...,x n} (which assigns a probability of 1/n to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set.