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The Viterbi algorithm is named after Andrew Viterbi, who proposed it in 1967 as a decoding algorithm for convolutional codes over noisy digital communication links. [2] It has, however, a history of multiple invention, with at least seven independent discoveries, including those by Viterbi, Needleman and Wunsch, and Wagner and Fischer. [3]
In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. [2] It is used in inductive inference theory and analyses of algorithms.
Any random graph model (at a fixed set of parameter values) results in a probability distribution on graphs, and those that are maximum entropy within the considered class of distributions have the special property of being maximally unbiased null models for network inference [2] (e.g. biological network inference).
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.
It starts from an assumption about a probabilistic distribution of the set of all possible inputs. This assumption is then used to design an efficient algorithm or to derive the complexity of a known algorithm. This approach is not the same as that of probabilistic algorithms, but the two may be combined.
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.
Thus the sampling distribution of the quantile of the sample maximum is the graph x 1/k from 0 to 1: the p-th to q-th quantile of the sample maximum m are the interval [p 1/k N, q 1/k N]. Inverting this yields the corresponding confidence interval for the population maximum of [m/q 1/k, m/p 1/k].
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).