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Krichevsky–Trofimov estimator

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In information theory, given an unknown stationary source π with alphabet A and a sample w from π, the Krichevsky–Trofimov (KT) estimator produces an estimate pi(w) of the probability of each symbol i ∈ A. This estimator is optimal in the sense that it minimizes the worst-case regret asymptotically.

For a binary alphabet and a string w with m zeroes and n ones, the KT estimator pi(w) is defined as:[1]

This corresponds to the posterior mean of a Beta-Bernoulli posterior distribution with prior . For the general case the estimate is made using a Dirichlet-Categorical distribution.

See also

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References

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  1. ^ Krichevsky, R. E.; Trofimov, V. K. (1981). "The Performance of Universal Encoding". IEEE Trans. Inf. Theory. IT-27 (2): 199–207. doi:10.1109/TIT.1981.1056331.