Krichevsky–Trofimov estimator

In information theory, given an unknown stationary source with alphabet A and a sample w from , 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:

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

Rule of succession Bayesian inference using conjugate priors for the categorical distribution

References