@MISC{Donoho02thekolmogorov, author = {David L. Donoho}, title = {The Kolmogorov sampler}, year = {2002} }

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Abstract

iid 2 Given noisy observations Xi = θi + Zi, i =1,...,n, with noise Zi ∼ N(0,σ), we wish to recover the signal θ with small mean-squared error. We consider the Minimum Kolmogorov Complexity Estimator (MKCE), defined roughly as the n-vector ˆ θ(X) solving the problem min Y K(Y) subject to �X − Y �2 l 2 n ≤ σ2 · n, where K(Y) denotes the length of the shortest computer program that can compute the finite-precision n-vector Y.Inwords, this is the simplest object that fits the data to within the lack-of-fit between θ and X that would be expected on statistical grounds. Suppose that the θi are successive samples from a stationary ergodic process obeying