Algorithmic Complexity Bounds on Future Prediction Errors

01/19/2007

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by   A. Chernov, et al.

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We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution mu by the algorithmic complexity of mu. Here we assume we are at a time t>1 and already observed x=x_1...x_t. We bound the future prediction performance on x_t+1x_t+2... by a new variant of algorithmic complexity of mu given x, plus the complexity of the randomness deficiency of x. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.