An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Convergence and Error Bounds for Universal Prediction of Nonbinary Sequences
EMCL '01 Proceedings of the 12th European Conference on Machine Learning
The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
Algorithmic Theories of Everything
Algorithmic Theories of Everything
Optimality of universal Bayesian sequence prediction for general loss and alphabet
The Journal of Machine Learning Research
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Convergence and loss bounds for Bayesian sequence prediction
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Algorithmic complexity bounds on future prediction errors
Information and Computation
Algorithmic randomness and monotone complexity on product space
Information and Computation
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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 μ by the algorithmic complexity of μ. Here we assume we are at a time t1 and already observed x=x1...xt. We bound the future prediction performance on xt+1xt+2... by a new variant of algorithmic complexity of μ 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.