Monotone Conditional Complexity Bounds on Future Prediction Errors

Details Monotone Conditional Complexity Bounds on Future Prediction Errors Monotone Conditional Complexity Bounds on Future Prediction Errors

2005-07-18

arxiv.org/abs/cs/0507041v1

Proc. 16th International Conf. on Algorithmic Learning Theory (ALT 2005) 414-428

Computer Science

Learning

16 LaTeX pages

Scientific paper

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 m by the algorithmic complexity of m. 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+1}x_{t+2}... by a new variant of algorithmic complexity of m 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.

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