Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Non-stochastic infinite and finite sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
New error bounds for Solomonoff prediction
Journal of Computer and System Sciences
Calibration with many checking rules
Mathematics of Operations Research
Algorithmic complexity bounds on future prediction errors
Information and Computation
IEEE Transactions on Information Theory
Complexity-based induction systems: Comparisons and convergence theorems
IEEE Transactions on Information Theory
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It has been recently shown that calibration with an error less than @D0 is almost surely guaranteed with a randomized forecasting algorithm, where forecasts are obtained by random rounding the deterministic forecasts up to @D. We show that this error cannot be improved for a vast majority of sequences: we prove that, using a probabilistic algorithm, we can effectively generate with probability close to one a sequence ''resistant'' to any randomized rounding forecasting with an error much smaller than @D. We also reformulate this result by means of a probabilistic game.