Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Introduction to algorithms
COLT '90 Proceedings of the third annual workshop on Computational learning theory
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Journal of the ACM (JACM)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
A game of prediction with expert advice
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Tight worst-case loss bounds for predicting with expert advice
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
Genral Linear Relations among Different Types of Predictive Complexity
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
On complexity of easy predictable sequences
Information and Computation
Predictive Complexity and Information
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
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Predictive complexity is a generalization of Kolmogorov complexity. It corresponds to an "optimal" prediction strategy which gives a lower bound to ability of any algorithm to predict elements of a sequence of outcomes. A variety of types of loss functions makes it interesting to study relations between corresponding predictive complexities. Non-linear inequalities (with variable coefficients) between predictive complexity KG(x) of non-logarithmic type and Kolmogorov complexity K(x) (which is close to predictive complexity for logarithmic loss function) are the main subject of consideration in this paper. We deduce from these inequalities an asymptotic relation sup K(x)/KG(x) ~ 1/a log n, x:l(x)=n when n驴驴, where a is a constant and l(x) is the length of a sequence x. An analogous asymptotic result holds for relative complexities K(x)/l(x) and KG(x)/l(x). To obtain these inequalities we present estimates of the cardinality of all sequences of given predictive complexity.