A new notion of predictive complexity and corresponding amount of information are considered. Predictive complexity is a generalization of Kolmogorov complexity which bounds the ability of any algorithm to predict elements of a sequence of outcomes. We consider predictive complexity for a wide class of bounded loss functions which are ... more >>>

Predictive complexity is a generalization of Kolmogorov complexity 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 between predictive complexity of non-logarithmic ... more >>>