General linear relations among different types of predictive complexity

Abstract

In this paper we introduce a general method that allows to prove tight linear inequalities between different types of predictive complexity and thus we generalise our previous results. The method relies upon probabilistic considerations and allows to describe (using geometrical terms) the sets of coefficients which correspond to true inequalities. We also apply this method to the square-loss and logarithmic complexity and describe their relations which were not covered by our previous research.