Loss Functions, Complexities, and the Legendre Transformation Authors: Yuri Kalnishkan, Michael V. Vyugin and Volodya Vovk . Source: Lecture Notes in Artificial Intelligence Vol. 2225, 2001, 181 - 189. Abstract. The paper introduces a way of re-constructing a loss function from predictive complexity. We show that a loss function and expectations of the corresponding predictive complexity w.r.t. the Bernoulli distribution are related through the Legendre transformation. It is shown that if two loss functions specify the same complexity then they are equivalent in a strong sense. ©Copyright 2001 Springer