Learning the Gain Values and Discount Factors of DCG
  Evaluation metrics are an essential part of a ranking system, and in the past many evaluation metrics have been proposed in information retrieval and Web search. Discounted Cumulated Gains (DCG) has emerged as one of the evaluation metrics widely adopted for evaluating the performance of ranking functions used in Web search. However, the two sets of parameters, gain values and discount factors, used in DCG are determined in a rather ad-hoc way. In this paper we first show that DCG is generally not coherent, meaning that comparing the performance of ranking functions using DCG very much depends on the particular gain values and discount factors used. We then propose a novel methodology that can learn the gain values and discount factors from user preferences over rankings. Numerical simulations illustrate the effectiveness of our proposed methods. Please contact the authors for the full version of this work. 
Ke Zhou, Hongyuan Zha, Gui-Rong Xue and Yong Yu
cs.IR