Generalized Minimum Bayes Risk System Combination

Minimum Bayes Risk (MBR) has been used as a decision rule for both singlesystem decoding and system combination in machine translation. For system combination, we argue that common MBR implementations are actually not correct, since probabilities in the hypothesis space cannot be reliably estimated. These implementations achieve the effect of consensus decoding (which may be beneficial in its own right), but does not reduce Bayes Risk in the true Bayesian sense. We introduce Generalized MBR, which parameterizes the loss function in MBR and allows it to be optimized in the given hypothesis space of multiple systems. This extension better approximates the true Bayes Risk decision rule and empirically improves over MBR, even in cases where the combined systems are of mixed quality.