论文标题
cramér-rao类型限制贝叶斯风险，而布雷格曼损失
A Cramér-Rao Type Bound for Bayesian Risk with Bregman Loss
论文作者
论文摘要
当证明了基础损失函数是布雷格曼分歧时，贝叶斯下限的一般类别。该类可以被视为温斯坦的扩展 - 均方误差的威斯界家族，依赖于寻找贝叶斯风险的变异表征。该方法允许推导特定于给定的Bregman Divergence的Cramér-rao结合的版本。当将损失函数视为欧几里得规范时，cramér-rao结合的新概括将减少到经典的概括。在泊松噪声设置和二项式噪声设置中评估了新结合的有效性。
A general class of Bayesian lower bounds when the underlying loss function is a Bregman divergence is demonstrated. This class can be considered as an extension of the Weinstein--Weiss family of bounds for the mean squared error and relies on finding a variational characterization of Bayesian risk. The approach allows for the derivation of a version of the Cramér--Rao bound that is specific to a given Bregman divergence. The new generalization of the Cramér--Rao bound reduces to the classical one when the loss function is taken to be the Euclidean norm. The effectiveness of the new bound is evaluated in the Poisson noise setting and the Binomial noise setting.
