On Bayes Risk Lower Bounds

Understand

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions.

• A lower bound on the Bayes risk not only serves as a lower bound on the minimax risk, but also characterizes the fundamental limit of any estimator given the prior knowledge.
• Our bounds are based on the notion of $f$-informativity, which is a function of the underlying class of probability measures and the prior.
• Application of our bounds requires upper bounds on the $f$-informativity, thus we derive new upper bounds on $f$-informativity which often lead to tight Bayes risk lower bounds.