论文标题
信息处理平等和信息风险桥梁
Information Processing Equalities and the Information-Risk Bridge
论文作者
论文摘要
我们为统计实验介绍了两种新的信息衡量标准，它们将$ ϕ $ -Diverences，积分概率指标，$ \ mathfrak {n} $ distances（mmd）和$（f，γ）$ divergences之间的两个或更多分布之间的$ ϕ $ -Diverence，积分概率指标，$ \ Mathfrak {n} $ distances（n} $ distances（mmathfrak {n} $）。这使我们能够在信息的度量与统计决策问题的贝叶斯风险之间得出简单的几何关系，从而将变异$ ϕ $ - 差异表示以完全对称的方式将多个分布扩展到多个分布。在马尔可夫运营商的行动下，新的分歧家庭被关闭，该家族产生了信息处理平等，这是经典数据处理不平等的改进和概括。这种平等使人深入了解假设类别在经典风险最小化中的重要性。
We introduce two new classes of measures of information for statistical experiments which generalise and subsume $ϕ$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,Γ)$ divergences between two or more distributions. This enables us to derive a simple geometrical relationship between measures of information and the Bayes risk of a statistical decision problem, thus extending the variational $ϕ$-divergence representation to multiple distributions in an entirely symmetric manner. The new families of divergence are closed under the action of Markov operators which yields an information processing equality which is a refinement and generalisation of the classical data processing inequality. This equality gives insight into the significance of the choice of the hypothesis class in classical risk minimization.
