论文标题
通过马尔可夫关系提取独特的信息
Extracting Unique Information Through Markov Relations
论文作者
论文摘要
我们提出了两项新的措施，以$ x $提取独特信息，而不是$ y $，当时$ x，y $和$ m $是带有给定联合分布的联合随机变量时。我们采用基于马尔可夫的方法，这是由公平机器学习中的问题激励的，并受到了基于马尔可夫的优化问题的启发，这些问题已在信息瓶颈和常见信息框架中使用。我们在高斯案例中（即$ x，y $和$ m $是共同的高斯人）中的定义完全表征。我们还研究了我们的定义与部分信息分解（PID）框架的一致性，并表明这些基于马尔可夫的定义在PID框架内实现了非负性，但不是对称性的。
We propose two new measures for extracting the unique information in $X$ and not $Y$ about a message $M$, when $X, Y$ and $M$ are joint random variables with a given joint distribution. We take a Markov based approach, motivated by questions in fair machine learning, and inspired by similar Markov-based optimization problems that have been used in the Information Bottleneck and Common Information frameworks. We obtain a complete characterization of our definitions in the Gaussian case (namely, when $X, Y$ and $M$ are jointly Gaussian), under the assumption of Gaussian optimality. We also examine the consistency of our definitions with the partial information decomposition (PID) framework, and show that these Markov based definitions achieve non-negativity, but not symmetry, within the PID framework.
