论文标题
复合信息瓶颈前景
The Compound Information Bottleneck Outlook
论文作者
论文摘要
我们制定和分析复合信息瓶颈编程。在此问题中，Markov链$ \ MATHSF {X} \ MATHSF {Y} \ RIGHTARROW \ MATHSF {Z} $是使用固定的边缘分布$ \ Mathsf {p} _ {p} _ {以及$ \ mathsf {x} $和$ \ mathsf {z} $之间的共同信息，以最大程度地提高$ \ mathsf {z} $的条件概率，从给定类别中，在\ textit contectit {fore textit {the Textit copeion { $（\ Mathsf {x}，\ Mathsf {y}）$来自其他类。我们考虑了基于以下极端的几个类：相互信息；最小相关性；总变异；和相对熵类。我们为此问题的特定实例提供值，边界和各种特征：二进制对称情况，标量高斯情况，矢量高斯病例和对称模量添加的情况。最后，对于一般情况，我们提出了一种类型的交替迭代算法，以找到对此问题的一致解决方案。
We formulate and analyze the compound information bottleneck programming. In this problem, a Markov chain $ \mathsf{X} \rightarrow \mathsf{Y} \rightarrow \mathsf{Z} $ is assumed with fixed marginal distributions $\mathsf{P}_{\mathsf{X}}$ and $\mathsf{P}_{\mathsf{Y}}$, and the mutual information between $ \mathsf{X} $ and $ \mathsf{Z} $ is sought to be maximized over the choice of conditional probability of $\mathsf{Z}$ given $\mathsf{Y}$ from a given class, under the \textit{worst choice} of the joint probability of the pair $(\mathsf{X},\mathsf{Y})$ from a different class. We consider several classes based on extremes of: mutual information; minimal correlation; total variation; and the relative entropy class. We provide values, bounds, and various characterizations for specific instances of this problem: the binary symmetric case, the scalar Gaussian case, the vector Gaussian case and the symmetric modulo-additive case. Finally, for the general case, we propose a Blahut-Arimoto type of alternating iterations algorithm to find a consistent solution to this problem.
