论文标题
缺乏相关性压缩功能的凸度
The Lack of Convexity of the Relevance-Compression Function
论文作者
论文摘要
在本文中，我们研究了信息瓶颈的相关性压缩函数的凸度和信息失真问题。这条曲线是速率延伸曲线的类似物，即凸。在本文中讨论的问题中，失真函数不是量化器的线性函数，相关压缩函数不一定是凸（凹），而是可以更改其凸度。我们将这种现象与相应的拉格朗日中存在的一阶相变为退火参数的函数。
In this paper we investigate the convexity of the relevance-compression function for the Information Bottleneck and the Information Distortion problems. This curve is an analog of the rate-distortion curve, which is convex. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer, and the relevance-compression function is not necessarily convex (concave), but can change its convexity. We relate this phenomena with existence of first order phase transitions in the corresponding Lagrangian as a function of the annealing parameter.
