The Lack of Convexity of the Relevance-Compression Function

Albert E Parker; Tomas Gedeon; Alexander Dimitrov

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arXiv · 2204.10957

The Lack of Convexity of the Relevance-Compression Function

Albert E Parker·Tomas Gedeon·Alexander Dimitrov

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Abstract

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.

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Albert E Parker, Tomas Gedeon, Alexander Dimitrov. 2022-04-22. The Lack of Convexity of the Relevance-Compression Function. https://arxiv.org/abs/2204.10957

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