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Open AccessFeature PaperArticle

Nonlinear Information Bottleneck

Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Department of Aeronautics & Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Complexity Science Hub, 1080 Vienna, Austria
Center for Bio-social Complex Systems, Arizona State University, Tempe, AZ 85281, USA
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1181;
Received: 16 October 2019 / Revised: 27 November 2019 / Accepted: 28 November 2019 / Published: 30 November 2019
(This article belongs to the Special Issue Information–Theoretic Approaches to Computational Intelligence)
Information bottleneck (IB) is a technique for extracting information in one random variable X that is relevant for predicting another random variable Y. IB works by encoding X in a compressed “bottleneck” random variable M from which Y can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete X and Y with small state spaces, and continuous X and Y with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a method for performing IB on arbitrarily-distributed discrete and/or continuous X and Y, while allowing for nonlinear encoding and decoding maps. Our approach relies on a novel non-parametric upper bound for mutual information. We describe how to implement our method using neural networks. We then show that it achieves better performance than the recently-proposed “variational IB” method on several real-world datasets.
Keywords: information bottleneck; mutual information; representation learning; neural networks information bottleneck; mutual information; representation learning; neural networks
MDPI and ACS Style

Kolchinsky, A.; Tracey, B.D.; Wolpert, D.H. Nonlinear Information Bottleneck. Entropy 2019, 21, 1181.

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