The information bottleneck method

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dc.creatorTishby, Naftali
dc.creatorPereira, Fernando C.
dc.creatorBialek, William
dc.date2000-04-24
dc.date.accessioned2026-07-07T05:44:02Z
dc.date.available2026-07-07T05:44:02Z
dc.descriptionWe define the relevant information in a signal $x\in X$ as being the information that this signal provides about another signal $y\in \Y$. Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. Understanding the signal $x$ requires more than just predicting $y$, it also requires specifying which features of $\X$ play a role in the prediction. We formalize this problem as that of finding a short code for $\X$ that preserves the maximum information about $\Y$. That is, we squeeze the information that $\X$ provides about $\Y$ through a `bottleneck' formed by a limited set of codewords $\tX$. This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure $d(x,\x)$ emerges from the joint statistics of $\X$ and $\Y$. This approach yields an exact set of self consistent equations for the coding rules $X \to \tX$ and $\tX \to \Y$. Solutions to these equations can be found by a convergent re-estimation method that generalizes the Blahut-Arimoto algorithm. Our variational principle provides a surprisingly rich framework for discussing a variety of problems in signal processing and learning, as will be described in detail elsewhere.
dc.identifierhttps://arxiv.org/abs/physics/0004057
dc.identifierhttp://arxiv.org/abs/physics/0004057
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/83480
dc.subjectData Analysis, Statistics and Probability
dc.subjectDisordered Systems and Neural Networks
dc.subjectMachine Learning
dc.subjectAdaptation and Self-Organizing Systems
dc.titleThe information bottleneck method
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