The information bottleneck method

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The information bottleneck method (1999)

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by Naftali Tishby , Fernando C. Pereira , William Bialek

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@MISC{Tishby99theinformation,
    author = {Naftali Tishby and Fernando C. Pereira and William Bialek},
    title = {The information bottleneck method},
    year = {1999}
}

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Abstract

We define the relevant information in a signal x ∈ X as being the information that this signal provides about another signal y ∈ 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 ˜X. 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 → ˜ X and ˜ X → 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.

Keyphrases

information bottleneck method distortion measure short code rich framework joint statistic convergent re estimation method blahut arimoto algorithm relevant information coding rule variational principle self consistent equation limited set face image signal processing maximum information constrained optimization problem rate distortion theory exact set

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