The information bottleneck method is a technique introduced by Naftali Tishby et al. for finding the best tradeoff between accuracy and complexity (compression) when summarizing (e.g. clustering) a random variable X, given a joint probability distribution between X and an observed relevant variable Y. Other applications include distributional clustering, and dimension reduction. In a well defined sense it generalized the classical notion of minimal sufficient statistics from parametric statistics to arbitrary distributions, not necessarily of exponential form. It does so by relaxing the sufficiency condition to capture some fraction of the mutual information with the relevant variable Y.
The compressed variable is and the algorithm minimises the following quantity
where are the mutual information between and respectively.
Read more about Information Bottleneck Method: Gaussian Information Bottleneck, Defining Decision Contours, Bibliography
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