A candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter , the role of the \textit{additive duality} of nonadditive statistics () in relating Tsallis entropies for ranges of the nonadditivity parameter and is described. Defining , , and to be the source alphabet, the compressed reproduction alphabet, and, the \textit{relevance variable} respectively, it is demonstrated that minimization of a generalized IB Lagrangian defined in terms of the nonadditivity parameter self-consistently yields the \textit{nonadditive effective distortion measure} to be the \textit{-deformed} generalized Kullback-Leibler divergence: . This result is achieved without enforcing any \textit{a-priori} assumptions. Finally, it is proven that the nonadditive free energy of the system in space is non-negative and convex. These results generalize critical features of the IB method to the case of Tsallis statistics.
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