On Iterative Algorithms with an Information Geometry Background

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Several extremum problems in Statistics and Artificial Intelligence, e.g., likelihood maximization, are often solved by iterative algorithms such as iterative scaling or the EM algorithm, admitting an intuitive “geometric” interpretatation as iterated projections in the sense of Kullback information divergence. Such iterative algorithms, including those using Bregman rather than Kullback divergences, will be surveyed. It will be hinted to that the celebrated belief propagation (or sum-product) algorithm may also admit a similar interpretation.