Information geometry on hierarchy of probability distributions

  title={Information geometry on hierarchy of probability distributions},
  author={Shun-ichi Amari},
  journal={IEEE Trans. Information Theory},
An exponential family or mixture family of probability distributions has a natural hierarchical structure. This paper gives an “orthogonal” decomposition of such a system based on information geometry. A typical example is the decomposition of stochastic dependency among a number of random variables. In general, they have a complex structure of dependencies. Pairwise dependency is easily represented by correlation, but it is more difficult to measure effects of pure triplewise or higher order… CONTINUE READING
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