# Information geometry on hierarchy of probability distributions

@article{Amari2001InformationGO, title={Information geometry on hierarchy of probability distributions}, author={S. Amari}, journal={IEEE Trans. Inf. Theory}, year={2001}, volume={47}, pages={1701-1711} }

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… Expand

#### 385 Citations

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Fields of Application of Information Geometry

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1.
Complexity measures can be geometrically built by using the information distance (Kullback–Leibler divergence) from families with restricted statistical dependencies. The Pythagorean geometry… Expand

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