The Volume of Bitnets
2004; American Institute of Physics; Linguagem: Inglês
10.1063/1.1835256
ISSN1935-0465
Autores Tópico(s)Data Management and Algorithms
ResumoA bitnet is a dag of binary nodes representing a manifold of probability distributions for a sequence of binary variables. Bitnets are riemannian manifolds of finite volume when Fisher information is used as the metric. I compute the exact volumes for several interesting topologies including the complete graph, the directed line of n nodes, the exploding star (naive bayes) and its reverse, the collapsing star. I show a fast algorithm for approximating the volumes of general bitnets. Computer experiments show that the average Ricci scalar of bitnets is always half an integer. Typically bitnets have singular boundaries obtained when some of the conditional probabilities for the binary variables are either zero or one. At the singular points the Ricci scalar becomes negative infinity.
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