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[0908.4425] Geometry of the restricted Boltzmann machine
"The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the first secant variety of the Segre variety of projective lines. We derive a dimension formula for the tropicalized model, and we use it to show that the restricted Boltzmann machine is identifiable in many cases. Our methods include coding theory and geometry of linear threshold functions."
I’ve Made a HUGIN Mistake « Quantum of Wantum
A sketch of a graphical models tutorial; pointers to papers.
Probabilistic Graphical Models - The MIT Press
D. Koller and N. Friedman's book. Amazingly, at US$ 95,00 it is still one of the more affordable books on this subject (compare price and number of pages with Lauritzen's or Wainwright and Jordan's)
http://www.stanford.edu/~montanar/BOOK/book.html
It should be an introduction to a rich and rapidly evolving research field at the interface between statistical physics, theretical computer science/discrete mathematics, and coding/information theory. It should be accessible to graduate students an researchers without specific training in any of these three fields.
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