Geometry of the Restricted Boltzmann Machine
By María Angélica Cueto, Jason Morton, Bernd Sturmfels. 2009
88 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computational Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/daea71d981d47455bbc500f1d922504e7e6e1c1d
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In Artificial Intelligence
In Computational Mathematics
In Computational Theory and Mathematics
- Paul Breiding
- Bernd Sturmfels
- Eric Katz
- Martyn Marshall
- Michael Joswig
- Jenia Tevelev
- Adam Van Tuyl
- Huy Tài Hà
Citations in the corpus
- Learning algebraic varieties from samples (2018, background): “For instance, the Lüroth hypersurface [4] in the space of ternary quartics has degree 54, and the restricted Boltzmann machine [17] on four binary random variables has degree 110.”