  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.
