Commutative Algebra of Statistical Ranking

@article{Sturmfels2011CommutativeAO,
  title={Commutative Algebra of Statistical Ranking},
  author={Bernd Sturmfels and Volkmar Welker},
  journal={CoRR},
  year={2011},
  volume={abs/1101.1597}
}
A model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are parameterized by rational function in the model parameters, so they define algebraic varieties. We study these varieties from the perspective of combinatorial commutative algebra. One of our models, the Plackett-Luce model, is non-toric. Five others are toric… CONTINUE READING