Commutative algebra of statistical ranking

DOI10.1016/j.jalgebra.2012.03.028zbMath1316.13042arXiv1101.1597OpenAlexW2962856509MaRDI QIDQ1931695

Volkmar Welker, Bernd Sturmfels

Publication date: 15 January 2013

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1597

zbMATH Keywords

polytopetoric ringstatistical ranking

Mathematics Subject Classification ID

Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

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Polytope volume by descent in the face lattice and applications in social choice, Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs, Algebraic properties of classes of path ideals of posets, Size-biased permutation of a finite sequence with independent and identically distributed terms, Markov degree of the Birkhoff model, The power of pyramid decomposition in Normaliz, Toric algebra of hypergraphs, A survey of discrete methods in (algebraic) statistics for networks, Multigraded commutative algebra of graph decompositions, Learning algebraic varieties from samples, Unnamed Item

Uses Software

• Normaliz
• 4ti2

Cites Work

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• Linear extension sums as valuations on cones
• On L-decomposability of random orderings
• Parametrizations of toric varieties over any field
• Lectures on algebraic statistics
• Normal polytopes arising from finite graphs
• Toric ideals generalized by quadratic binomials
• Proof of a conjecture of Chan, Robbins, and Yuen
• Algebraic algorithms for sampling from conditional distributions
• MM algorithms for generalized Bradley-Terry models.
• Decomposing sets of inversions
• Evolution on distributive lattices
• Markov bases for noncommutative Fourier analysis of ranked data
• Toric fiber products
• On the toric algebra of graphical models
• Sysygies of unimodular Lawrence ideals
• Spectra of Symmetrized Shuffling Operators
• The asymptotic volume of the Birkhoff polytope
• Algebraic statistics for a directed random graph model with reciprocation
• Facets of the linear ordering polytope
• On the Volume of a Certain Polytope
• 0, 1/2‐Cuts and the Linear Ordering Problem: Surfaces That Define Facets
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes
• Algebraic Statistics for Computational Biology