Name
Abstract | ||
|---|---|---|
We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our methods refine rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semi-graphoids. Submodular rank tests are classified by the faces of the cone of submodular functions, or by Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Graphical tests correspond to both graphical models and to graph associahedra, and they have excellent statistical and algorithmic properties. |
Year | Venue | Keywords |
|---|---|---|
2006 | Probabilistic Graphical Models | partially ordered set,linear extension,symmetric group,conditional independence,ordinal data,non parametric statistics,statistical test,graphical model |
Field | DocType | Citations |
Discrete mathematics,Combinatorics,Ordinal data,Permutation,Permutohedron,Submodular set function,Equivalence class,Graphical model,Partially ordered set,Mathematics,Sign test | Conference | 2 |
PageRank | References | Authors |
0.92 | 3 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jason Morton | 1 | 20 | 5.42 |
| Lior Pachter | 2 | 1026 | 121.08 |
| Anne Shiu | 3 | 87 | 14.47 |
| Bernd Sturmfels | 4 | 926 | 136.85 |
| Oliver Wienand | 5 | 30 | 4.69 |