Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications

Abstract : The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation Σ of a finite set, {1,. .. , n} with n ≥ 1 say. As it sheds light onto only one aspect of Σ's distribution P , it may neglect other informative features. It is the purpose of this paper to define analogues of quantiles, ranks and statistical procedures based on such quantities for the analysis of ranking data by means of a metric-based notion of depth function on the symmetric group. Overcoming the absence of vector space structure on S n , the latter defines a center-outward ordering of the permutations in the support of P and extends the classic metric-based formulation of consensus ranking (medians corresponding then to the deepest permutations). The axiomatic properties that ranking depths should ideally possess are listed, while computational and generalization issues are studied at length. Beyond the theoretical analysis carried out, the relevance of the novel concepts and methods introduced for a wide variety of statistical tasks are also supported by numerous numerical experiments.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03537148
Contributor : Morgane GOIBERT Connect in order to contact the contributor
Submitted on : Thursday, January 20, 2022 - 11:41:32 AM
Last modification on : Tuesday, February 15, 2022 - 3:38:20 AM
Long-term archiving on: : Thursday, April 21, 2022 - 6:48:41 PM

File

Depth_function_ranking_AISTATS...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03537148, version 1

Collections

Citation

Morgane Goibert, Stéphan Clémençon, Ekhine Irurozki, Pavlo Mozharovskyi. Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications. 25th International Conference on Artificial Intelligence and Statistics AISTATS 2022, Mar 2022, Valence, Spain. ⟨hal-03537148⟩

Share

Metrics

Record views

58

Files downloads

8