2010/07/14 by Sergey M. Plis, Sergey Plis, Plis, Sergey M. +4 · 1 citation
Computer Science · Mathematics · Medicine · #Bayesian Methods and Mixture Models #Data-Driven Disease Surveillance #FOS: Computer and information sciences #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference #stat.ML
paper · pdf · doi:10.48550/arxiv.1007.2450
arxiv created 2010/07/14 · openalex publication_date 2010/07/14 · arxiv updated 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (n!). It makes the direct definition of a multinomial distribution over permutation space impractical for all but a very small n. In this work we propose an embedding of all n! permutations for a given n in a surface of a hypersphere defined in \mathbbmR(n-1)2. As a result of the embedding, we acquire ability to define continuous distributions over a hypersphere with all the benefits of directional statistics. We provide polynomial time projections between the continuous hypersphere representation and the n!-element permutation space. The framework provides a way to use continuous directional probability densities and the methods developed thereof for establishing densities over permutations. As a demonstration of the benefits of the framework we derive an inference procedure for a state-space model over permutations. We demonstrate the approach with applications.