Related papers: Mallows permutation models with $L^1$ and $L^2$ di…
Introduced by Mallows in statistical ranking theory, Mallows permutation model is a class of non-uniform probability measures on the symmetric group $S_n$ that depend on a distance metric $d(\sigma,\tau)$ on $S_n$ and a scale parameter…
Introduced by Mallows as a ranking model in statistics, Mallows permutation model is a class of non-uniform probability distributions on the symmetric group $S_n$. The model depends on a distance metric on $S_n$ and a scale parameter…
The Mallows model occupies a central role in parametric modelling of ranking data to learn preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice…
\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows,…
In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we…
The Mallows measure is measure on permutations which was introduced by Mallows in connection with ranking problems in statistics. Under this measure, the probability of a permutation $\pi$ is proportional to $q^{Inv(\pi)}$ where $q$ is a…
Many applications motivate the distance measure between rankings, such as comparing top-k lists and rank aggregation for voting, and intrigue great interest to researchers. For example, for a search engine, the use of different ranking…
BayesMallows is an R package for analyzing data in the form of rankings or preferences with the Mallows rank model, and its finite mixture extension, in a Bayesian probabilistic framework. The Mallows model is a well-known model, grounded…
We study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the Mallows measure. Under this measure, the probability of a permutation pi in S_n is proportional to q^{inv(pi)} where q…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
We study the lengths of monotone subsequences for permutations drawn from the Mallows measure. The Mallows measure was introduced by Mallows in connection with ranking problems in statistics. Under this measure, the probability of a…
In this paper, we develop the metric geometry of ranking statistics, proving that the two major permutation distances in the statistics literature -- Kendall tau and Spearman footrule -- extend naturally to incomplete rankings with both…
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we…
We use various combinatorial and probabilistic techniques to study growth rates for the probability that a random permutation from the Mallows distribution avoids consecutive patterns. The Mallows distribution behaves like a $q$-analogue of…
The Mallows measure on the symmetric group $S_n$ is the probability measure such that each permutation has probability proportional to $q$ raised to the power of the number of inversions, where $q$ is a positive parameter and the number of…
Asymptotics of the normalizing constant is computed for a class of one parameter exponential families on permutations which includes Mallows model with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE, and a…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…
This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this…