Related papers: Commutative Algebra of Statistical Ranking
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general…
The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple model of computation in which states of computations are…
Plackett-Luce gradient estimation enables the optimization of stochastic ranking models within feasible time constraints through sampling techniques. Unfortunately, the computational complexity of existing methods does not scale well with…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructing a quiver with potential. The rank of the cluster algebra…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…
Categorical responses arise naturally within various scientific disciplines. In many circumstances, there is no predetermined order for the response categories, and the response has to be modeled as nominal. In this study, we regard the…
Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all…
Convex rank tests are 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. Each class consists of the…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Proportional ranking rules aggregate approval-style preferences of agents into a collective ranking such that groups of agents with similar preferences are adequately represented. Motivated by the application of live Q&A platforms, where…