Related papers: Commutative Algebra of Statistical Ranking
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Learning-to-rank (LTR) is a class of supervised learning techniques that apply to ranking problems dealing with a large number of features. The popularity and widespread application of LTR models in prioritizing information in a variety of…
We consider the problem of ranking $n$ experts according to their abilities, based on the correctness of their answers to $d$ questions. This is modeled by the so-called crowd-sourcing model, where the answer of expert $i$ on question $k$…
PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…
The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a…
We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…
Ranking lists are often provided at regular time intervals in a range of applications, including economics, sports, marketing, and politics. Most popular methods for rank-order data postulate a linear specification for the latent scores,…
We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum…
We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
The widely used Plackett-Luce ranking model assumes that individuals rank items by making repeated choices from a universe of items. But in many cases the universe is too big for people to plausibly consider all options. In the choice…
Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…
In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…