Related papers: Commutative Algebra of Statistical Ranking
Choice behavior and preferences typically involve numerous and subjective aspects that are difficult to be identified and quantified. For this reason, their exploration is frequently conducted through the collection of ordinal evidence in…
Ranking systems produce ordered lists from scalar scores, yet the ranking itself depends only on pairwise comparisons. We develop a mathematical theory that takes this observation seriously, centering the analysis on pairwise margins rather…
We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
We continue the study on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We…
Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…
We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…
In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…
Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…
We consider the problem of active coarse ranking, where the goal is to sort items according to their means into clusters of pre-specified sizes, by adaptively sampling from their reward distributions. This setting is useful in many social…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
There is an innate human tendency, one might call it the "league table mentality," to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
We reformulate explanation quality assessment as a ranking problem rather than a generation problem. Instead of optimizing models to produce a single "best" explanation token-by-token, we train reward models to discriminate among multiple…
Ranking data represent a peculiar form of multivariate ordinal data taking values in the set of permutations. Despite the numerous methodological contributions to increase the flexibility of ranked data modeling, the application of more…
The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…
We introduce the notion of a majority category --- the categorical counterpart of varieties of universal algebras admitting a majority term. This notion can be thought to capture properties of the category of lattices, in a way that…