Related papers: Theoretical properties of the eigenvector method

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…

This paper consists of a few results, discovered and proved during the 2012-2013 research group at Eastern Oregon University. Inertia tables are a visual representation of the possible inertias of a given graph. The inertia of a graph…

Fair ranking problems arise in many decision-making processes that often necessitate a trade-off between accuracy and fairness. Many existing studies have proposed correction methods such as adding fairness constraints to a ranking model's…

We focus on the one-to-one two-sided matching model with two disjoint sets of agents of equal size, where each agent in a set has preferences on the agents in the other set modeled by a linear order. A matching mechanism associates a set of…

Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the…

The paper provides important insights into understanding the factors that influence tie strength in social networks. Using local network measures that take into account asymmetry of social interactions we show that the observed tie strength…

Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…

Recommendation algorithms typically build models based on historical user-item interactions (e.g., clicks, likes, or ratings) to provide a personalized ranked list of items. These interactions are often distributed unevenly over different…

A key to causal inference with observational data is achieving balance in predictive features associated with each treatment type. Recent literature has explored representation learning to achieve this goal. In this work, we discuss the…

In models using pair-wise (ratio) comparisons among alternatives, a cardinal ranking vector should be deduced from a reciprocal matrix. The right Perron eigenvector (RP) was traditionally used, though several other options have emerged. We…

This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is…

The comparison of different medical treatments from observational studies or across different clinical studies is often biased by confounding factors such as systematic differences in patient demographics or in the inclusion criteria for…

We consider the problem of evaluating preferences for criteria used by university students when selecting a hotel for accommodation during a professional development program in a foreign country. Input data for analysis come from a survey…

In deriving large n probability distribution function of the rightmost eigenvalue from the classical Random Matrix Theory Ensembles, one is faced with que question of finding large n asymptotic of certain coupled set of functions. This…

A yet unmet challenge in algorithmic fairness is the problem of intersectionality, that is, achieving fairness across the intersection of multiple groups -- and verifying that such fairness has been attained. Because intersectional groups…

A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is…

We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenvalue result is well known to a broad…

A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…

Pairwise ranking models have been widely used to address recommendation problems. The basic idea is to learn the rank of users' preferred items through separating items into \emph{positive} samples if user-item interactions exist, and…

Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…