Related papers: On the similarity between ranking vectors in the p…
Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure…
The Graham-Diaconis inequality shows the equivalence between two well-known methods of measuring the similarity of two given ranked lists of items: Spearman's footrule and Kendall's tau. The original inequality assumes unweighted items in…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a general and more realistic setup. Specifically, the comparison graph…
Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national…
This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian…
An overview of current debates and contemporary research devoted to the modeling of decision making processes and their facilitation directs attention to the Analytic Hierarchy Process (AHP). At the core of the AHP are various…
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…
Multileaved comparison methods generalize interleaved comparison methods to provide a scalable approach for comparing ranking systems based on regular user interactions. Such methods enable the increasingly rapid research and development of…
For $J \ge 2$ independent groups, the paper deals with testing the global hypothesis that all $J$ groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes…
In the paper the maximum and the minimum of the ratio of the difference of the arithmetic mean and the geometric mean, and the difference of the power mean and the geometric mean of $n$ variables, are studied. A new optimization argument…
Learning to rank is an effective recommendation approach since its introduction around 2010. Famous algorithms such as Bayesian Personalized Ranking and Collaborative Less is More Filtering have left deep impact in both academia and…
In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's…
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…
We compare three popular techniques of rating content: the ubiquitous five star rating, the less used pairwise comparison, and the recently introduced (in crowdsourcing) magnitude estimation approach. Each system has specific advantages and…
We consider the problem of ranking objects from noisy pairwise comparisons, for example, ranking tennis players from the outcomes of matches. We follow a standard approach to this problem and assume that each object has an unobserved…
We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…
We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain…
In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…