Related papers: Theoretical properties of the eigenvector method
We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements,…
Learning from implicit user feedback is challenging as we can only observe positive samples but never access negative ones. Most conventional methods cope with this issue by adopting a pairwise ranking approach with negative sampling.…
Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic…
Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An…
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…
How can one meaningfully make a measurement, if the meter does not conform to any standard and its scale expands or shrinks depending on what is measured? In the present work it is argued that current evaluation practices for…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
This paper provides a theoretical analysis of a new learning problem for recommender systems where users provide feedback by comparing pairs of items instead of rating them individually. We assume that comparisons stem from latent user and…
Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to…
Economic choices are often stochastic: the same person may make a different choice when facing the same alternatives repeatedly. Standard models assume that the degree of randomness reflects the size of utility differences, but choice…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…
Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web…
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…
The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a large number of nodes…
An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of…
For research to go in the right direction, it is essential to be able to compare and quantify performance of different algorithms focused on the same problem. Choosing a suitable evaluation metric requires deep understanding of the pursued…
In this article, we propose two quantitative methods for calculating weight vectors for incomplete pairwise comparison matrices using reference values. Both procedures are extensions of arithmetic and geometric heuristic estimation (HRE)…
For arrays of identical linear systems coupled through relative actuation four problems are studied: controllability, positive controllability, pairwise controllability, and positive pairwise controllability. To this end, related to the…