Related papers: Pairwise Comparisons Simplified
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of $k$ cycles of given lengths has a very simple formula: it is $n^{k-1}$ where $n$ is the rank of the underlying symmetric group…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…
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…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
This is an improved version of the talk of the author given at the Antalya Algebra Days VII on May 21, 2005. We present an introduction to the theory of the invariants under the action of GL(n,C) by simultaneous conjugation of d matrices of…
We construct a short presentation of the ring of n x n matrices over Z with only 2 generators and 3 relations.
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary.…
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
Given a number of pairwise preferences of items, a common task is to rank all the items. Examples include pairwise movie ratings, New Yorker cartoon caption contests, and many other consumer preferences tasks. What these settings have in…
The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…
The graphical representation of the correlation matrix by means of different multivariate statistical methods is reviewed, a comparison of the different procedures is presented with the use of an example data set, and an improved…
Efficient vectors are the natural set from which to choose a cardinal ranking vector for a pairwise comparison matrix. Such vectors are the key to certain business project selection models. Many ways to construct specific efficient vectors…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…