Related papers: Rating alternatives from pairwise comparisons by s…
Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance…
The remarkable success of Artificial Intelligence in advancing automated decision-making is evident both in academia and industry. Within the plethora of applications, ranking systems hold significant importance in various domains. This…
In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the…
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…
We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
We produce new combinatorial methods for approaching the tropical maximal rank conjecture, including inductive procedures for deducing new cases of the conjecture on graphs of increasing genus from any given case. Using explicit…
Audio signal processing algorithms are frequently assessed through subjective listening tests in which participants directly score degraded signals on a unidimensional numerical scale. However, this approach is susceptible to…
We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
The main mathematical focus of this paper is a class of parametrised polynomial systems that we refer to as being tropically transverse. We show how their generic number of solutions can be expressed as the mixed volume of a modified…