Related papers: Using tropical optimization techniques to evaluate…
We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is arXiv:1509.07453, where a tropical-algebraic correspondence theorem…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…
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…
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
We propose a multi-criteria Composite Index Method (CIM) to compare the performance of alternative approaches to solving an optimization problem. The CIM is convenient in those situations when neither approach dominates the other when…
Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…
Recommender systems can be formulated as a matrix completion problem, predicting ratings from user and item parameter vectors. Optimizing these parameters by subsampling data becomes difficult as the number of users and items grows. We…
Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based…
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…
Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…