Related papers: Lorenz map, inequality ordering and curves based o…
Categories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…
This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
Unsupervised performance estimation, or evaluating how well models perform on unlabeled data is a difficult task. Recently, a method was proposed by Garg et al. [2022] which performs much better than previous methods. Their method relies on…
In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…
In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the…
In an environment where a manipulator needs to execute multiple consecutive tasks, the act of object manoeuvre will change the underlying configuration space, affecting all subsequent tasks. Previously free configurations might now be…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
In this article the Lorenz dynamical system is revived and revisited and the current state of the art results for one step ahead forecasting for the Lorenz trajectories are published. Multitask learning is shown to help learning the hard to…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…