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Probability maps are additive and normalised maps taking values in the unit interval of a lattice ordered Abelian group. They appear in theory of affine representations and they are also a semantic counterpart of Hajek's probability logic.…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure…
In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
We propose a new model for aggregating preferences over a set of indivisible items based on a quantile value. In this model, each agent is endowed with a specific quantile, and the value of a given bundle is defined by the corresponding…
In the growing field of Shared Micromobility Systems, which holds great potential for shaping urban transportation, fairness-oriented approaches remain largely unexplored. This work addresses such a gap by investigating the balance between…
Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation properties of INNs have also been established recently.…
The vast majority of US public school districts use school attendance boundaries to determine which student addresses are assigned to which schools. Existing work shows how redrawing boundaries can be a powerful policy lever for increasing…
In the inverse problem in particle physics, given an unexpected observation, one aims to identify a unique choice from amongst several competing hypotheses. We explore a novel approach of applying self-organizing maps to the inverse problem…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
This paper focuses on the estimation of the concentration curve of a finite population, when data are collected according to a complex sampling design with different inclusion probabilities. A (design-based) Hajek type estimator for the…
Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
This article presents a set of tools for the modeling of a spatial allocation problem in a large geographic market and gives examples of applications. In our settings, the market is described by a network that maps the cost of travel…
Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of nonlinear functions of finite population totals - such as ratios, correlation coefficients or measures of income…
Ranking systems produce ordered lists from scalar scores, yet the ranking itself depends only on pairwise comparisons. We develop a mathematical theory that takes this observation seriously, centering the analysis on pairwise margins rather…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…
We introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics, bipartite entanglement, and quantum coherence. In particular, we show…
We propose a novel rank aggregation method based on converting permutations into their corresponding Lehmer codes or other subdiagonal images. Lehmer codes, also known as inversion vectors, are vector representations of permutations in…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…