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Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
This paper proposes a general framework for inference on three types of almost dominances: almost Lorenz dominance, almost inverse stochastic dominance, and almost stochastic dominance. We first generalize almost Lorenz dominance to almost…
Now that machine learning algorithms lie at the center of many resource allocation pipelines, computer scientists have been unwittingly cast as partial social planners. Given this state of affairs, important questions follow. What is the…
The problem of optimizing social welfare objectives on multi sided ride hailing platforms such as Uber, Lyft, etc., is challenging, due to misalignment of objectives between drivers, passengers, and the platform itself. An ideal solution…
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend…
Effective mixed traffic control requires balancing efficiency, fairness, and safety. Existing approaches excel at optimizing efficiency and enforcing safety constraints but lack mechanisms to ensure equitable service, resulting in…
We propose a new covariance matrix called Gini covariance matrix (GCM), which is a natural generalization of univariate Gini mean difference (GMD) to the multivariate case. The extension is based on the covariance representation of GMD by…
Over the past decade alternatives to traditional insurance and banking have grown in popularity. The desire to encourage local participation has lead products such as peer-to-peer insurance, reciprocal contracts, and decentralized finance…
Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…
We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with…
Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…
A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
Inequality is an inherent part of our lives: we see it in the distribution of incomes, talents, resources, and citations, amongst many others. Its intensity varies across different environments: from relatively evenly distributed ones, to…
We call a kind of mappings induced by a kind of weighted Laplace operator as complex valued kernel $\alpha$-harmonic mappings. In this article, for this class of mappings, the Heinz type lemma is established, and the best Heinz type…
This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F_1,F_2 and stochastic orderings between their inverses F_1^(-1),F_2^(-1). This underlies some theories of utility in the case of…
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…