Related papers: Fair Measures for Countable-to-one Maps

Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these fairness…

In this paper, an approach for generalizing the Gromov-Hausdorff metric is presented, which applies to metric spaces equipped with some additional structure. A special case is the Gromov-Hausdorff-Prokhorov metric between measured metric…

The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is…

Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…

We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.

Algorithmic fairness has received increased attention in socially sensitive domains. While rich literature on mean fairness has been established, research on quantile fairness remains sparse but vital. To fulfill great needs and advocate…

We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure…

Since its introduction as a computable approximation of the Reeb graph, the Mapper graph has become one of the most popular tools from topological data analysis for performing data visualization and inference. However, finding an…

We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space ("cake") and non-atomic, additive individual preference measures - or utilities - we show that…

In this paper, we define several measures induced by a finite directed graph. The study themselves is interesting ont only in the noncommutative probability point of view but also in the algebraic structure point of view, since to define…

Fair machine learning works have been focusing on the development of equitable algorithms that address discrimination of certain groups. Yet, many of these fairness-aware approaches aim to obtain a unique solution to the problem, which…

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in…

This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data.…

We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…

It is widely accepted that biased data leads to biased and thus potentially unfair models. Therefore, several measures for bias in data and model predictions have been proposed, as well as bias mitigation techniques whose aim is to learn…

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…

The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand,…

We study the equilibrium behaviour of a two-sided topological Markov shift with a countable number of states. We assume the potential associated with this shift is Walters with finite first variation and that the shift is topologically…