Related papers: Amenability, Folner sets, and cooling functions

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite…

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than…

In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of…

There has been much interest in generalizing Kesten's criterion for amenability in terms of a random walk to other contexts, such as determining amenability of a deck covering group by the bottom of the spectrum of the Laplacian or entropy…

We prove a version of ergodic theorem for an action of an amenable group, where a F{\o} lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.

In this paper we classify countable locally finite-by-abelian groups up to coarse isomorphism. This classification is derived from a coarse classification of amenable shift-homogeneous metric spaces.

In this paper, we provide several characterisations for uniform amenability concerning a family of finitely generated groups. More precisely, we show that the Hulanicki-Reiter condition for uniform amenability can be weakened in several…

Probabilistic predictions can be evaluated through comparisons with observed label frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic fairness has started to look at a growing variety of…

The Schelling model of segregation looks to explain the way in which a population of agents or particles of two types may come to organise itself into large homogeneous clusters, and can be seen as a variant of the Ising model in which the…

We consider an assignment problem that has aspects of fair division as well as social choice. In particular, we investigate the problem of assigning a small subset from a set of indivisible items to multiple players so that the chosen…

Let $\Gamma$ be a countable group acting on a countable set $X$ by permutations. We give a necessary and sufficient condition for the action to have a quasi-invariant mean with a given cocycle. This can be viewed as a combinatorial analogue…

Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…

We propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…

By classifying $S$-maximal amenable subgroups of algebraic groups over a global field of characteristic zero, we obtain a complete classification of maximal amenable subgroups up to commensurability in the respective arithmetic groups.…

We define two different weakenings of coarse amenability (also known as Yu's property A), namely fibred coarse amenability and coarse amenability at infinity. These two properties allow us to prove that a residually finite group is coarsely…

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set…

Most work in algorithmic fairness to date has focused on discrete outcomes, such as deciding whether to grant someone a loan or not. In these classification settings, group fairness criteria such as independence, separation and sufficiency…

The Fairness, Accountability, and Transparency in Machine Learning (FAT-ML) literature proposes a varied set of group fairness metrics to measure discrimination against socio-demographic groups that are characterized by a protected feature,…

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…