Related papers: Classification Aggregation without Unanimity
We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of the quasi-symmetric generating function. We give…
Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…
For any pair of bounded observables $A$ and $B$ with pure point spectra, we construct an associated "joint observable" which gives rise to a notion of a joint (projective) measurement of $A$ and $B$, and which conforms to the intuition that…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
Census data provide detailed information about population characteristics at a coarse resolution. Nevertheless, fine-grained, high-resolution mappings of population counts are increasingly needed to characterize population dynamics and to…
We present a Bayesian method for the identification and classification of objects from sets of astronomical catalogs, given a predefined classification scheme. Identification refers here to the association of entries in different catalogs…
Classification is one of the most important tasks of machine learning. Although the most well studied model is the two-class problem, in many scenarios there is the opportunity to label critical items for manual revision, instead of trying…
The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…
This paper discusses how crowd and machine classifiers can be efficiently combined to screen items that satisfy a set of predicates. We show that this is a recurring problem in many domains, present machine-human (hybrid) algorithms that…
We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of "category" for which equality…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
The responsibility gap is a set of outcomes of a collective decision-making mechanism in which no single agent is individually responsible. In general, when designing a decision-making process, it is desirable to minimise the gap. The paper…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…
Ensemble classification is an emerging approach to land cover mapping whereby the final classification output is a result of a consensus of classifiers. Intuitively, an ensemble system should consist of base classifiers which are diverse…
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…