Related papers: Valuations and Metrics on Partially Ordered Sets
Measure and integral are two closely related, but distinct objects of study. Nonetheless, they are both real-valued lattice valuations: order preserving real-valued functions $\phi$ on a lattice $L$ which are modular, i.e.,…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
We study set-valued classification for a Bayesian model where data originates from one of a finite number $N$ of possible hypotheses. Thus we consider the scenario where the size of the classified set of categories ranges from 0 to $N$.…
State of the art machine learning algorithms are highly optimized to provide the optimal prediction possible, naturally resulting in complex models. While these models often outperform simpler more interpretable models by order of…
The notion of preferences plays an important role in many disciplines including service robotics which is concerned with scenarios in which robots interact with humans. These interactions can be favored by robots taking human preferences…
The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…
We consider the concept of rank as a measure of the vertical levels and positions of elements of partially ordered sets (posets). We are motivated by the need for algorithmic measures on large, real-world hierarchically-structured data…
In this paper we give an overview of partial orders on the space of probability distributions that carry a notion of information content and serve as a generalisation of the Bayesian order given in (Coecke and Martin, 2011). We investigate…
The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
We present a representation of partial confidence in belief and preference that is consistent with the tenets of decision-theory. The fundamental insight underlying the representation is that if a person is not completely confident in a…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
We present a novel multilabel/ranking algorithm working in partial information settings. The algorithm is based on 2nd-order descent methods, and relies on upper-confidence bounds to trade-off exploration and exploitation. We analyze this…
In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.
We explore recently introduced definition modeling technique that provided the tool for evaluation of different distributed vector representations of words through modeling dictionary definitions of words. In this work, we study the problem…
Estimating a causal query from observational data is an essential task in the analysis of biomolecular networks. Estimation takes as input a network topology, a query estimation method, and observational measurements on the network…
The search engine evaluation research has quite a lot metrics available to it. Only recently, the question of the significance of individual metrics started being raised, as these metrics' correlations to real-world user experiences or…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…