Related papers: Interval-Valued Rank in Finite Ordered Sets
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the (persistent…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
The comparison of alternative rankings of a set of items is a general and prominent task in applied statistics. Predictor variables are ranked according to magnitude of association with an outcome, prediction models rank subjects according…
Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the…
Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue…
Ranks estimated from data are uncertain and this poses a challenge in many applications. However, estimated ranks are deterministic functions of estimated parameters, so the uncertainty in the ranks must be determined by the uncertainty in…
Decision making is challenging when there is more than one criterion to consider. In such cases, it is common to assign a goodness score to each item as a weighted sum of its attribute values and rank them accordingly. Clearly, the ranking…
A metric graph is a geometric realization of a finite graph by identifying each edge with a real interval. A divisor on a metric graph $\Gamma$ is an element of the free abelian group on $\Gamma$. The rank of a divisor on a metric graph is…
In this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…
We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of…
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…
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an…
We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its…
For better or for worse, rankings of institutions, such as universities, schools and hospitals, play an important role today in conveying information about relative performance. They inform policy decisions and budgets, and are often…
Confidence interval procedures used in low dimensional settings are often inappropriate for high dimensional applications. When a large number of parameters are estimated, marginal confidence intervals associated with the most significant…
We introduce a framework for benchmarking optimizers according to multiple criteria over various test functions. Based on a recently introduced union-free generic depth function for partial orders/rankings, it fully exploits the ordinal…