Related papers: Interval-Valued Rank in Finite Ordered Sets
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
We define a model for rank one measure preserving transformations in the sense of [2]. This is done by defining a new Polish topology on the space of codes, which are infinite rank one words, for symbolic rank one systems. We establish that…
A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields. Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on one of the most…
We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…
Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…
We introduce concepts of intermediate rank for countable groups that "interpolate" between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic…
In general, representations of interval orders may use an arbitrary set of interval lengths. We can define subclasses of interval orders by restricting the allowable lengths of intervals. Motivated by a recent paper of Keller, Trenk, and…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
We study functions that produce a ranking of $n$ individuals from $n$ such rankings and are impartial in the sense that the position of an individual in the output ranking does not depend on the input ranking submitted by that individual.…
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…
Items from a database are often ranked based on a combination of multiple criteria. A user may have the flexibility to accept combinations that weigh these criteria differently, within limits. On the other hand, this choice of weights can…
The statistical rank tests play important roles in univariate non-parametric data analysis. If one attempts to generalize the rank tests to a multivariate case, the problem of defining a multivariate order will occur. It is not clear how to…
Moffat recently commented on our previous work. Our work focused on how laying the foundations of our evaluation methodology into the theory of measurement can improve our knowledge and understanding of the evaluation measures we use in IR…