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Ranking functions and rankings on languages
, 2006
"... The Spohnian paradigm of ranking functions is in many respects like an orderofmagnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W—defined on a field of pro ..."
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Cited by 15 (8 self)
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The Spohnian paradigm of ranking functions is in many respects like an orderofmagnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W—defined on a field
Learning to rank using gradient descent
 In ICML
, 2005
"... We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data f ..."
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Cited by 534 (17 self)
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We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data
Rank Aggregation Methods for the Web
, 2010
"... We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wed ..."
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Cited by 478 (6 self)
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We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations
Learnability of Bipartite Ranking Functions
 PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON LEARNING THEORY
, 2005
"... The problem of ranking, in which the goal is to learn a realvalued ranking function that induces a ranking or ordering over an instance space, has recently gained attention in machine learning. We define a model of learnability for ranking functions in a particular setting of the ranking problem k ..."
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Cited by 12 (2 self)
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The problem of ranking, in which the goal is to learn a realvalued ranking function that induces a ranking or ordering over an instance space, has recently gained attention in machine learning. We define a model of learnability for ranking functions in a particular setting of the ranking problem
On the impossibility of certain ranking functions
 International Mathematical Journal
"... Suppose all the individuals in a field are linearly ordered. Groups of individuals form teams. Is there a perfect ranking function of each team based on the members of the team? We prove that under a very mild and reasonable set of axioms for the ranking function, no such ranking function exists. AM ..."
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Cited by 1 (0 self)
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Suppose all the individuals in a field are linearly ordered. Groups of individuals form teams. Is there a perfect ranking function of each team based on the members of the team? We prove that under a very mild and reasonable set of axioms for the ranking function, no such ranking function exists
Eventual Linear Ranking Functions
"... Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These systems are largely based on techniques and tools coming from the ..."
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the field of declarative constraint programming. In this paper, we first recall an algorithm based on Farkas ’ Lemma for discovering linear ranking functions proving termination of a certain class of loops. Then we propose an extension of this method for showing the existence of eventual linear ranking
On Rank Functions of Graphs
, 2013
"... We study rank functions (also known as graph homomorphisms onto Z), ways of imposing graded poset structures on graphs. We first look at a variation on rank functions called discrete Lipschitz functions. We relate the number of Lipschitz functions of a graph G to the number of rank functions of both ..."
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We study rank functions (also known as graph homomorphisms onto Z), ways of imposing graded poset structures on graphs. We first look at a variation on rank functions called discrete Lipschitz functions. We relate the number of Lipschitz functions of a graph G to the number of rank functions
Rank Functions of Fuzzy Greedoids
, 2015
"... Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank function ..."
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Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank
Ranking functions, AGM style
, 1999
"... Ranking functions, having their first appearance under the name „ordinale Konditionalfunktionen“ in my Habilitationsschrift submitted in 1983, had several precursors of which I was only incompletely aware, among them Shackle’s functions of potential surprise (see Shackle 1969), Rescher’s plausibilit ..."
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Cited by 5 (0 self)
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Ranking functions, having their first appearance under the name „ordinale Konditionalfunktionen“ in my Habilitationsschrift submitted in 1983, had several precursors of which I was only incompletely aware, among them Shackle’s functions of potential surprise (see Shackle 1969), Rescher’s
Ranking Functions for LinearConstraint Loops
, 2013
"... Ranking functions are a tool successfully used in termination analysis, complexity analysis, and program parallelization. Among the different types of ranking functions and approaches to finding them, this talk will concentrate on functions that are found by linear programming techniques. The settin ..."
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Cited by 5 (0 self)
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Ranking functions are a tool successfully used in termination analysis, complexity analysis, and program parallelization. Among the different types of ranking functions and approaches to finding them, this talk will concentrate on functions that are found by linear programming techniques
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