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EXTENDING FUNCTIONS TO NATURAL EXTENSIONS

by Georges Hansoul, Bruno Teheux
"... Abstract. We investigate the problem of extending maps between al-gebras of a finitely generated prevariety to their natural extensions. As for canonical extension of lattice-based algebras, a new topology has to be introduced in order to be able to define an algebra inside its natural extension. Un ..."
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Abstract. We investigate the problem of extending maps between al-gebras of a finitely generated prevariety to their natural extensions. As for canonical extension of lattice-based algebras, a new topology has to be introduced in order to be able to define an algebra inside its natural extension

Conglomerable Natural Extension

by Enrique Miranda, Marco Zaffalon, Gert De Cooman - 7TH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS, INNSBRUCK, AUSTRIA , 2011
"... We study the weakest conglomerable model that is implied by desirability or probability assessments: the conglomerable natural extension. We show that taking the natural extension of the assessments while imposing conglomerability—the procedure adopted in Walley’s theory—does not yield, in general, ..."
Abstract - Cited by 10 (8 self) - Add to MetaCart
We study the weakest conglomerable model that is implied by desirability or probability assessments: the conglomerable natural extension. We show that taking the natural extension of the assessments while imposing conglomerability—the procedure adopted in Walley’s theory—does not yield, in general

Independent natural extension

by Gert de Cooman, Enrique Miranda, Marco Zaffalon - IN: IPMU 2010: PROCEEDINGS OF THE 13TH INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS CONFERENCE , 2010
"... We introduce a general definition for the independence of a number of finite-valued variables, based on coherent lower previsions. Our definition has an epistemic flavour: it arises from personal judgements that a number of variables are irrelevant to one another. We show that a number of already ..."
Abstract - Cited by 18 (9 self) - Add to MetaCart
existing notions, such as strong independence, satisfy our definition. Moreover, there always is a least-committal independent model, for which we provide an explicit formula: the independent natural extension. Our central result is that the independent natural extension satisfies so-called marginalisation

Robustness of natural extension

by Matthias C M Troffaes , Robert Hable , Germany Robert Hable@uni , -Bayreuth De - In ISIPTA ’11. SIPTA , 2011
"... Abstract How sensitive is the natural extension of an upper prevision against small perturbations in the assessments? We revise some basic results from the theory of systems of linear inequalities and equalities, and linear programming, and apply them to the theory of upper previsions. We find that ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Abstract How sensitive is the natural extension of an upper prevision against small perturbations in the assessments? We revise some basic results from the theory of systems of linear inequalities and equalities, and linear programming, and apply them to the theory of upper previsions. We find

Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories

by Cordelia Schmid - In CVPR
"... This paper presents a method for recognizing scene categories based on approximate global geometric correspondence. This technique works by partitioning the image into increasingly fine sub-regions and computing histograms of local features found inside each sub-region. The resulting “spatial pyrami ..."
Abstract - Cited by 1923 (47 self) - Add to MetaCart
pyramid ” is a simple and computationally efficient extension of an orderless bag-of-features image representation, and it shows significantly improved performance on challenging scene categorization tasks. Specifically, our proposed method exceeds the state of the art on the Caltech-101 database

The Natural Extension of the Beta-Transformation

by Karma Dajani, Cor Kraaikamp, Boris Solomyak , 1996
"... For each real number fi ? 1 the fi-transformation is defined by T fi x = fix(mod1). In this paper the natural extension T fi of the ergodic system underlying T fi is explicitly given. Furthermore, it is shown that a certain induced system of this natural extension is Bernoulli. Since T fi is weakly ..."
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For each real number fi ? 1 the fi-transformation is defined by T fi x = fix(mod1). In this paper the natural extension T fi of the ergodic system underlying T fi is explicitly given. Furthermore, it is shown that a certain induced system of this natural extension is Bernoulli. Since T fi is weakly

Estimating the Support of a High-Dimensional Distribution

by Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson , 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
Abstract - Cited by 783 (29 self) - Add to MetaCart
algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...

The Nature and Growth of Vertical Specialization in World Trade

by David Hummels - Journal of International Economics
"... Abstract: Dramatic changes are occurring in the nature of international trade. Production processes increasingly involve a sequential, vertical trading chain stretching across many countries, with each country specializing in particular stages of a good’s production sequence. We document a key aspe ..."
Abstract - Cited by 481 (20 self) - Add to MetaCart
Abstract: Dramatic changes are occurring in the nature of international trade. Production processes increasingly involve a sequential, vertical trading chain stretching across many countries, with each country specializing in particular stages of a good’s production sequence. We document a key

Computing the Conglomerable Natural Extension

by Enrique Miranda, Marco Zaffalon - 8TH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS, COMPIÈGNE, FRANCE , 2013
"... Given a coherent lower prevision P, we consider the problem of computing the smallest coherent lower prevision F ≥ P that is conglomerable, in case it exists. F is called the conglomerable natural extension. Past work has showed that F can be approximated by an increasing sequence (E n)n∈N of cohere ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Given a coherent lower prevision P, we consider the problem of computing the smallest coherent lower prevision F ≥ P that is conglomerable, in case it exists. F is called the conglomerable natural extension. Past work has showed that F can be approximated by an increasing sequence (E n

The Extended Linear Complementarity Problem

by O. L. Mangasarian, Jong-Shi Pang , 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
Abstract - Cited by 788 (30 self) - Add to MetaCart
We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
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