Results 1  10
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1,308
Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph learning al ..."
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Cited by 578 (16 self)
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algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely
Utility Representation of an Incomplete Preference Relation
, 2000
"... We consider the problem of representing a (possibly) incomplete preference relation by means of a vectorvalued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize ..."
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Cited by 64 (6 self)
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generalize some of the classical utility representation theorems of the theory of individual choice, and paves the way towards developing a consumer theory that realistically allows individuals to exhibit some “indecisiveness” on occasion.
A Generalized Representer Theorem
 In Proceedings of the Annual Conference on Computational Learning Theory
, 2001
"... Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and ..."
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Cited by 222 (17 self)
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Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers
A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. ..."
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Cited by 234 (48 self)
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semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type
A Theory of Networks for Approximation and Learning
 Laboratory, Massachusetts Institute of Technology
, 1989
"... Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, t ..."
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Cited by 235 (24 self)
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, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nonlinear mappings in terms of simpler functions
NonClassical Expected Utility Theory ∗
, 2006
"... In this paper we extend Savage’s theory of decisionmaking under uncertainty from a classical environment into a nonclassical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. 1 ..."
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Cited by 1 (0 self)
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In this paper we extend Savage’s theory of decisionmaking under uncertainty from a classical environment into a nonclassical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. 1
Representation Theorems and Theorem Proving in NonClassical Logics
 In Proceedings of the 29th IEEE International Symposium on MultipleValued Logic. IEEE Computer Sociaty
, 1999
"... In this paper we present a method for automated theorem proving in nonclassical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestleystyle representation for distributive lattices with operators in order to define a class of ..."
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Cited by 1 (1 self)
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In this paper we present a method for automated theorem proving in nonclassical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestleystyle representation for distributive lattices with operators in order to define a class
PCLASSIC: A tractable probabilistic description logic
 In Proceedings of AAAI97
, 1997
"... Knowledge representation languages invariably reflect a tradeoff between expressivity and tractability. Evidence suggests that the compromise chosen by description logics is a particularly successful one. However, description logic (as for all variants of firstorder logic) is severely limited in i ..."
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Cited by 119 (4 self)
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in its ability to express uncertainty. In this paper, we present PCLASSIC, a probabilistic version of the description logic CLASSIC. In addition to terminological knowledge, the language utilizes Bayesian networks to express uncertainty about the basic properties of an individual, the number of fillers
Behavioral theories and the neurophysiology of reward,
 Annu. Rev. Psychol.
, 2006
"... ■ Abstract The functions of rewards are based primarily on their effects on behavior and are less directly governed by the physics and chemistry of input events as in sensory systems. Therefore, the investigation of neural mechanisms underlying reward functions requires behavioral theories that can ..."
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Cited by 187 (0 self)
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the frequency of the behavior that results in reward. In Pavlovian, or classical, conditioning, the outcome follows the conditioned stimulus (CS) irrespective of any behavioral reaction, and repeated pairing of stimuli with outcomes leads to a representation of the outcome that is evoked by the stimulus
Representation Theorems and the Semantics of NonClassical Logics , and Applications to Automated Theorem Proving
, 2002
"... We give a uniform presentation of representation and decidability results related to the Kripkestyle semantics of several nonclassical logics. We show that a general representation theorem (which has as particular instances the representation theorems as algebras of sets for Boolean algebras, d ..."
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Cited by 8 (2 self)
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We give a uniform presentation of representation and decidability results related to the Kripkestyle semantics of several nonclassical logics. We show that a general representation theorem (which has as particular instances the representation theorems as algebras of sets for Boolean algebras
Results 1  10
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1,308