Results 1  10
of
257
A Smooth Model of Decision Making Under Ambiguity
 Econometrica
, 2005
"... for helpful discussions and suggestions. We also thank three referees and A. Postlewaite, the coeditor, for offering very useful comments and advice. We also thank a number of seminar and conference audiences. We thank MEDS at Northwestern University, ICER at the University of Torino, and Eurequa a ..."
Abstract

Cited by 156 (18 self)
 Add to MetaCart
for helpful discussions and suggestions. We also thank three referees and A. Postlewaite, the coeditor, for offering very useful comments and advice. We also thank a number of seminar and conference audiences. We thank MEDS at Northwestern University, ICER at the University of Torino, and Eurequa at the University of Paris 1 for their hospitality during the visits when part of the research was completed. Mukerji gratefully acknowledges financial support from the
A Model of Inductive Bias Learning
 Journal of Artificial Intelligence Research
, 2000
"... A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonablysized training sets. Typically such bias is suppl ..."
Abstract

Cited by 144 (0 self)
 Add to MetaCart
A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonablysized training sets. Typically such bias is supplied by hand through the skill and insights of experts. In this paper a model for automatically learning bias is investigated. The central assumption of the model is that the learner is embedded within an environment of related learning tasks. Within such an environment the learner can sample from multiple tasks, and hence it can search for a hypothesis space that contains good solutions to many of the problems in the environment. Under certain restrictions on the set of all hypothesis spaces available to the learner, we show that a hypothesis space that performs well on a sufficiently large number of training tasks will also perform well when learning novel tasks in the same environment. Exp...
Countable Borel Equivalence Relations
 J. MATH. LOGIC
"... This paper is a contribution to a new direction in descriptive set theory that is being extensively pursued over the last decade or so. It deals with the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related s ..."
Abstract

Cited by 45 (7 self)
 Add to MetaCart
This paper is a contribution to a new direction in descriptive set theory that is being extensively pursued over the last decade or so. It deals with the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This study is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects, up to some notion of equivalence, by invariants, and creating a mathematical framework for measuring the complexity of such classification problems. (For an extensive discussion of these matters, see, e.g., Hjorth [00], Kechris [99, 00a].) This theory is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of its broad scope, there are natural interactions of it with other areas of mathematics, such as model theory, recursion theory, the theory of topological groups and their representations, topological dynamics, ergodic theory, and operator algebras
Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations
"... This paper is a contribution to the theory of countable Borel equivalence relations on standard Borel spaces. As usual, by a standard Borel space we mean a Polish (complete separable metric) space equipped with its #algebra of Borel sets. An equivalence relation E on a standard Borel space X is Bor ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
This paper is a contribution to the theory of countable Borel equivalence relations on standard Borel spaces. As usual, by a standard Borel space we mean a Polish (complete separable metric) space equipped with its #algebra of Borel sets. An equivalence relation E on a standard Borel space X is Borel if it is a Borel subset of X². Given two
Topological groups: where to from here?
, 2000
"... This is an account of one man’s view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological groups on compacta, embeddings of topological groups, free t ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
This is an account of one man’s view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological groups on compacta, embeddings of topological groups, free topological groups, and ‘massive’ groups (such as groups of homeomorphisms of compacta and groups of isometries of various metric spaces).
Dynamic Psychological Games
, 2006
"... The motivation of decision makers who care for emotions, reciprocity, or social conformity may depend directly on beliefs (about choices, beliefs, or information). Geanakoplos, Pearce & Stacchetti (Games and Economic Behavior, 1989) point out that traditional game theory is illequipped to address s ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
The motivation of decision makers who care for emotions, reciprocity, or social conformity may depend directly on beliefs (about choices, beliefs, or information). Geanakoplos, Pearce & Stacchetti (Games and Economic Behavior, 1989) point out that traditional game theory is illequipped to address such matters, and they pioneer a new framework which does. However, their toolbox — psychological game theory — incorporates several restrictions that rule out plausible forms of beliefdependent motivation. Building on recent work on dynamic interactive epistemology, we propose a more general framework. Updated higherorder beliefs, beliefs of others, and plans of action may influence motivation, and we can capture dynamic psychological effects (such as sequential reciprocity, psychological forward induction, regret, and anxiety) that were previously ruled out. We develop solution concepts, provide examples, and explore properties.
On the Complexity of the Isomorphism Relation for Finitely Generated Groups
, 1998
"... Working within the framework of descriptive set theory, we show that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group on two genera ..."
Abstract

Cited by 20 (11 self)
 Add to MetaCart
Working within the framework of descriptive set theory, we show that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group on two generators. The proofs are grouptheoretic, and we refer to descriptive set theory only for the relevant definitions and for motivation for the results. Introduction Given a class K of structures for a fixed first order language L, one may ask what kinds of complete invariants can be used to classify the elements of K up to isomorphism. For those classes consisting of the countable models of some L ! 1 ;! sentence, Friedman and Stanley [FS] proposed to use the methods of descriptive set theory to study their possible invariants and defined the notion of Borel reducibility between such classes of structures. In [HK], Hjorth and Kechris continued this study and situated it within the general the...
Vector Expected Utility and Attitudes toward Variation
, 2007
"... This paper analyzes a model of decision under ambiguity, deemed vector expected utility or VEU. According to the proposed model, an act f: Ω → X is evaluated via the functional V (f) = ..."
Abstract

Cited by 19 (3 self)
 Add to MetaCart
This paper analyzes a model of decision under ambiguity, deemed vector expected utility or VEU. According to the proposed model, an act f: Ω → X is evaluated via the functional V (f) =