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263
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 ..."
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Cited by 157 (19 self)
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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 ..."
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Cited by 143 (0 self)
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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 ..."
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Cited by 44 (7 self)
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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
Turbulence, amalgamation, and generic automorphisms of homogeneous structures
 Proc. London Math. Soc
, 2004
"... Abstract. We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group ad ..."
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Cited by 34 (6 self)
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Abstract. We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphism group of the Cantor space has a comeager conjugacy class (answering a question of AkinHurleyKennedy). Finally, we study Polish groups that admit comeager conjugacy classes in any dimension (in which case the groups are said to admit ample generics). We show that Polish groups with ample generics have the small index property (generalizing results of HodgesHodkinsonLascarShelah) and arbitrary homomorphisms from such groups into separable groups are automatically continuous. Moreover, in the case of oligomorphic permutation groups, they have uncountable cofinality and the Bergman property. These results in particular apply to automorphism groups of many ωstable, ℵ0categorical structures and of the random graph. In this connection, we also show that the infinite symmetric group S ∞ has a unique nontrivial separable group topology. For several interesting groups we also establish Serre’s properties (FH) and (FA). 1.
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 ..."
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Cited by 25 (6 self)
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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 ..."
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Cited by 22 (2 self)
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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 ..."
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Cited by 21 (1 self)
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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 ..."
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Cited by 20 (11 self)
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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...
Games with secure equilibria
 In Logic in Computer Science
, 2004
"... Abstract. In 2player nonzerosum games, Nash equilibria capture the options for rational behavior if each player attempts to maximize her payoff. In contrast to classical game theory, we consider lexicographic objectives: first, each player tries to maximize her own payoff, and then, the player tr ..."
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Cited by 19 (7 self)
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Abstract. In 2player nonzerosum games, Nash equilibria capture the options for rational behavior if each player attempts to maximize her payoff. In contrast to classical game theory, we consider lexicographic objectives: first, each player tries to maximize her own payoff, and then, the player tries to minimize the opponent’s payoff. Such objectives arise naturally in the verification of systems with multiple components. There, instead of proving that each component satisfies its specification no matter how the other components behave, it often suffices to prove that each component satisfies its specification provided that the other components satisfy their specifications. We say that a Nash equilibrium is secure if it is an equilibrium with respect to the lexicographic objectives of both players. We prove that in graph games with Borel winning conditions, which include the games that arise in verification, there may be several Nash equilibria, but there is always a unique maximal payoff profile of a secure equilibrium. We show how this equilibrium can be computed in the case of ωregular winning conditions, and we characterize the memory requirements of strategies that achieve the equilibrium.