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53
A Natural Law of Succession
, 1995
"... Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we presen ..."
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Cited by 35 (3 self)
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Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we present a new solution to this fundamental problem in statistics and demonstrate that our solution outperforms standard approaches, both in theory and in practice.
From inheritance relation to nonaxiomatic logic
 International Journal of Approximate Reasoning
, 1994
"... NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intensi ..."
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Cited by 33 (25 self)
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NonAxiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a NonAxiomatic Logic is de ned. It has a termoriented language and an experiencegrounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.
The Interpretation of Fuzziness
 IEEE Transactions on Systems, Man, and Cybernetics
, 1996
"... From laserscanned data to feature human model: a system based on ..."
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Cited by 25 (13 self)
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From laserscanned data to feature human model: a system based on
Probabilistic EntityRelationship Models, PRMs, and Plate
, 2007
"... In this chapter, we introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of ..."
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Cited by 18 (0 self)
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In this chapter, we introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of this model—the directed acyclic probabilistic entityrelationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. In addition to describing the new language, we discuss important facets of modeling relational data, including the use of restricted relationships, self relationships, and probabilistic relationships. Many examples are provided.
Probabilistic logic and probabilistic networks
, 2008
"... While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches ..."
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Cited by 17 (13 self)
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While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. Specifically, we show in Part I that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question: the standard probabilistic semantics (which takes probability functions as models), probabilistic argumentation (which considers the probability of a hypothesis being a logical consequence of the available evidence), evidential probability (which handles reference classes and frequency data), classical statistical inference
A Scoring Function for Learning Bayesian Networks based on Mutual Information and Conditional Independence Tests
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare di ..."
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Cited by 17 (0 self)
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We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a nonBayesian scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the KullbackLeibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the wellknown K2, BDeu and BIC/MDL scores are also presented.
Spherical Subfamily Models
, 1999
"... A new method is presented for modeling lowdimensional representations of highdimensional multinomial and compositional data. The data are fit to subfamilies of the multinomial family which are defined using the multinomial information geometry. These collections of spherical subfamilies have a ..."
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Cited by 14 (0 self)
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A new method is presented for modeling lowdimensional representations of highdimensional multinomial and compositional data. The data are fit to subfamilies of the multinomial family which are defined using the multinomial information geometry. These collections of spherical subfamilies have a number of advantages over the affine subfamilies contructed by methods such as canonical and correspondence analysis, traditionally fit to such data. First, they can describe more complex shapes in the data, and are particularly wellsuited to modelling sparse data.
The Rational Basis of Representativeness
 23rd Annual Conference of the Cognitive Science Society
, 2001
"... Representativeness is a central explanatory construct in cognitive science but suffers from the lack of a principled theoretical account. Here we present a formal definition of one sense of representativeness  what it means to be a good example of a process or category in the context of Bayes ..."
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Cited by 14 (7 self)
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Representativeness is a central explanatory construct in cognitive science but suffers from the lack of a principled theoretical account. Here we present a formal definition of one sense of representativeness  what it means to be a good example of a process or category in the context of Bayesian inference. This analysis clarifies the relation between representativeness as an intuitive statistical heuristic and normative principles of inductive inference. It also leads to strong quantitative predictions about people 's judgments, which compare favorably to alternative accounts based on likelihood or similarity when evaluated on data from two experiments. Why do people think that Linda, the politically active, single, outspoken, and very bright 31yearold, is more likely to be a feminist bankteller than to be a bankteller, even though this is logically impossible? Why do we think that the sequence HHTHT is more likely than the sequence HHHHH to be produced by flipping a fa...
When did Bayesian inference become “Bayesian"?
 BAYESIAN ANALYSIS
, 2006
"... While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesi ..."
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Cited by 10 (1 self)
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While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian developments, beginning with Bayes’ posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when “Bayesian” emerged as the label of choice for those who advocated Bayesian methods.