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29
A Bayesian method for the induction of probabilistic networks from data
 Machine Learning
, 1992
"... Abstract. This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computerassisted hypothesis testing, automated scientific discovery, and automated construction of ..."
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Cited by 1081 (27 self)
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Abstract. This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computerassisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.
Rationality and its Roles in Reasoning
 Computational Intelligence
, 1994
"... The economic theory of rationality promises to equal mathematical logic in its importance for the mechanization of reasoning. We survey the growing literature on how the basic notions of probability, utility, and rational choice, coupled with practical limitations on information and resources, in ..."
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Cited by 109 (4 self)
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The economic theory of rationality promises to equal mathematical logic in its importance for the mechanization of reasoning. We survey the growing literature on how the basic notions of probability, utility, and rational choice, coupled with practical limitations on information and resources, influence the design and analysis of reasoning and representation systems. 1 Introduction People make judgments of rationality all the time, usually in criticizing someone else's thoughts or deeds as irrational, or in defending their own as rational. Artificial intelligence researchers construct systems and theories to perform or describe rational thought and action, criticizing and defending these systems and theories in terms similar to but more formal than those of the man or woman on the street. Judgments of human rationality commonly involve several different conceptions of rationality, including a logical conception used to judge thoughts, and an economic one used to judge actions or...
In Defense of Probability
 In Proceedings of the Ninth International Joint Conference on Artificial Intelligence
, 1985
"... In this paper, it is argued that probability theory, when used correctly, is sufficient for the task of reasoning under uncertainty. Since numerous authors have rejected probability as inadequate for various reasons, the bulk of the paper is aimed at refuting these claims and indicating the sources ..."
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Cited by 80 (0 self)
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In this paper, it is argued that probability theory, when used correctly, is sufficient for the task of reasoning under uncertainty. Since numerous authors have rejected probability as inadequate for various reasons, the bulk of the paper is aimed at refuting these claims and indicating the sources of error. In particular, the definition of probability as a measure of belief rather than a frequency ratio is advocated, since a frequency interpretation of probability drastically restricts the domain applicability. Other sources of error include the confusion between relative and absolute probability, the distinction between probability and the uncertainty of that probability. Also, the interaction of logic and probability is discussed and it is argued that many extensions of logic, such as "default logic" are better understood in a probabilistic framework. The main claim of this paper is that the numerous schemes for representing and reasoning about uncertainty that have appeared in the AI literature are unnecessary  probability is all that is needed.
Random Worlds and Maximum Entropy
 In Proc. 7th IEEE Symp. on Logic in Computer Science
, 1994
"... Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can conside ..."
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Cited by 49 (12 self)
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Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or firstorder models, with domain f1; : : : ; Ng that satisfy KB , and compute the fraction of them in which ' is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying ' and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximumentropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are...
SetBased Bayesianism
, 1992
"... . Problems for strict and convex Bayesianism are discussed. A setbased Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique realvalued probability function in any decisionmaking context but also the re ..."
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Cited by 26 (1 self)
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. Problems for strict and convex Bayesianism are discussed. A setbased Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique realvalued probability function in any decisionmaking context but also the requirement of convexity for a setbased representation of uncertainty. Levi's Eadmissibility decision criterion is retained and is shown to be applicable in the nonconvex case. Keywords: Uncertainty, decisionmaking, maximum entropy, Bayesian methods. 1. Introduction. The reigning philosophy of uncertainty representation is strict Bayesianism. One of its central principles is that an agent must adopt a single, realvalued probability function over the events recognized as relevant to a given problem. Prescriptions for defining such a function for a given agent in a given situation range from the extreme personalism of deFinetti (1964, 1974) and Savage (1972) to the objective Bayesianism of...
Soft Evidential Update for Probabilistic Multiagent Systems
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2000
"... We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation ..."
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Cited by 26 (5 self)
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We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation
A Stochastic Model of Actions and Plans for Anytime Planning under Uncertainty
, 1994
"... Building planning systems that operate in real domains requires coping with both uncertainty and time pressure. This paper describes a model of reaction plans, which are generated using a formalization of actions and of state descriptions in probabilistic logic, as a basis for anytime planning under ..."
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Cited by 25 (5 self)
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Building planning systems that operate in real domains requires coping with both uncertainty and time pressure. This paper describes a model of reaction plans, which are generated using a formalization of actions and of state descriptions in probabilistic logic, as a basis for anytime planning under uncertainty. The model has the following main features. At the action level, we handle incomplete and ambiguous domain information, and reason about alternative action effects whose probabilities are given. On this basis, we generate reaction plans that specify different courses of action, reflecting the domain uncertainty and alternative action effects; if generation time was insufficient, these plans may be left unfinished, but they can be reused, incrementally improved, and finished later. At the planning level, we develop a framework for measuring the quality of plans that takes domain uncertainty and probabilistic information into account using Markov chain theory; based on this framew...
Cluster Expansions And Iterative Scaling For Maximum Entropy Language Models
 Maximum Entropy and Bayesian Methods
, 1995
"... . The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable increase in computational requirements. In this paper we pre ..."
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Cited by 20 (1 self)
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. The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable increase in computational requirements. In this paper we present a technique, closely related to the classical cluster expansion from statistical mechanics, for reducing the computational demands necessary to calculate conditional maximum entropy language models. 1. Introduction In this paper we present a computational technique that can enable faster calculation of maximum entropy models. The starting point for our method is an algorithm [1] for constructing maximum entropy distributions that is an extension of the generalized iterative scaling algorithm of Darroch and Ratcliff [2,3]. The extended algorithm relaxes the assumption of [2,3] that the constraint functions sum to a constant, and results in a set of decoupled polynomial equations, one fo...
Probabilistic Logic Programming under Maximum Entropy
 In Proc. ECSQARU99, LNCS 1638
, 1999
"... . In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by defining probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an efficient linear programming char ..."
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Cited by 18 (5 self)
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. In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by defining probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an efficient linear programming characterization for the problem of deciding whether a probabilistic logic program is satisfiable. Finally, and as a central contribution of this paper, we introduce an efficient technique for approximative probabilistic logic programming under maximum entropy. This technique reduces the original entropy maximization task to solving a modified and relatively small optimization problem. 1 Introduction Probabilistic propositional logics and their various dialects are thoroughly studied in the literature (see especially [19] and [5]; see also [15] and [16]). Their extensions to probabilistic firstorder logics can be classified into firstorder logics in which probabilities are defined over the do...
Asymptotic Conditional Probabilities for FirstOrder Logic
 In Proc. 24th ACM Symp. on Theory of Computing
, 1992
"... Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder formulas. That is, given firstorder formulas ' and `, we consider the number of structures with domain f1; : : : ; Ng that satisfy `, and comput ..."
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Cited by 13 (7 self)
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Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder formulas. That is, given firstorder formulas ' and `, we consider the number of structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this probability as N gets large. This is closely connected to the work on 01 laws that considers the limiting probability of firstorder formulas, except that now we are considering asymptotic conditional probabilities. Although work has been done on special cases of asymptotic conditional probabilities, no general theory has been developed. This is probably due in part to the fact that it has been known that, if there is a binary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We show that in this general case, almost all the questions one might want to ask (such as d...