Random Worlds and Maximum Entropy

Grove, Adam J.; Halpern, Joseph Y.; Koller, Daphne

doi:10.1613/jair.61

Cited by 48 publications

(37 citation statements)

References 21 publications

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“…This means, that P |= G KB holds if the conditional probability P (φ * | ψ * ) equals α for any ground conditional (φ * | ψ * )[α] in G(KB ). To perform reasoning we employ the principle of maximum entropy [24,20,43,44]. The entropy H of a probability distribution P is defined as…”

Section: Example 215mentioning

confidence: 99%

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An integrated development environment for probabilistic relational reasoning

Finthammer

Thimm

2012

Logic Journal of IGPL

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This paper presents KReator, a versatile integrated development environment for probabilistic inductive logic programming currently under development. The area of probabilistic inductive logic programming (or statistical relational learning) aims at applying probabilistic methods of inference and learning in relational or first-order representations of knowledge. In the past ten years the community brought forth a lot of proposals to deal with problems in that area which mostly extend existing propositional probabilistic methods like Bayes Nets and Markov Networks on relational settings. Only few developers provide prototypical implementations of their approaches and the existing applications are often difficult to install and to use. Furthermore, due to different languages and frameworks used for the development of different systems the task of comparing various approaches becomes hard and tedious. KReator aims at providing a common and simple interface for representing, reasoning, and learning with different relational probabilistic approaches. It is a general integrated development environment which enables the integration of various frameworks within the area of probabilistic inductive logic programming and statistical relational learning. Currently, KReator implements Bayesian logic programs, Markov logic networks, and relational maximum entropy under grounding semantics. More approaches will be implemented in the near future or can be implemented by researchers themselves as KReator is open-source and available under public license. In this paper, we provide some background on probabilistic inductive logic programming and statistical relational learning and illustrate the usage of KReator on several examples using the three approaches currently implemented in KReator. Furthermore, we give an overview on its system architecture.

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Section: Example 215mentioning

confidence: 99%

“…we obtain the most unbiased representation of the knowledge in G(KB ), cf. [24,20,43,44] for the formal properties and uniqueness theorems. The approach of maximum entropy yields a model-based inference procedure and reasoning on KB is now solely performed using the probability distribution P ME G,KB .…”

Section: Example 215mentioning

confidence: 99%

An integrated development environment for probabilistic relational reasoning

Finthammer

Thimm

2012

Logic Journal of IGPL

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“…Th is principle, which can be traced back some 100 years, to the works of Boltzman n, M axwell, Gibbs and Planck an d has been introduced in its modern form by Jaynes (1957 ) and Tribus (1961 ), proved its e ciency in various ® elds of Physics, Statistics, Information Th eory, Pattern R ecogn ition, Signal Processing, etc. (Grove et al 1994, Goldszmidt et al 1990, A czel and Forte 1986, Justice 1986, Jaynes 1985, Skyrms 1985, W illiams 1980, Jaynes 1979, Tribus 1961, Jaynes 1957.…”

Section: Evidence Versus Probab Ilitymentioning

confidence: 99%

Explaining by evidence

Lozinskii¹

2000

Journal of Experimental & Theoretical Artificial Intelligen

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Given a system description an d its observed behaviour, there usually exist several possible explanations of the situation. DiOE erent explanations may contradict one an other and suggest con¯icting actions. So, in order to take proper actions sanctioned by the real situation, we need to single out an explanation that is most adequate to the reality. Existing methods for determining of such a best explanation require an extensive statistical knowledge about the system behaviour, which often is either only partially availa ble or not satisfactorily reliable. Trying to overcome this lack of data, we introduce the notion of evidence as a measure of credibility of beliefs based on the seman tic information contained in the system and supplied by the observations. Reasoning by evidence is ap plied to the process of determining a best abductive explanation. Th e notion of conjecture is presented as a generalization of explanation. Then reasoning by evidence is applied to testing and re® ning of diagnoses.

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“…As a credulous alternative, one can select a specific probability distribution from the models of the knowledge base and do reasoning by just using this probability distribution. A reasonable choice for such a model is the one probability distribution with maximum entropy [15,27,20]. This probability distribution satisfies several desirable properties for commonsense reasoning and is uniquely determined among the probability distributions that satisfy a given set of probabilistic conditionals, see [15,27,20] for the theoretical foundations.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we will present a model-based inductive inference operator that is based on the principle of maximum entropy for each of the two semantics. The idea of application is quite simple and similar to the propositional case: Having defined the set of models of a relational probabilistic knowledge base (according to each of the semantics), one chooses the unique probability distribution among these models that has maximal entropy, if possible, and therefore allows us to reason precisely (i. e. with precise probabilities, not based on intervals), but in a most cautious way (see [15,20] for the theoretical foundations). Examples will illustrate in which respects these inference operators differ, but we will show that both inference operators comply with all postulates.…”

Section: Introductionmentioning

confidence: 99%

On probabilistic inference in relational conditional logics

Thimm¹,

Kern-Isberner²

2012

Logic Journal of IGPL

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The principle of maximum entropy has proven to be a powerful approach for commonsense reasoning in probabilistic conditional logics on propositional languages. Due to this principle, reasoning is performed based on the unique model of a knowledge base that has maximum entropy. This kind of model-based inference fulfills many desirable properties for inductive inference mechanisms and is usually the best choice for reasoning from an information theoretical point of view. However, the expressive power of propositional formalisms for probabilistic reasoning is limited and in the past few years many proposals have been given for probabilistic reasoning in relational settings. It seems to be a common view that in order to interpret probabilistic first-order sentences, either a statistical approach that counts (tuples of) individuals has to be used, or the knowledge base has to be grounded to make a possible worlds semantics applicable, for a subjective interpretation of probabilities. Most of these proposals of the second type rely on extensions of traditional probabilistic models like Bayes nets or Markov networks whereas there are only few works on first-order extensions of probabilistic conditional logic. Here, we take an approach of lifting maximum entropy methods to the relational case by employing a relational version of probabilistic conditional logic. First, we propose two different semantics and model theories for interpreting first-order probabilistic conditional logic. We address the problems of ambiguity that are raised by the difference between subjective and statistical views, and develop a comprehensive list of desirable properties for inductive model-based probabilistic inference in relational frameworks. Finally, by applying the principle of maximum entropy in the two different semantical frameworks, we obtain inference operators that fulfill these properties and turn out to be reasonable choices for reasoning in first-order probabilistic conditional logic.

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Random Worlds and Maximum Entropy

Cited by 48 publications

References 21 publications

An integrated development environment for probabilistic relational reasoning

An integrated development environment for probabilistic relational reasoning

Explaining by evidence

On probabilistic inference in relational conditional logics

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