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Foundations for Bayesian networks
, 2001
"... Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probabi ..."
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Cited by 11 (7 self)
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Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the
Machine Learning and the Philosophy of Science: a Dynamic Interaction
 In Proceedings of the ECMLPKDD01 Workshop on Machine Leaning as Experimental Philosophy of Science
, 2001
"... I posit here a dynamic interaction between machine learning and the philosophy of science, and illustrate this claim with the use of a case study involving the foundations of Bayesian networks. ..."
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Cited by 4 (1 self)
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I posit here a dynamic interaction between machine learning and the philosophy of science, and illustrate this claim with the use of a case study involving the foundations of Bayesian networks.
A dynamic interaction between machine learning and the philosophy of science
 Minds and Machines
, 2004
"... The relationship between machine learning and the philosophy of science can be classed as a dynamic interaction: a mutually beneficial connection between two autonomous fields that changes direction over time. I discuss the nature of this interaction and give a case study highlighting interactions b ..."
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Cited by 3 (1 self)
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The relationship between machine learning and the philosophy of science can be classed as a dynamic interaction: a mutually beneficial connection between two autonomous fields that changes direction over time. I discuss the nature of this interaction and give a case study highlighting interactions between research on Bayesian networks in machine learning and research on causality and probability in the philosophy of science.
Bayesian networks for logical reasoning
 in Proceedings of the AAAI Fall Symposium on Using Uncertainty in Computation
, 2001
"... By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied ..."
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Cited by 2 (0 self)
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By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied
The Actual Frequency Interpretation of Probability
, 1999
"... Von Mises' interpretation of probability, where probability is limiting relative frequency in an innite collective, is perhaps the most widely accepted frequency interpretation. Here I argue that such a theory makes various idealisations which are controversial and unnecessary. The actual frequency ..."
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Von Mises' interpretation of probability, where probability is limiting relative frequency in an innite collective, is perhaps the most widely accepted frequency interpretation. Here I argue that such a theory makes various idealisations which are controversial and unnecessary. The actual frequency interpretation, which avoids these assumptions, is more plausible and useful than might at rst be thought. Frequency interpretations of probability have generally been based around von Mises' approach as formulated in [von Mises 1928]. The idea here is that one can dene the frequency of an attribute or property as the limiting relative frequency of that property in a collective. This collective is a denumerable sequence of properties from an attribute space, a mutually exclusive and exhaustive set of properties. Von Mises invoked two empirical laws, the rst of which claimed that for any naturally occurring collective, the relative frequency of an attribute A in the rst n places of the ...