Bayesian Nets and Causality: Philosophical and Computational by Jon Williamson

By Jon Williamson

Bayesian nets are wide-spread in synthetic intelligence as a calculus for informal reasoning, permitting machines to make predictions, practice diagnoses, take judgements or even to find informal relationships. yet many philosophers have criticized and finally rejected the critical assumption on which such paintings is based-the causal Markov situation. So should still Bayesian nets be deserted? What explains their luck in man made intelligence? This booklet argues that the Causal Markov holds as a default rule: it frequently holds yet may have to be repealed within the face of counter examples. hence, Bayesian nets are the appropriate software to take advantage of via default yet naively utilising them can result in difficulties. The publication develops a scientific account of causal reasoning and indicates how Bayesian nets may be coherently hired to automate the reasoning procedures of a man-made agent. The ensuing framework for causal reasoning contains not just new algorithms, but additionally new conceptual foundations. likelihood and causality are taken care of as psychological notions - a part of an agent's trust country. but chance and causality also are aim - diverse brokers with an analogous history wisdom should undertake an analogous or comparable probabilistic and causal ideals. This ebook, aimed toward researchers and graduate scholars in machine technology, arithmetic and philosophy, offers a common creation to those philosophical perspectives in addition to exposition of the computational ideas that they motivate.

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Note though that if necessary one can easily modify the adding-arrows algorithm to produce a technique for constructing a Bayesian net that does not require a choice of approximation subspace. The balanced adding-arrows algorithm works the same way as the standard adding-arrows algorithm except that each arrow A −→ B is weighed by the conditional mutual information I(A, B|Par B ) divided by the increase in size that would arise if the arrow were added. This balances degree of fit with increase in size, and, as Fig.

This way of constructing a Bayesian net requires prior knowledge of causal relationships and hinges on three key assumptions about the nature of causality. First, it is assumed that the concept of direct causality is a relation between variables. Second, that the causal graph on V will be acyclic. , 1993; Sucar and Gillies, 1994; Kwoh and Gillies, 1996) 49 50 CAUSAL NETS: FOUNDATIONAL PROBLEMS ✓✏ ✓✏ ✲ LD ✲ S ❍ ✒✑ ✒✑ ❅ ❍❍ ✒ ✓✏ ❍ ❥ ❍ ❅ M ❅ ✯✒✑ ✟ ✟ ✟❅ ✓✏ ✓✏ ✓✏ ❘ ❅ ✟✟ ✲ ✲ SD D V ✒✑ ✒✑ ✒✑ Fig. 1. Causal graph for part of a colonoscopy system.

25. Average number of graphs stored at steps of the adding-arrows algorithm, where the approximation subspace is the set of nets whose variables have no more than two parents. 25 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of variables Fig. 26. Average number of nets output by the adding-arrows algorithm, where the approximation subspace is the whole space of Bayesian nets. 5 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of variables Fig. 27. Average number of nets output by the adding-arrows algorithm, where the approximation subspace is the set of nets whose variables have no more than two parents.

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