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Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches
Ex-Bradford University, 22 Wrenbury Crescent, Leeds LS16 7EG, UK
Received: 20 April 2011; in revised form: 23 May 2011 / Accepted: 23 June 2011 / Published: 18 July 2011
Abstract: Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian) network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME) are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.
Keywords: maximum entropy; sequential maximum entropy; causal networks; Method of Tribus; independence
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Markham, M.J. Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches. Entropy 2011, 13, 1281-1304.
Markham MJ. Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches. Entropy. 2011; 13(7):1281-1304.
Markham, Michael J. 2011. "Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches." Entropy 13, no. 7: 1281-1304.