2016/07/28 by Manuele Leonelli, Leonelli, Manuele, Eva Riccomagno +3
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Computational Drug Discovery Methods #FOS: Computer and information sciences #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1607.08485
openalex publication_date 2016/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Influence diagrams provide a compact graphical representation of decision\nproblems. Several algorithms for the quick computation of their associated\nexpected utilities are available in the literature. However, often they rely on\na full quantification of both probabilistic uncertainties and utility values.\nFor problems where all random variables and decision spaces are finite and\ndiscrete, here we develop a symbolic way to calculate the expected utilities of\ninfluence diagrams that does not require a full numerical representation.\nWithin this approach expected utilities correspond to families of polynomials.\nAfter characterizing their polynomial structure, we develop an efficient\nsymbolic algorithm for the propagation of expected utilities through the\ndiagram and provide an implementation of this algorithm using a computer\nalgebra system. We then characterize many of the standard manipulations of\ninfluence diagrams as transformations of polynomials. We also generalize the\ndecision analytic framework of these diagrams by defining asymmetries as\noperations over the expected utility polynomials.\n