Probabilistic decision graphs for optimization under uncertainty

• Ahlmann-Ohlsen KS, Jensen FV, Nielsen TD, Pedersen O, Vomlelova M (2009) A comparsion of two approaches for solving unconstrained influence diagrams. Int J Approx Reason 50: 153–173

  Article  Google Scholar 

• Bhattacharjya D, Shachter RD (2007) Evaluating influence diagrams with decision circuits. In: Proceedings of the twentythird conference on Uncertainty in Artificial Intelligence (UAI). pp 9–16

• Bhattacharjya D, Shachter RD (2008) Sensitivity analysis in decision circuits. In: Proceedings of the twentyfourth conference on Uncertainty in Artificial Intelligence (UAI). pp 34–42

• Bielza C, Ríos-Insua S, Gómez M, del Pozo JAF (2000) Sensitivity analysis in ictneo. In: Lecture notes in statistics, Robust Bayesian analysis, vol 152. Springer, Berlin, pp 317–334

• Cano A, Gómez M, Moral S (2006) A forward-backward Monte Carlo method for solving influence diagrams. Int J Approx Reason 42(1–2): 119–135

  Article  Google Scholar 

• Charnes JM, Shenoy PP (2004) Multistage monte carlo method for solving influence diagrams using local computation. Manag Sci 50: 405–418

  Article  Google Scholar 

• Cobb B (2006) Continuous decision MTE influence diagrams. In: Proceedings of the third European workshop on probabilistic graphical models. pp 67–74

• Cobb BR, Shenoy PP (2004) Hybrid influence diagrams using mixtures of truncated exponentials. In: Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI). pp 85–93

• Cobb BR, Shenoy PP (2008) Decision making with hybrid influence diagrams using mixtures of truncated exponentials. Eur J Oper Res 186(1): 261–275

  Article  Google Scholar 

• Cooper GF (1988) A method for using belief networks as influence diagrams. In: Proceedings of the fourth conference on uncertainty in artificial intelligence. pp 55–63

• Cooper GF (1990) The computational complexity of probabilistic inference using Bayesian belief networks. Artif Intell 42(2–3): 393–405

  Article  Google Scholar 

• Darwiche A (2003) A differential approach to inference in Bayesian networks. J ACM 50(3): 280–305

  Article  Google Scholar 

• Darwiche A (2009) Modeling and reasoning with Bayesian networks. Cambridge University Press, Cambridge

  Google Scholar 

• Dechter R (2000) An anytime approximation for optimizing policies under uncertainty. In: In workshop on decision theoretic planning, at the 5th international conference on artificial intelligence planning systems (AIPS-2000)

• Dittmer SL, Jensen FV (1997) Myopic value of information in influence diagrams. In: Geiger D, Shenoy PP (eds) Proceedings of the thirteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 142–149

  Google Scholar 

• Felli JC, Hazen GB (1999) Sensitivity analysis and the expected value of perfect information. Med Decis Mak 18: 95–109

  Article  Google Scholar 

• Gal Y, Pfeffer A (2003) A language for modeling agents’ decision making processes in games. In: Proceedings of the second international joint conference on autonomous agents and multiagent systems. ACM Press, New york, pp 265 – 272

• Gal Y, Pfeffer A (2008) Networks of influence diagrams: a formalism for representing agent’s beliefs and decision making processes. J Artif Intell Res 33: 109–147

  Google Scholar 

• Garcia-Sanchez D, Druzdzel M (2007) An efficient exhaustive anytime sampling algorithm for influence diagrams. In: Lucas P, Gmez J, Salmern A (eds) Advances in probabilistic graphical models, studies in fuzziness and soft computing, vol 214. Springer, Berlin, pp 255–273

  Google Scholar 

• Gmytrasiewicz PJ, Durfee EH, Wehe DK (1991) A decision-theoretic approach to coordinating multiagent interactions. In: Proceedings of the twelfth international joint conference on artificial intelligence. pp 62–68

• Horsch MC, Poole D (1998) An anytime algorithm for decision making under uncertainty. In: Cooper GF, Moral S (eds) Proceedings of the fourteenth conference on Uncertainty in Artificial Intelligence (UAI). Morgan Kaufmann Publishers, Los Altos, pp 246–255

  Google Scholar 

• Howard RA, Matheson JE (1981) Influence diagrams. In: Howard RA, Matheson JE (eds) The principles and applications of decision analysis vol 2, chap 37. Strategic Decision Group, Menlo Park, pp 721–762

  Google Scholar 

• Jensen F, Jensen FV, Dittmer SL (1994) From influence diagrams to junction trees. In: Mantaras RL, Poole D (eds) Proceedings of the tenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 367–373

  Google Scholar 

• Jensen FV, Gatti E (2010) Information enhancement for approximate representation of optimal strategies for influence diagrams. In: Proceedings of the fifth European workshop on probabilistic graphical models. pp 102–9

• Jensen FV, Nielsen TD (2007) Bayesian networks and decision graphs, 2nd edn. Springer, New York ISBN: 0-387-68281-3

  Book  Google Scholar 

• Jensen FV, Vomlelova M (2002) Unconstrained influence diagrams. In: Darwiche A, Friedman N (eds) Proceedings of the eighteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 234–241

  Google Scholar 

• Jensen FV, Nielsen TD, Shenoy PP (2006) Sequential influence diagrams: a unified framework. Int J Approx Reason 42: 101–118

  Article  Google Scholar 

• Kjaerulff UB, Madsen AL (2008) Bayesian networks and influence diagrams, 1st edn. Springer, New York ISBN: 978-0-387-74100-0

  Book  Google Scholar 

• Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT Press, Cambridge

  Google Scholar 

• Koller D, Milch B (2001) Multi-agent influence diagrams for representing and solving games. In: Proceedings of the seventeenth international joint conference on artificial intelligence. pp 1027–1036

• Koller D, Milch B (2003) Multi-agent influence diagrams for representing and solving games. Games Econ Behav 45(1): 181–221

  Article  Google Scholar 

• Korb KB, Nicholson AE (2004) Bayesian artificial intelligence, 1st edn. Chapman and Hall, London ISBN:1-58488-387-1

  Google Scholar 

• Lauritzen SL, Nilsson D (2001) Representing and solving decision problems with limited information. Manag Sci 47(9): 1235–1251

  Article  Google Scholar 

• Li Y, Shenoy PP (2010) Solving hybrid influence diagrams with deterministic variables. In: Proceedings of the twentysixth conference on Uncertainty in Artificial Intelligence (UAI). pp 322–331

• Liao W, Ji Q (2008) Efficient non-myopic value-of-information computation for influence diagrams. Int J Approx Reason 49: 436–450

  Article  Google Scholar 

• Luque M, Díez FJ (2010) Variable elimination for influence diagrams with super value nodes. Int J Approx Reason 51: 615–631

  Article  Google Scholar 

• Madsen AL (2008) New methods for marginalization in lazy propagation. In: Jaeger M, Nielsen TD (eds) Proceedings of the fourth European workshop on probabilistic graphical models. pp 193–200

• Madsen AL, Jensen F (2005) Solving linear-quadratic conditional Gaussian influence diagrams. Int J Approx Reason 38: 263–282

  Article  Google Scholar 

• Madsen AL, Jensen FV (1999) Lazy evaluation of symmetric Bayesian decision problems. In: Laskey KB, Prade H (eds) Proceedings of the fifteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 382–390

  Google Scholar 

• Madsen AL, Nilsson D (2001) Solving influence diagrams using HUGIN, Shafer-Shenoy, and lazy propagation. In: Proceedings of the seventeenth conference on Uncertainty in Artificial Intelligence (UAI). Morgan Kaufmann Publishers, Los Altos, pp 337–345

• Moral S, Rumí R, Salmerón A (2001) Mixtures of truncated exponentials in hybrid Bayesian networks. In: Proceedings of the sixth European conference on symbolic and quantitative approaches to reasoning with uncertainty, lecture notes in artificial intelligence, vol 2143. Springer, Berlin, pp 145–167

• Nielsen TD (2001) Decomposition of influence diagrams. In: Benferhat S, Besnard P (eds) Proceedings of the sixth European conference on symbolic and quantitative approaches to reasoning with uncertainty. Springer, no. 2143 in Lecture Notes in Artificial Intelligence, pp 144–155

• Nielsen TD, Jensen FV (1999) Well-defined decision scenarios. In: Laskey KB, Prade H (eds) Proceedings of the fifteenth Conference on Uncertainty in Artificial Intelligence (UAI). Morgan Kaufmann Publishers, Los Altos, pp 502–511

• Nielsen TD, Jensen FV (2003) Sensitivity analysis in influence diagrams. IEEE Trans Syst Man Cybern Part A Syst Hum 33(2): 223–234

  Article  Google Scholar 

• Nilsson D, Lauritzen SL (2000) Evaluating influence diagrams using LIMIDs. In: Boutilier C, Goldszmidt M (eds) Proceedings of the sixteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 436–445

  Google Scholar 

• Pearl J (1988) Probabilistic reasoning in intelligent systems. representation and reasoning. Morgan Kaufmann Publishers, San Mateo. ISBN 0-934613-73-7

• Raiffa H, Schlaifer R (1961) Applied statistical decision theory. MIT press, Cambridge

  Google Scholar 

• Shachter RD (1986) Evaluating influence diagrams. Oper Res 34(6): 871–882

  Article  Google Scholar 

• Shachter RD (1999) Efficient value of information computation. In: Laskey KB, Prade H (eds) Proceedings of the fifteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 594–601

  Google Scholar 

• Shachter RD, Bhattacharjya D (2010) Dynamic programming in influence diagrams with decision circuits. In: Proceedings of the twentysixth conference on Uncertainty in Artificial Intelligence (UAI). pp 509–516

• Shachter RD, Kenley CR (1989) Gaussian influence diagrams. Manag Sci 35(5): 527–550

  Article  Google Scholar 

• Shachter RD, Peot MA (1992) Decision making using probabilistic inference methods. In: Dubois D, Wellman MP, D’Ambrosio B, Smets P (eds) Proceedings of the eighth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 276–283

  Google Scholar 

• Shafer GR, Shenoy PP (1990) Probability Propagation. Ann Math Artif Intell 2: 327–352

  Article  Google Scholar 

• Shenoy PP (1992) Valuation-based systems for Bayesian decision analysis. Oper Res 40(3): 463–484

  Article  Google Scholar 

• Shenoy PP (2000) Valuation network representation and solution of asymmetric decision problems. Eur J Oper Res 121(3): 579–608

  Article  Google Scholar 

• Shenoy PP, West JC (2009) Mixtures of polynomials in hybrid bayesian networks with deterministic variables. In: Proceedings of the eighth workshop on uncertainty processing. pp 202–212

• Virto MA, Martín J, Insua DR, Moreno-Díaz A (2002) Approximate solutions of complex influence diagrams through mcmc methods. In: Proceedings of the first European workshop on probabilistic graphical models

• Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior, 1st edn. Wiley, New York

  Google Scholar 

• Yuan C, Wu X (2010) Solving influence diagrams using heuristic search. In: Proceedings of the eleventh international symposium on artificial intelligence and mathematics

• Yuan C, Wu X, Hansen E (2010) Solving multistage influence diagrams using branch-and-bound search. In: Proceedings of the twentysixth conference on Uncertainty in Artificial Intelligence (UAI). Catalina Island, CA

• Zhang NL (1998) Probabilistic inference in influence diagrams. In: Cooper GF, Moral S (eds) Proceedings of the fourteenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Los Altos, pp 514–522

  Google Scholar 

Download references