Marco Baioletti
ABSTRACT
Probabilistic reasoning is an important tool for using uncertainty in AI, especially for automated reasoning. Partial probability assessments are a way of expressing partial probabilistic knowledge on a set of events. These assessments contain only the information about "interesting" events (hence it can be easily assessed by an expert). On the other hand, partial assessments can cause consistency problems. In this paper we show how to formulate the main tasks of probabilistic reasoning on partial probability assessments, namely check of coherence, correction, and inference, as QUBO problems. This transformation allows to solve these problems with a quantum or a digital annealer and thus providing new computational methods to perform these tasks.
- Kim Allan Andersen and Daniele Pretolani. 2001. Easy Cases of Probabilistic Satisfiability. Ann. Math. Artif. Intell. 33, 1 (2001), 69--91. Google Scholar
Digital Library
- Marco Baioletti and Andrea Capotorti. 2019. A L1 based probabilistic merging algorithm and its application to statistical matching. Appl. Intell. 49, 1 (2019), 112--124. Google ScholarDigital Library
- Marco Baioletti, Andrea Capotorti, and Sauro Tulipani. 2006. An empirical complexity study for a 2CPA solver. In Modern Information Processing, Bernadette Bouchon-Meunier, Giulianella Coletti, and Ronald R. Yager (Eds.). Elsevier Science, Amsterdam, 73--84. Google ScholarCross Ref
- Marco Baioletti, Andrea Capotorti, Sauro Tulipani, and Barbara Vantaggi. 2000. Elimination of Boolean variables for probabilistic coherence. Soft Comput. 4, 2 (2000), 81--88. Google ScholarCross Ref
- Marco Baioletti, Andrea Capotorti, Sauro Tulipani, and Barbara Vantaggi. 2002. Simplification Rules for the Coherent Probability Assessment Problem. Ann. Math. Artif. Intell. 35, 1--4 (2002), 11--28. Google ScholarDigital Library
- Zhengbing Bian, Fabián A. Chudak, William G. Macready, Aidan Roy, Roberto Sebastiani, and Stefano Varotti. 2020. Solving SAT (and MaxSAT) with a quantum annealer: Foundations, encodings, and preliminary results. Inf. Comput. 275 (2020), 104609. Google ScholarCross Ref
- Andrea Capotorti, Giuliana Regoli, and Francesca Vattari. 2010. Correction of incoherent conditional probability assessments. Int. J. Approx. Reason. 51, 6 (2010), 718--727. Google ScholarDigital Library
- Giulanella Coletti and Romano Scozzafava. 2002. Probabilistic Logic in a Coherent Setting. Dordrecht: Kluwer.Google Scholar
- Fábio Gagliardi Cozman and Lucas Fargoni di Ianni. 2015. Probabilistic satisfiability and coherence checking through integer programming. Int. J. Approx. Reason. 58 (2015), 57--70. Google ScholarDigital Library
- Bruno de Finetti. 1974. Theory of probability. London: Wiley & Sons.Google Scholar
- Marcelo Finger and Glauber De Bona. 2011. Probabilistic Satisfiability: Logic-Based Algorithms and Phase Transition. In IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16--22, 2011, Toby Walsh (Ed.). IJCAI/AAAI, 528--533. Google ScholarCross Ref
- George F. Georgakopoulos, Dimitris J. Kavvadias, and Christos H. Papadimitriou. 1988. Probabilistic satisfiability. J. Complex. 4, 1 (1988), 1--11. Google ScholarDigital Library
- Brigitte Jaumard, Pierre Hansen, and Marcus Poggi de Aragão. 1991. Column Generation Methods for Probabilistic Logic. INFORMS J. Comput. 3, 2 (1991), 135--148. Google ScholarCross Ref
- Nils J. Nilsson. 1986. Probabilistic Logic. Artif. Intell. 28, 1 (1986), 71--87. Google ScholarDigital Library
- Judea Pearl. 1989. Probabilistic reasoning in intelligent systems - networks of plausible inference. Morgan Kaufmann.Google Scholar
- Luc De Raedt and Angelika Kimmig. 2015. Probabilistic (logic) programming concepts. Mach. Learn. 100, 1 (2015), 5--47. Google ScholarDigital Library
- I.G. Rosenberg. 1975. Reduction of bivalent maximization to the quadratic case. Cahiers du Centre d'Etudes de Recherche Opérationnelle 17 (1975), 71--74.Google Scholar
- Amit Verma, Mark Lewis, and Gary Kochenberger. 2021. Efficient QUBO transformation for Higher Degree Pseudo Boolean Functions. Google ScholarCross Ref
Index Terms
- Probabilistic reasoning as quadratic unconstrained binary optimization
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