Value of Information in Probabilistic Logic Programs

Sarthak Ghosh
(Stony Brook University)
C. R. Ramakrishnan
(Stony Brook University)

In medical decision making, we have to choose among several expensive diagnostic tests such that the certainty about a patient's health is maximized while remaining within the bounds of resources like time and money. The expected increase in certainty in the patient's condition due to performing a test is called the value of information (VoI) for that test. In general, VoI relates to acquiring additional information to improve decision-making based on probabilistic reasoning in an uncertain system. This paper presents a framework for acquiring information based on VoI in uncertain systems modeled as Probabilistic Logic Programs (PLPs). Optimal decision-making in uncertain systems modeled as PLPs have already been studied before. But, acquiring additional information to further improve the results of making the optimal decision has remained open in this context.

We model decision-making in an uncertain system with a PLP and a set of top-level queries, with a set of utility measures over the distributions of these queries. The PLP is annotated with a set of atoms labeled as "observable"; in the medical diagnosis example, the observable atoms will be results of diagnostic tests. Each observable atom has an associated cost. This setting of optimally selecting observations based on VoI is more general than that considered by any prior work. Given a limited budget, optimally choosing observable atoms based on VoI is intractable in general. We give a greedy algorithm for constructing a "conditional plan" of observations: a schedule where the selection of what atom to observe next depends on earlier observations. We show that, preempting the algorithm anytime before completion provides a usable result, the result improves over time, and, in the absence of a well-defined budget, converges to the optimal solution.

In Bart Bogaerts, Esra Erdem, Paul Fodor, Andrea Formisano, Giovambattista Ianni, Daniela Inclezan, German Vidal, Alicia Villanueva, Marina De Vos and Fangkai Yang: Proceedings 35th International Conference on Logic Programming (Technical Communications) (ICLP 2019), Las Cruces, NM, USA, September 20-25, 2019, Electronic Proceedings in Theoretical Computer Science 306, pp. 71–84.
Published: 19th September 2019.

ArXived at: https://dx.doi.org/10.4204/EPTCS.306.14 bibtex PDF
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