Decision Making with Linear Constraints on Probabilities
Techniques for decision making with knowledge of linear constraints on condition probabilities are examined. These constraints arise naturally in many situations: upper and lower condition probabilities are known; an ordering among the probabilities is determined; marginal probabilities or bounds on such probabilities are known, e.g., data are available in the form of a probabilistic database (Cavallo and Pittarelli, 1987a); etc. Standard situations of decision making under risk and uncertainty may also be characterized by linear constraints. Each of these types of information may be represented by a convex polyhedron of numerically determinate condition probabilities. A uniform approach to decision making under risk, uncertainty, and partial uncertainty based on a generalized version of a criterion of Hurwicz is proposed, Methods for processing marginal probabilities to improve decision making using any of the criteria discussed are presented.
Code (0)
등록된 구현이 없습니다.
Tasks
Decision MakingSimilar Papers 제목 키워드 기반
Identification of Probabilities of Causation: A Complete Characterization
Probabilities of causation are fundamental to modern decision-making. Pearl first introduced three binary probabilities of causation, and Tian and Pearl later derived tight bounds for them using Balke's linear programmin…
Decision MakingMathematical ProofsRecovering Event Probabilities from Large Language Model Embeddings via Axiomatic Constraints
Rational decision-making under uncertainty requires coherent degrees of belief in events. However, event probabilities generated by Large Language Models (LLMs) have been shown to exhibit incoherence, violating the axiom…
Decision Making Under UncertaintyLanguage ModelingLanguage ModellingLarge Language ModelQuantum Uncertainty in Decision Theory
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the c…
Decision MakingBounding Probabilities of Causation with Partial Causal Diagrams
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard ava…
Decision MakingTractable Inference in Credal Sentential Decision Diagrams
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined…