6533b830fe1ef96bd1297a3b
RESEARCH PRODUCT
Order-distance and other metric-like functions on jointly distributed random variables
Ehtibar N. DzhafarovJanne V. Kujalasubject
FOS: Computer and information sciencesMeasurable functionComputer Science - Artificial IntelligenceGeneral MathematicsMathematics - Statistics TheoryStatistics Theory (math.ST)Quantitative Biology - Quantitative Methods01 natural sciences050105 experimental psychologyJoint probability distribution0103 physical sciencesFOS: Mathematics0501 psychology and cognitive sciences010306 general physicsQuantitative Methods (q-bio.QM)60B99 (Primary) 81Q99 91E45 (Secondary)Probability measureMathematicsDiscrete mathematicsTriangle inequalityApplied MathematicsProbability (math.PR)05 social sciencesFunction (mathematics)Artificial Intelligence (cs.AI)Distribution (mathematics)FOS: Biological sciencesSample spaceRandom variableMathematics - Probabilitydescription
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in dealing with the problem of selective probabilistic causality encountered in behavioral sciences and in quantum physics. The problem reduces to that of ascertaining the existence of a joint distribution for a set of variables with known distributions of certain subsets of this set. Any violation of the triangle inequality or its consequences by one of our functions when applied to such a set rules out the existence of this joint distribution. We focus on an especially versatile and widely applicable pseudo-quasi-metric called an order-distance and its special case called a classification distance.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-05-15 | Proceedings of the American Mathematical Society |