Dempster–Shafer theory
In plain wordsA theory of reasoning with uncertain evidence that lets you hold back belief — in effect saying 'I don't know' — instead of being forced to divide all your confidence among the possibilities.
A theory of evidence that extends probability by letting belief rest on sets of possibilities, not only on single outcomes. A mass function distributes a total of one over subsets of a frame of discernment: mass on a set containing several outcomes expresses evidence that does not discriminate among them, and mass on the whole frame expresses ignorance. From it come belief, the total support committed to a hypothesis, and plausibility, the support not committed against it, which bound an interval for that hypothesis. Dempster's rule of combination fuses independent bodies of evidence by intersecting their focal sets and renormalizing to discard conflict. The theory was used in expert systemsexpert system, n.: A program that stores a human specialist's know-how as many if–then rules and uses them to give advice or make decisions in a narrow field, such as diagnosing infections or configuring computers. and remains common in sensor fusion and reliability analysis, but the combination rule can give counterintuitive results under strong conflict, as Lotfi Zadeh showed in 1979, and computation grows exponentially with the size of the frame.
Origin
Arthur Dempster introduced upper and lower probabilities in 1967, and Glenn Shafer developed them into a theory of evidence in A Mathematical Theory of Evidence (1976). AI researchers took it up in the 1980s as an alternative to the certainty factors of MYCINMYCIN, prop. n.: A 1970s Stanford program that advised doctors on blood infections and antibiotics by applying hundreds of if–then rules from specialists. It performed about as well as experts but was never used on patients. and to Bayesian networksBayesian network, n.: A diagram of causes and effects with probabilities attached — say, how rain and a sprinkler can each make grass wet — that lets a computer update its beliefs about hidden causes when it sees evidence..
Related
- fuzzy logicfuzzy logic, n.: A kind of logic that allows degrees of truth, so a statement like 'the room is warm' can be 70 percent true, which helps machines handle vague everyday categories.
- Bayesian networkBayesian network, n.: A diagram of causes and effects with probabilities attached — say, how rain and a sprinkler can each make grass wet — that lets a computer update its beliefs about hidden causes when it sees evidence.
- rule-based systemrule-based system, n.: A computer system that makes decisions by following a list of 'if… then…' rules written by people, rather than by learning from examples.
- uncertainty quantificationuncertainty quantification, n.: Measuring how unsure an AI system's predictions are, and why, so that people know when to trust an answer and when to double-check it.
- expert systemexpert system, n.: A program that stores a human specialist's know-how as many if–then rules and uses them to give advice or make decisions in a narrow field, such as diagnosing infections or configuring computers.
- Bayesian inferenceBayesian inference, n.: Reasoning that treats unknowns as uncertain beliefs and updates them with evidence using Bayes' theorem. The result is not one answer but a range of answers, each with a probability.
Sources
- Dempster, A. P. (1967). Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals of Mathematical Statistics 38(2), 325–339.
- Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton University Press.