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Stable marriage problem. In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of ...
Probability matching. Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a probability-matching strategy will predict ...
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first ...
Result in combinatorics and graph theory. In mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficientcondition for an object to exist: The combinatorialformulation answers whether a finitecollection of setshas a transversal ...
Secretary problem. Graphs of probabilities of getting the best candidate (red circles) from n applications, and k / n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [ 1][ 2] that is studied extensively in the fields of applied probability, statistics, and decision theory.
Banach's match problem is a classic problem in probability attributed to Stefan Banach. Feller [1] says that the problem was inspired by a humorous reference to Banach's smoking habit in a speech honouring him by Hugo Steinhaus, but that it was not Banach who set the problem or provided an answer. Suppose a mathematician carries two matchboxes ...
Gale–Shapley algorithm. In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm, [ 1] propose-and-reject algorithm, [ 2] or Boston Pool algorithm[ 1]) is an algorithm for finding a solution to the stable matching problem. It is named for David Gale and Lloyd Shapley, who ...
The Hidden Matching Problem is a computation complexity problem that can be solved using quantum protocols: Let be a positive even integer. In the Hidden Matching Problem, Alice is given and Bob is given ( denotes the family of all possible perfect matchings on nodes). Their goal is to output a tuple such that the edge belongs to the matching and .