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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 (for unlabeled examples) a class label of "positive" on 60% of instances ...
The matching with contracts problem is a generalization of matching problem, in which participants can be matched with different terms of contracts. [17] An important special case of contracts is matching with flexible wages. [18]
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).
Comparing p(n) = probability of a birthday match with q(n) = probability of matching your birthday. In the birthday problem, neither of the two people is chosen in advance. By contrast, the probability q(n) that at least one other person in a room of n other people has the same birthday as a particular person (for example, you) is given by
Radius matching: all matches within a particular radius are used -- and reused between treatment units. Kernel matching: same as radius matching, except control observations are weighted as a function of the distance between the treatment observation's propensity score and control match propensity score. One example is the Epanechnikov kernel.
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.
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. It is also known as the marriage problem , the sultan's dowry problem , the fussy suitor problem , the googol game , and the best choice problem .
As shown by Mulmuley, Vazirani and Vazirani, [8] the problem of minimum weight perfect matching is converted to finding minors in the adjacency matrix of a graph. Using the isolation lemma, a minimum weight perfect matching in a graph can be found with probability at least 1 ⁄ 2.