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 (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances.

The optimal Bayesian decision strategy (to maximize the number of correct predictions, see Duda, Hart & Stork (2001)) in such a case is to always predict "positive" (i.e., predict the majority category in the absence of other information), which has 60% chance of winning rather than matching which has 52% of winning (where p is the probability of positive realization, the result of matching would be $p^{2}+(1-p)^{2}$ , here $.6\times .6+.4\times .4$ ). The probability-matching strategy is of psychological interest because it is frequently employed by human subjects in decision and classification studies (where it may be related to Thompson sampling).

References

Duda, Richard O.; Hart, Peter E.; Stork, David G. (2001), Pattern Classification (2nd ed.), New York: John Wiley & Sons

Shanks, D. R., Tunney, R. J., & McCarthy, J. D. (2002). A re‐examination of probability matching and rational choice. Journal of Behavioral Decision Making, 15(3), 233-250.

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