Nonparametric Bayes error estimation using unclassified samples

The key measure of performance in a pattern recognition problem is the cost of making a decision. For the special case in which the relative cost of a correct decision is zero and the relative cost of an incorrect decision is unity, this cost is equal to the probability of an incorrect decision or error. A pattern recognition system may be viewed as a decision rule which transforms measurements into class assignments. The Bayes error is the minimum achievable error, where the minimization is with respect to all decision rules. The Bayes error is a function of the prior probabilities and the probability density functions of the respective classes. Unfortunately, in many applications, the probability density functions are unknown and therefore the Bayes error is unknown.