The probability of encountering an accidental DSM similarity in the presence of counter examples

Abstract

The "combinatorial explosion" of DSM hypotheses can be explained by the occurrence of DSM similarities only due to an accidental coincidence of several non-essential properties of training examples. The standard mechanisms for reducing the number of hypotheses are increasing the border by the number of parent examples and prohibition of counter examples. Considering the Bernoulli trials (for each training example and each attribute) with success probability pj for the jth non-essential attribute, we model a random training sample set for the occurrence of accidental DSM similarity. The same method is used to specify a set of counter examples. For this model, we compute the generating function of an accidental resemblance to the b parent examples at m potential counter examples.