A stopping rule for trainable signal detection

A stopping rule is developed for a class of threshold learning processes (TLPs) that includes the training procedures occurring in certain pattern classifiers, psycho-physical and neural models of perception and in stochastic approximation. The present work is restricted to one-dimensional pattern spaces. Of the published work on stopping rules, all but Farrell assume that the sequence of observations are independent and identically distributed. The TLP model discussed here gives rise to sequential samples from independent non-identical distributions. The stopping rule presented is a result of the technique developed here for obtaining a bounded length confidence interval for a parameter which varies from trial to trial in these distributions. Training is stopped when the interval falls within pre-specified limits, thereby assuring a specified performance at any desired confidence level. The rule is illustrated by a numerical example. In the example, both variable and small fixed increment training are considered. An expression is also given for the limit to which the probability of acquiring the stopping criterion converges in probability.