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A previous paper [2] showed how to generate a linear discriminant network(LDN) that computes likely faults for a noisy fault detection problem by usinga modification of the perceptron learning algorithm called the pocketalgorithm. Here we compare the performance of this connectionist model withperformance of the optimal Bayesian decision rule for the example that waspreviously described. We find that for this particular problem theconnectionist model performs about 97% as well as the optimal Bayesianprocedure. We then define a more general class of noisy single-pattern boolean(NSB) fault detection problems where each fault corresponds to a single:pattern of boolean instrument readings and instruments are independentlynoisy. This is equivalent to specifying that instrument readings areprobabilistic but conditionally independent given any particular fault. Weprove:  1. The optimal Bayesian decision rule for every NSB fault detection problemis representable by an LDN containing no intermediate nodes. (This slightlyextends a result first published by Minsky & Selfridge.) 2. Given an NSB faultdetection problem, then with arbitrarily high probability after sufficientiterations the pocket algorithm will generate an LDN that computes an optimalBayesian decision rule for that problem. In practice we find that a reasonablenumber of iterations of the pocket algorithm produces a network with good, butnot optimal, performance.

Bayesian Assessment of a Connectionist Model for Fault Detection