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Rodney M. Goodman B.Sc., Ph.D., C.Eng., SMIEEE, FIEE.

Rule Based Networks

Rodney M. Goodman
Dr. John Lindal

What is a rule based network?

ITRule uses the rules it has discovered to build a parallel inference network rather like a neural network. However, unlike a neural network which is an implicit "black box" predictor, the ITRule Rule Based Network has an explicit architecture and operation. The architecture is explicit because links in the network correspond to rules. The inference is explicit because the weights on the links correspond to the "weight of evidence" associated with each rule. That is, our belief in the truth of the rule RHS, given that the rule LHS has fired.
The explicit nature of the Rule Based Network allows all its decisions to be audited by humans, and if necessary shown to a third party or judge to prove that it is operating in the desired manner.The Rule Based Network is a powerful new extension of a simple first-order Bayesian classifier. The network is capable of acting as a classifier or, much more powerfully, outputting probability or "confidence" estimates for each output decision. This enables a higher level decision maker (such as a human) to make the final decision. The advantage here is that situations in which a completely unknown input is presented can be identified by low confidence on all the outputs. This alerts the system to the fact that more training is necessary to derive rules to handle the new situation.

A Medical Example: Cancer Database

A common technique in breast cancer diagnosis is to obtain a fine needle aspirate (FNA) from a patient under examination. The FNA sample is evaluated under a microscope by a physician who makes a diagnosis. All patients evaluated as malignant, and some of those labeled as benign, later undergo biopsy which confirms or disconfirms the original diagnosis - the other patients diagnosed as benign undergo later re-examination to provide a true measurement of their condition. Since biopsy is roughly eight times as costly as the FNA technique, it is important that unnecessary biopsies be kept to a minimum. Hence, it is important that any automated decision maker outputs the confidence in its decisions, so that the physician can make a final decision. Also it is important that the automated system can explain its decisions in meaningful terms to the physician - hence an ideal domain for a Rule Based Network.

The data is in the form of nine subjectively evaluated characteristics of the FNA sample for each of 535 patients. These features describe general characteristics of the FNA sample as seen under a microscope, such as uniformity of cell size, marginal adhesion and mitoses (W.H. Wolberg and O.L. Mangasarian, "Multisurface method of pattern separation for medical diagnosis applied to breast cytology," Proceedings of the National Academy of Sciences, U.S.A., 87, 9193-9196, 1990.) Ground truth in the form of class labels (benign or malignant) was obtained by biopsy.

The rule based network learned by ITRule is shown in Figure 1(pdf). After training on only the first 50 examples, the network is able to predict the remaining 485 examples with 95% accuracy. Furthermore, when ITRule makes a wrong decision the confidence outputs are always very low - thus showing that the network really does not have the data to make a good decision in these cases.

Rule Info. Strength
IF cell size uniformity = 1 AND mitoses = 1THEN diagnosis benign 0.297 5.9
IF bare nuclei = 1 AND normal nucleoli = 1 THEN diagnosis benign 0.289 6.2
IF bare nuclei = 1 AND epithelial cell size = 2á THEN diagnosis benign 0.271 8.0
IF bare nuclei = 10THEN diagnosis malignant 0.231 -4.4
IF clump thickness = 10 THEN diagnosis malignant 0.145 -5.7
IF cell size uniformity = 10 THEN diagnosis malignant 0.111 -5.3
IF normal nucleoli = 10THEN diagnosis malignant 0.103 -5.2
IF marginal adhesion = 10 THEN diagnosis malignant 0.085 -4.2
IF cell size uniformity = 5THEN diagnosis malignant 0.057 -4.5
IF epithelial cell size = 10THEN diagnosis malignant 0.056 -3.8
IF bland chromatin = 8 THEN diagnosis malignant 0.045 -4.2

More Info on Rule Based nets:
R.M. Goodman, P. Smyth, C.M. Higgins & J. Miller, ôRule-Based Neural Networks for Classification and Probability Estimation, "Neural Computation", Vol. 4, No. 6, pp. 781-804, November 1992.

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