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1231 The KBANN Algorithm
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The KBANN algorithm exemplifies the initialize-the-hypothesisapproach to using domain theories It assumes a domain theory represented by a set of propositional, nonrecursive Horn clauses A Horn clause is propositional if it contains no variables The input and output of KBANN are as follows:
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KBANN(Domain-Theory, Training_Examples) Domain-Theory: Set of propositional, nonrecursive Horn clauses TrainingJxamples: Set of (input output) pairs of the targetfunction Analytical step: Create an initial network equivalent to the domain theory 1 For each instance attribute create a network input 2 For each Horn clause in the Domain-Theory, create a network unit as follows: 0 Connect the inputs of this unit to the attributes tested by the clause antecedents For each non-negated antecedent of the clause, assign a weight of W to the corresponding sigmoid unit input For each negated antecedent of the clause, assign a weight of -W to the corresponding sigmoid unit input 0 Set the threshold weight wo for this unit to -(n - 5)W, where n is the number of non-negated antecedents of the clause 3 Add additional connections among the network units, connecting each network unit at depth i from the input layer to all network units at depth i 1 Assign random near-zero weights to these additional connections Inductive step: Refine the initial network 4 Apply the BACKPROPAGATION algorithm to adjust the initial network weights to fit the Training-Examples
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TABLE 122 The KBANN algorithm The domain theory is translated into an equivalent neural network (steps algorithm (step 4) A typical value 1-3), which is inductively refined using the BACKPROPAGATION for the constant W is 40
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A set of training examples A domain theory consisting of nonrecursive, propositional Horn clauses
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An artificial neural network that fits the training examples, biased by the domain theory
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The two stages of the KBANN algorithm are first to create an artificial neural network that perfectly fits the domain theory and second to use the BACKPROPACATION algorithm to refine this initial network to fit the training examples The details of this algorithm, including the algorithm for creating the initial network, are given in Table 122 and illustrated in Section 1232
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An Illustrative Example
To illustrate the operation of KBANN, consider the simple learning problem summarized in Table 123, adapted from Towel1 and Shavlik (1989) Here each instance describes a physical object in terms of the material from which it is made, whether it is light, etc The task is to learn the target concept Cup defined over such physical objects Table 123 describes a set of training examples and a domain theory for the Cup target concept Notice the domain theory defines a C u p
Domain theory:
Cup t Stable, Lzpable, OpenVessel Stable t BottomIsFlat Lijiable t Graspable, Light Graspable t HasHandle OpenVessel t HasConcavity, ConcavityPointsUp
Training examples: