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121 Consider learning the target concept GoodCreditRisk defined over instances de-
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scribed by the four attributes HasStudentLoan, HasSavingsAccount, Isstudent, OwnsCar Give the initial network created by KBANN for the following domain theory, including all network connections and weights
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GoodCreditRisk t Employed, LowDebt Employed t -1sStudent LowDebt t -HasStudentLoan, HasSavingsAccount
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122 KBANN converts a set of propositional Horn clauses into an initial neural network
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Consider the class of n-of-m clauses, which are Horn clauses containing m literals in the preconditions (antecedents), and an associated parameter n where n m The preconditions of an n-of-m Horn clause are considered to be satisfied if at least n of its m preconditions are satisfied For example, the clause
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Young, Studies; n = 2
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asserts that one is a Student if at least two of these three preconditions are satisfied Give an algorithm similar to that used by KBANN, that accepts a set of propositional n-of-m clauses and constructs a neural network consistent with the domain theory 123 Consider extending KBANN to accept a domain theory consisting of first-order rather than propositional Horn clauses (ie, Horn clauses containing variables, as in 10) Either give an algorithm for constructing a neural network equivalent to a set of Horn clauses, or discuss the difficulties that prevent this 124 This exercise asks you to derive a gradient descent rule analogous to that used by TANGENTPROP Consider the instance space X consisting of the real numbers, and consider the hypothesis space H consisting of quadratic functions of x That is,
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each hypothesis h ( x ) is of the form
( a ) Derive a gradient descent rule that minimizes the same criterion as BACKPROP-
AGATION; is, the sum of squared errors between the hypothesis and target that values of the training data (b) Derive a second gradient descent rule that minimizes the same criterion as TANGENTPROP Consider only the single transformation s ( a , x ) = x + a 125 EBNN extracts training derivatives from explanations by examining the weights and activations of the neural networks that make up the explanation Consider the simple example in which the explanation is formed by a single sigmoid unit with n inputs Derive a procedure for extracting the derivative where xi is a particular training instance input to the unit, f ( x ) is the sigmoid unit output, and xi denotes the jth input to the sigmoid unit You may wish to use the notation x! to refer to the jth component of xi Hint: The derivation is similar to the derivation of the BACKPROPAGATION rule training 126 Consider again the search trace of FOCL shown in Figure 128 Suppose that the hypothesis selected at the first level in the search is changed to
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-HasHandle
Describe the second-level candidate hypotheses that will be generated by FOCL as successors to this hypothesis You need only include those hypotheses generated by FOCL's second search operator, which uses its domain theory Don't forget to post-prune the sufficient conditions Use the training data from Table 123 127 This chapter discussed three approaches to using prior knowledge to impact the search through the space of possible hypotheses Discuss your ideas for how these three approaches could be integrated Can you propose a specific algorithm that integrates at least two of these three for some specific hypothesis representation What advantages and disadvantages would you anticipate from this integration 128 Consider again the question from Section 1221, regarding what criterion to use for choosing among hypotheses when both data and prior knowledge are available Give your own viewpoint on this issue
REFERENCES
Abu-Mostafa, Y S (1989) Learning from hints in neural networks Journal of Complexity, 6(2), 192-198 Bergadano, F, & Giordana, A (1990) Guiding induction with domain theories In R Michalski et al (Eds), Machine learning: An art$cial intelligence approach 3 (pp 474-492) San Mateo, CA: Morgan Kaufmann Bradshaw, G, Fozzard, R, & Cice, L (1989) A connectionist expert system that really works In Advances in neural information processing San Mateo, CA: Morgan Kaufmam Caruana, R (1996) Algorithms and applications for multitask learning Proceedings of the 13th International Conference on Machine Learning San Francisco: Morgan Kaufmann Cooper, G C, & Herskovits, E (1992) A Bayesian method for the induction of probabilistic networks from data Machine Learning, 9, 309-347 Craven, M W (1996) Extracting comprehensible modelsfrom trained neural networks (PhD thesis) (UW Technical Report CS-TR-96-1326) Department of Computer Sciences, University of Wisconsin-Madison
Craven, M W, & Shavlik, J W (1994) Using sampling and queries to extract rules from trained neural networks Proceedings of the 11th International Conference on Machine Learning (pp 3745) San Mateo, CA: Morgan Kaufmann Fu, L M (1989) Integration of neural heuristics into knowledge-based inference ConnectionScience, 1(3), 325-339 Fu, L M (1993) Knowledge-based connectionism for revising domain theories IEEE Transactions on Systems, Man, and Cybernetics, 23(1), 173-182 Gallant, S I (1988) Connectionist expert systems CACM, 31(2), 152-169 Koppel, M, Feldman, R, & Segre, A (1994) Bias-driven revision of logical domain theories Journal of Artificial Intelligence, 1, 159-208 http:llwwwcswashingtonedulresearch/jairhomehtml Lacher, R, Hmska, S, & Kuncicky, D (1991) Backpropagation learning in expert networks (Dept of Computer Science Technical Report TR91-015) Florida State University, Tallahassee Mach, R, & Shavlik, J (1993) Using knowledge-based neural networks to improve algorithms: Refining the Chou-Fasman algorithm for protein folding Machine Learning, 11(3), 195-215 Mitchell, T M, & Thrun, S B (1993a) Explanation-based neural network learning for robot control In S Hanson, J Cowan, & C Giles (Eds), Advances in neural infomtionprocessing systems 5 (pp 287-294) San Mateo, CA: Morgan-Kaufmann Press Mitchell, T M, & Thrun, S B (1993b) Explanation-based learning: A comparison of symbolic and neural network approaches Tenth International Conference on Machine Learning, Amherst, MA Mooney, R (1993) Induction over the unexplained: Using overly-general domain theories to aid concept learning Machine Learning, lO(1) O'Sullivan, J, Mitchell, T, & Thrun, S (1997) Explanation-based learning for mobile robot perception In K Ikeuchi & M Veloso (Eds), Symbolic Visual Learning (pp 295-324) Ourston, D, & Mooney, R J (1994) Theory refinement combining analytical and empirical methods Arti2cial Intelligence, 66(2) Pazzani, M J, & Brunk, C (1993) Finding accurate frontiers: A knowledge-intensive approach to relational learning Proceedings of the I993 National Conference on Artificial Intelligence (pp 328-334) AAAI Press Pazzani, M J, Brunk, C A, & Silverstein, G (1991) A knowledge-intensive approach to learning relational concepts Proceedings of the Eighth International Workshop on Machine Learning (pp 432436) San Mateo, CA: Morgan Kaufmann Pazzani, M J, & Kibler, D (1992) The utility of knowledge in inductive learning MachineLearning, 9(1), 57-94 neural Pratt, L Y (1993a) Transferring previously learned BACKPROPAGATION networks to new learning tasks (PhD thesis) Department of Computer Science, Rutgers University, New Jersey (Also Rutgers Computer Science Technical Report ML-TR-37) Pratt, L Y (1993b) Discriminability-based transfer among neural networks In J E Moody et al (Eds), Advances in Nerual Infomtion Processing Systems 5 San Mateo, CA: Morgan Kaufmann Rosenbloom, P S, & Aasman, J (1990) Knowledge level and inductive uses of chunking (ebl) Proceedings of the Eighth National Conference on Artificial Intelligence (pp 821-827) AAAI Press Russell, S, Binder, J, Koller, D, & Kanazawa, K (1995) Local learning in probabilistic networks with hidden variables Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal Morgan Kaufmann Shavlik, J, & Towell, G (1989) An approach to combining explanation-based and neural learning algorithms Connection Science, 1(3), 233-255 Simard, P S, Victoni, B, LeCun, Y, & Denker, J (1992) Tangent prop-A formalism for specifying selected invariances in an adaptive network In J Moody et al (Eds), Advances in Neural Inforination Processing System 4 San Mateo, CA: Morgan Kaufmann Sudharth, S C, & Holden, A D C (1991) Symbolic-neural systems and the use of hints for developing complex systems International Journal of Man-Machine Studies, 35(3), 291-3 11
Thrun, S (1996) Explanation based neural network learning: A lifelong learning approach Boston: Kluwer Academic Publishers Thrun, S, & Mitchell, T M (1993) Integrating inductive neural network learning and explanationbased learning Proceedings of the 1993 International Joint Conference on Artificial Intelligence Thrun, S, & Mitchell, T M (1995) Learning one more thing Proceedings of the 1995 International Joint Conference on Artificial Intelligence, Montreal Towell, G, & Shavlik, J (1989) An approach to combining explanation-based and neural learning algorithms Connection Science, (I), 233-255 Towell, G, & Shavlik, J (1994) Knowledge-based artificial neural networks Artificial Intelligence, 70(1-2), 119-165 Towell, G, Shavlik, J, & Noordewier, M (1990) Refinement of approximate domain theories by knowledge-based neural networks Proceedings of the Eighth National Conference on Artijcial Intelligence (pp 861-866) Cambridge, MA: AAAI, MIT Press Yang, Q, & Bhargava, V (1990) Building expert systems by a modified perceptron network with rule-transfer algorithms (pp 77-82) International Joint Conference on Neural Networks, IEEE
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