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Separate-and-Conquer Rule Learning

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Abstract

This paper is a survey of inductive rule learning algorithms that use a separate-and-conquer strategy. This strategy can be traced back to the AQ learning system and still enjoys popularity as can be seen from its frequent use in inductive logic programming systems. We will put this wide variety of algorithms into a single framework and analyze them along three different dimensions, namely their search, language and overfitting avoidance biases.

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References

  • Adé, H., De Raedt, L. & Bruynooghe, M. (1995). Declarative Bias for Specific-to-General ILP Systems. Machine Learning 20(1–2): 119-154. Special Issue on Bias Evaluation and Selection.

    Google Scholar 

  • Ali, K. M. & Pazzani, M. J. (1993). HYDRA: A Noise-Tolerant Relational Concept Learning Algorithm. In Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 1064-1071. Morgan Kaufmann: Chambèry, France.

    Google Scholar 

  • Bain, M. (1991). Experiments in Non-Monotonic Learning. In Proceedings of the 8th International Workshop on Machine Learning (ML-91), 380-384. Evanston, Illinois.

  • Bergadano, F. & Giordana, A. (1988). A Knowledge Intensive Approach to Concept Induction. In Proceedings of the 5th International Conference on Machine Learning (ML-88), 305-317. Ann Arbor, Michigan.

  • Bergadano, F., Giordana, A. & Ponsero, S. (1989). Deduction in Top-Down Inductive Learning. In Proceedings of the 6th International Workshop on Machine Learning (ML-89), 23-25.

  • Bergadano, F., Giordana, A. & Saitta, L. (1988). Automated Concept Acquisition in Noisy Environments. IEEE Transactions on Pattern Analysis and Machine Intelligence 10: 555-578.

    Google Scholar 

  • Bergadano, F. & Gunetti, D. (1993). An Interactive System to Learn Functional Logic Programs. In Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 1044-1049. Morgan Kaufmann.

  • Bergadano, F. & Gunetti, D. (1995). Inductive Logic Programming — From Machine Learning to Software Engineering. Logic Programming Series. The MIT Press: Cambridge, MA.

    Google Scholar 

  • Bergadano, F., Matwin, S., Michalski, R. S. & Zhang, J. (1992). Learning Two-Tiered Descriptions of Flexible Concepts: The POSEIDON System. Machine Learning 8: 5-43.

    Google Scholar 

  • Blockeel, H. & De Raedt, L. (1997). Top-Down Induction of Logical Decision Trees. Tech. rep. CW 247, Katholieke Universiteit Leuven, Department of Computer Science, Leuven, Belgium.

    Google Scholar 

  • Bloedorn, E. & Michalski, R. S. (1991). Constructive Induction From Data in AQ17-DCI: Further Experiments. Tech. rep. MLI 91-12, Artificial Intelligence Center, George Mason University, Fairfax, VA.

    Google Scholar 

  • Bloedorn, E., Michalski, R. S. & Wnek, J. (1993). Multistrategy Constructive Induction: AQ17-MCI. In Proceedings of the 2nd International Workshop on Multistrategy Learning, 188-203.

  • Boström, H. (1995). Covering vs. Divide-and-Conquer for Top-Down Induction of Logic Programs. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95), 1194-1200.

  • Botta, M., Giordana, A. & Saitta, L. (1992). Comparison of Search Strategies in Learning Relations. In Neumann, B. (ed.) Proceedings of the 10th European Conference on Artificial Intelligence (ECAI-92), 451-455. John Wiley & Sons: Vienna, Austria.

    Google Scholar 

  • Botta, M. & Giordana, A. (1993). SMART+: A Multi-Strategy Learning Tool. In Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 937-944. Morgan Kaufmann: Chambèry, France.

    Google Scholar 

  • Breiman, L., Friedman, J., Olshen, R. & Stone, C. (1984). Classification and Regression Trees. Wadsworth & Brooks: Pacific Grove, CA.

    Google Scholar 

  • Brunk, C. A. & Pazzani, M. J. (1991). An Investigation of Noise-Tolerant Relational Concept Learning Algorithms. In Proceedings of the 8th International Workshop on Machine Learning (ML-91), 389-393. Morgan Kaufmann: Evanston, Illinois.

    Google Scholar 

  • Buntine, W. & Niblett, T. (1992). A Further Comparison of Splitting Rules for Decision-Tree Induction. Machine Learning 8: 75-85.

    Google Scholar 

  • Cameron-Jones, R. M. (1996). The Complexity of Batch Approaches to Reduced Error Rule Set Induction. In Foo, N. & Goebel, R. (eds.) Proceedings of the 4th Pacific Rim International Conference on Artificial Intelligence (PRICAI-96), 348-359. Springer-Verlag: Cairns, Australia.

    Google Scholar 

  • Cameron-Jones, R. M. & Quinlan, J. R. (1993). Avoiding Pitfalls When Learning Recursive Theories. In Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 1050-1057. Chambèry, France.

  • Cendrowska, J. (1987). PRISM: An Algorithm for Inducing Modular Rules. International Journal of Man-Machine Studies 27: 349-370.

    Google Scholar 

  • Clark, P. & Boswell, R. (1991). Rule Induction with CN2: Some Recent Improvements. In Proceedings of the 5th European Working Session on Learning (EWSL-91), 151-163. Springer-Verlag: Porto, Portugal.

    Google Scholar 

  • Clark, P. & Niblett, T. (1989). The CN2 Induction Algorithm. Machine Learning 3(4): 261-283.

    Google Scholar 

  • Cohen, W. W. (1993). Efficient Pruning Methods for Separate-and-Conquer Rule Learning Systems. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 988-994. Morgan Kaufmann: Chambèry, France.

    Google Scholar 

  • Cohen, W. W. (1994). Grammatically Biased Learning: Learning Logic Programs Using an Explicit Antecedent Description Language. Artificial Intelligence 68(2): 303-366.

    Google Scholar 

  • Cohen, W. W. (1995). Fast Effective Rule Induction. In Prieditis, A. & Russell, S. (eds.) Proceedings of the 12th International Conference on Machine Learning (ML-95), 115-123. Morgan Kaufmann: Lake Tahoe, CA.

    Google Scholar 

  • De Raedt, L. (1992). Interactive Theory Revision: An Inductive Logic Programming Approach. Academic Press.

  • De Raedt, L. (ed.) (1995). Advances in Inductive Logic Programming, Vol. 32 of Frontiers in Artificial Intelligence and Applications. IOS Press.

  • De Raedt, L, & Bruynooghe, M. (1990). Indirect Relevance and Bias in Inductive Concept Learning. Knowledge Acquisition 2: 365-390.

    Google Scholar 

  • De Raedt, L. & Van Laer, W. (1995). Inductive Constraint Logic. In Proceedings of the 5th Workshop on Algorithmic Learning Theory (ALT-95), 80-94. Springer-Verlag.

  • Dehaspe, L. & De Raedt, L. (1996). DLAB: A Declarative Language Bias Formalism. In Proceedings of the International Symposium on Methodologies for Intelligent Systems (ISMIS-96), 613-622.

  • Domingos, P. (1996a). Linear-Time Rule Induction. In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), 96-101. AAAI Press.

  • Domingos, P. (1996b). Unifying Instance-Based and Rule-Based Induction. Machine Learning 24: 141-168.

    Google Scholar 

  • Džeroski, S. & Bratko, I. (1992). Handling Noise in Inductive Logic Programming. In Proceedings of the International Workshop on Inductive Logic Programming (ILP-92), 109-125. Tokyo, Japan.

  • Džeroski, S., Schulze-Kremer, S., Heidtke, K. R., Siems, K. & Wettschereck, D. (1996). Applying ILP to Diterpene Structure Elucidation from 13C NMR Spectra. In Proceedings of the MLnet Familiarization Workshop on Data Mining with Inductive Logic Programming (ILP for KDD), 12-24.

  • Fensel, D. & Wiese, M. (1993). Refinement of Rule Sets with JoJo. In Brazdil, P. (ed.) Proceedings of the 6th European Conference on Machine Learning (ECML-93), No. 667 in Lecture Notes in Artificial Intelligence, 378-383. Springer-Verlag.

  • Fensel, D. & Wiese, M. (1994). From JoJo to Frog: Extending a Bidirectional Strategy to a More Flexible Three-Directional Search. In Globig, C. & Althoff, K.-D. (eds.) Beiträge zum 7. Fachgruppentreffen Maschinelles Lernen, Forschungbericht No. LSA-95-01, 37-44. University of Kaiserslautern. Zentrum für Lernende Systeme und Anwendungen.

  • Fürnkranz, J. (1994a). Efficient Pruning Methods for Relational Learning. Ph.D. thesis, Vienna University of Technology.

  • Fürnkranz, J. (1994b). FOSSIL: A Robust Relational Learner. In Bergadano, F. & De Raedt, L. (eds.) Proceedings of the 7th European Conference on Machine Learning (ECML-94), Vol. 784 of Lecture Notes in Artificial Intelligence, 122-137. Springer-Verlag: Catania, Italy.

    Google Scholar 

  • Fürnkranz, J. (1994c). Top-Down Pruning in Relational Learning. In Cohn, A. (ed.) Proceedings of the 11th European Conference on Artificial Intelligence (ECAI-94), 453-457. John Wiley & Sons: Amsterdam, The Netherlands.

    Google Scholar 

  • Fürnkranz, J. (1995). A Tight Integration of Pruning and Learning (Extended Abstract). In Lavrač, N. & Wrobel, S. (eds.) Proceedings of the 8th European Conference on Machine Learning (EMCL-95), Vol. 912 of Lecture Notes in Artificial Intelligence, 291-294. Springer-Verlag: Heraclion, Greece.

    Google Scholar 

  • Fürnkranz, J. (1997). Pruning Algorithms for Rule Learning. Machine Learning 27(2): 139-171.

    Google Scholar 

  • Fürnkranz, J. & Widmer, G. (1994). Incremental Reduced Error Pruning. In Cohen W. & Hirsh, H. (eds.) Proceedings of the 11th International Conference on Machine Learning (ML-94), 70-77. Morgan Kaufmann: New Brunswick, NJ.

    Google Scholar 

  • Georgeff, M. P. & Wallace, C. S. (1984). A General Criterion for Inductive Inference. In O'Shea, T. (ed.) Proceedings of the Sixth European Conference on Artificial Intelligence (ECAI-84), 473-482. Elsevier: Amsterdam.

    Google Scholar 

  • Giordana, A. & Sale, C. (1992). Learning Structured Concepts Using Genetic Algorithms. In Sleeman, D. & Edwards, P. (eds.) Proceedings of the 9th International Workshop on Machine Learning (ML-92), 169-178. Morgan Kaufmann: Edinburgh.

    Google Scholar 

  • Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley: Reading, MA.

    Google Scholar 

  • Goodman, R. M. & Smyth, P. (1988). Information-Theoretic Rule Induction. In Kodratoff, Y. (ed.) Proceedings of the 8th European Conference on Artificial Intelligence (ECAI-88), 357-362. Pitman: London.

    Google Scholar 

  • Grobelnik, M. (1992). Markus — An Optimized Model Inference System. In Rouveirol, C. (ed.) Proceedings of the ECAI-92 Workshop on Logical Approaches to Machine Learning. Vienna, Austria.

  • Hart, P. E., Nilsson, N. J. & Raphael, B. (1968). A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics 4(2): 100-107.

    Google Scholar 

  • Helft, N. (1989). Induction as Nonmonotonic Inference. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, 149-156.

  • Holte, R., Acker L. & Porter, B. (1989). Concept Learning and the Problem of Small Disjuncts. In Proceedings of the 11th International Joint Conference on Artificial Intelligence (IJCAI-89), 813-818. Morgan Kaufmann: Detroit, MI.

    Google Scholar 

  • Karalič, A. (1995). First Order Regression. Ph.D. thesis, University of Ljubljana, Faculty of Electrical Engineering and Computer Science, Slovenia.

    Google Scholar 

  • Kietz, J.-U. & Wrobel, S. (1992). Controlling the Complexity of Learning in Logic Through Syntactic and Task-Oriented Models. In Muggleton, S. H. (ed.) Inductive Logic Programming, chap. 16, 335-359. Academic Press Ltd.: London.

    Google Scholar 

  • Kijsirikul, B., Numao, M. & Shimura, M. (1991). Efficient Learning of Logic Programs with Non-Determinate, Non-Discriminating Literals. In Proceedings of the 8th International Workshop on Machine Learning (ML91), 417-421. Evanston, Illinois.

  • Kijsirikul, B., Numao, M. & Shimura, M. (1992). Discrimination-Based Constructive Induction of Logic Programs. In Proceedings of the 10th National Conference on Artificial Intelligence (AAAI-92), 44-49.

  • Kirkpatrick, S., Gelatt, C. & Vecchi, M. (1983). Optimization by Simulated Annealing. Science 220: 671-680.

    Google Scholar 

  • Kohavi, R. (1995). Wrappers for Performance Enhancement and Oblivious Decision Graphs. Ph.D. thesis, Stanford University, Dept. of Computer Science.

  • Kohavi, R. & John, G. H. (1995). Automatic Parameter Selection by Minimizing Estimated Error. In Prieditis, A. & Russell, S. (eds.) Proceedings of the 12th International Conference on Machine Learning (ICML-95), 304-312. Morgan Kaufmann.

  • Kononenko, I. & Kovačič, M. (1992). Learning as Optimization: Stochastic Generation of Multiple Knowledge. In Sleeman, D. & Edwards, P. (eds.) Proceedings of the 9th International Workshop on Machine Learning (ML-92), 257-262. Morgan Kaufmann.

  • Kovačič, M. (1991). Markovian Neural Networks. Biological Cybernetics 64: 337-342.

    Google Scholar 

  • Kovačič, M. (1994a). MDL-Heuristics in ILP Revised. In Proceedings of the ML-COLT-94 Workshop on Applications of Descriptional Complexity to Inductive, Statistical, and Visual Inference.

  • Kovačič, M. (1994b). Stochastic Inductive Logic Programming. Ph.D. thesis, Department of Computer and Information Science, University of Ljubljana.

  • Kramer, S. (1994). CN2-MCI: A Two-Step Method for Constructive Induction. In Proceedings of the ML-COLT-94 Workshop on Constructive Induction and Change of Representation.

  • Kramer, S. (1996). Structural Regression Trees. In Proceedings of the 13th National Conference on Artificial Intelligence (AAAI-96), 812-819. AAAI Press.

  • Langley, P., Simon, H. A. & Bradshaw, G. L. (1987). Heuristics for Empirical Discovery. In Bolc, L. (ed.) Computational Models of Learning. Springer-Verlag. Reprinted in Shavlik, J. W. & Dietterich, T. G. (ed.) Reading in Machine Learning. Morgan Kaufmann, 1991.

  • Lavrač, N., Džeroski, S. & Grobelnik, M. (1991). Learning Nonrecursive Definitions of Relations with LINUS. In Proceedings of the 5th European Working Session on Learning (EWSL-91), 265-281. Springer-Verlag: Porto, Portugal.

    Google Scholar 

  • Lloyd, J. W. (1987). Foundations of Logic Programming (2nd, extended edition). Springer-Verlag: Berlin.

    Google Scholar 

  • Matheus, C. J. (1989). A Constructive Induction Framework. In Proceedings of the 6th International Workshop on Machine Learning, 474-475.

  • Michalski, R. S. (1969). On the Quasi-Minimal Solution of the Covering Problem. In Proceedings of the 5th International Symposium on Information Processing (FCIP-69), Vol. A3 (Switching Circuits), 125-128. Bled, Yugoslavia.

    Google Scholar 

  • Michalski, R. S. (1973). AQVAL/1 — Computer Implementation of a Variable-Valued Logic System VL1 and Examples of Its Application to Pattern Recognition. In Proceedings of the 1st International Joint Conference on Pattern Recognition, 3-17.

  • Michalski, R. S. (1980). Pattern Recognition and Rule-Guided Inference. IEEE Transactions on Pattern Analysis and Machine Intelligence 2: 349-361.

    Google Scholar 

  • Michalski, R. S. (1983). A Theory and Methodology of Inductive Learning. Artificial Intelligence 20(2): 111-162.

    Google Scholar 

  • Michalski, R. S., Mozetič, I., Hong, J. & Lavrač, N. (1986). The Multi-Purpose Incremental Learning System AQ15 and Its Testing Application to Three Medical Domains. In Proceedings of the 5th National Conference on Artificial Intelligence (AAAI-86), 1041-1045. Philadephia, PA.

  • Mingers, J. (1989). An Empirical Comparison of Selection Measures for Decision-Tree Induction. Machine Learning 3: 319-342.

    Google Scholar 

  • Mitchell, T. M. (1980). The Need for Biases in Learning Generalizations. Tech. rep., Computer Science Department, Rutgers University, New Brunswick, MA. Reprinted in Shavlik, J. W. & Dietterich, T. G. (eds.) Readings in Machine Learning. Morgan Kaufmann, 1991.

    Google Scholar 

  • Mittenecker, E. (1977). Planung und statistische Auswertung von Experimenten (8th edition). Verlag Franz Deuticke: Vienna, Austria. In German.

    Google Scholar 

  • Mladenić, D. (1993) Combinatorial Optimization in Inductive Concept Learning. In Proceedings of the 10th International Conference on Machine Learning (ML-93), 205-211. Morgan Kaufmann.

  • Mooney, R. J. (1995). Encouraging Experimental Results on Learning CNF. Machine Learning 19: 79-92.

    Google Scholar 

  • Mooney, R. J. & Califf, M. E. (1995). Induction of First-Order Decision Lists: Results on Learning the Past Tense of English Verbs. Journal of Artificial Intelligence Research 3: 1-24.

    Google Scholar 

  • Muggleton, S., Bain, M., Hayes-Michie, J. & Michie, D. (1989). An Experimental Comparison of Human and Machine Learning Formalisms. In Proceedings of the 6th International Workshop on Machine Learning (ML-93), 113-118. Morgan Kaufmann.

  • Muggleton, S. H. (ed.) (1992). Inductive Logic Programming. Academic Press Ltd.: London.

    Google Scholar 

  • Muggleton, S. H. (1995). Inverse Entailment and Progol. New Generation Computing 13(3,4): 245-286. Special Issue on Inductive Logic Programming.

    Google Scholar 

  • Muggleton, S. H. & Feng, C. (1990). Efficient Induction of Logic Programs. In Proceedings of the 1st Conference on Algorithmic Learning Theory, 1-14. Tokyo, Japan.

  • Nédellec, C., Rouveirol, C., Adé, H., Bergadano, F. & Tausend, B. (1996). Declarative Bias in ILP. In De Raedt, L. (ed.) Advances in Inductive Logic Programming, Vol. 32 of Frontiers in Artificial Intelligence and Applications, 82-103. IOS Press: Amsterdam.

    Google Scholar 

  • Pagallo, G. & Haussler, D. (1990). Boolean Feature Discovery in Empirical Learning. Machine Learning 5: 71-99.

    Google Scholar 

  • Pazzani, M. & Kibler, D. (1992). The Utility of Knowledge in Inductive Learning. Machine Learning 9: 57-94.

    Google Scholar 

  • Pazzani, M., Merz, C., Murphy, P., Ali, K., Hume, T. & Brunk, C. (1994). Reducing Misclassification Costs. In Cohen, W.W. & Hirsh, H. (eds.) Proceedings of the 11th International Conference on Machine Learning (ML-94), 217-225. Morgan Kaufmann: New Brunswick.

    Google Scholar 

  • Pfahringer, B. (1994a). Controlling Constructive Induction in CiPF: An MDL Approach. In Brazdil, P. B. (ed.) Proceedings of the 7th European Conference on Machine Learning (ECML-94), Lecture Notes in Artificial Intelligence, 242-256. Springer-Verlag, Catania, Sicily.

    Google Scholar 

  • Pfahringer, B. (1994b). Robust Constructive Induction. In Nebel, B. & Dreschler-Fischer, F. (eds.) Proceedings of the 18th German Annual Conference on Artificial Intelligence (KI-94), Lecture Notes in Artificial Intelligence, 118-129. Springer-Verlag.

  • Pfahringer, B. (1995a). A New MDL Measure for Robust Rule Induction (Extended Abstract). In Lavrač, N. & Wrobel, S. (eds.), Proceedings of the 8th European Conference on Machine Learning (ECML-95), No. 912 in Lecture Notes in Artificial Intelligence, 331-334. Springer-Verlag: Heraclion, Greece.

    Google Scholar 

  • Pfahringer, B. (1995b). Practical Uses of the Minimum Description Length Principle in Inductive Learning. Ph.D. thesis, Technische Universität Wien.

  • Plotkin, G. D. (1970). A Note on Inductive Generalisation. In Meltzer B. & Michie, D. (eds.) Machine Intelligence 5, 153-163. Elsevier North-Holland/New York.

  • Plotkin, G. D. (1971). A Further Note on Inductive Generalisation. In Meltzer B. & Michie, D. (eds.) Machine Intelligence 6, 101-124. Elsevier North-Holland/New York.

  • Pompe, U., Kovačič, M. & Kononenko, I. (1993). SFOIL: Stochastic Approach to Inductive Logic Programming. In Proceedings of the 2nd Slovenian Conference on Electrical Engineering and Computer Science (ERK-93), Vol. B, 189-192. Portorož, Slovenia.

    Google Scholar 

  • Quinlan, J. R. (1983). Learning Efficient Classification Procedures and Their Application to Chess End Games. In Michalski, R. S., Carbonell, J. G. & Mitchell, T. M. (eds.) Machine Learning. An Artificial Intelligence Approach, 463-482. Tioga: Palo Alto, CA.

    Google Scholar 

  • Quinlan, J. R. (1986). Induction of Decision Trees. Machine Learning 1: 81-106.

    Google Scholar 

  • Quinlan, J. R. (1987a). Generating Production Rules from Decision Trees. In Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI-87), 304-307. Morgan Kaufmann.

  • Quinlan, J. R. (1987b). Simplifying Decision Trees. International Journal of Man-Machine Studies 27: 221-234.

    Google Scholar 

  • Quinlan, J. R. (1990). Learning Logical Definitions from Relations. Machine Learning 5: 239-266.

    Google Scholar 

  • Quinlan, J. R. (1991). Determinate Literals in Inductive Logic Programming. In Proceedings of the 8th International Workshop on Machine Learning (ML-91), 442-446.

  • Quinlan, J. R. (1993). C4.5: Programs for Machine Learning. Morgan Kaufmann: San Mateo, CA.

    Google Scholar 

  • Quinlan, J. R. (1994). The Minimum Description Length Principle and Categorical Theories. In Cohen, W. & Hirsh, H. (eds.) Proceedings of the 11th International Conference on Machine Learning (ML-94), 233-241. Morgan Kaufmann: New Brunswick, NJ.

    Google Scholar 

  • Quinlan, J. R. (1996). Learning First-Order Definitions of Functions. Journal of Artificial Intelligence Research 5: 139-161.

    Google Scholar 

  • Quinlan, J. R. & Cameron-Jones, R. M. (1995a). Induction of Logic Programs: FOIL and Related Systems. New Generation Computing 13(3,4): 287-312. Special Issue on Inductive Logic Programming.

    Google Scholar 

  • Quinlan, J. R. & Cameron-Jones, R. M. (1995b). Oversearching and Layered Search in Empirical Learning. In Mellish, C. (ed.) Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95), 1019-1024. Morgan Kaufmann.

  • Rissanen, J. (1978). Modeling by Shortest Data Description. Automatica 14: 465-471.

    Google Scholar 

  • Rivest, R. L. (1987). Learning Decision Lists. Machine Learning 2: 229-246.

    Google Scholar 

  • Rouveirol, C. (1992). Extensions of Inversion of Resolution Applied to Theory Completion. In Muggleton, S. H. (ed.) Inductive Logic Programming, 63-92. Academic Press Ltd.: London.

    Google Scholar 

  • Rouveirol, C. (1994). Flattering and Saturation: Two Representation Changes for Generalization. Machine Learning 14: 219-232. Special Issue on Evaluating and Changing Representation.

    Google Scholar 

  • Saitta, L. & Bergadano, F. (1993). Pattern Recognition and Valiant's Learning Framework. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(2): 145-154.

    Google Scholar 

  • Schaffer, C. (1993). Overfitting Avoidance as Bias. Machine Learning 10: 153-178.

    Google Scholar 

  • Segal, R. & Etzioni, O. (1994). Learning Decision Lists Using Homogeneous Rules. In Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94), 619-625. AAAI Press: Cambridge, MA.

    Google Scholar 

  • Shapiro, E. Y. (1981). An Algorithm that Infers Theories from Facts. In Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI-81), 446-451.

  • Silverstein, G. & Pazzani, M. J. (1991). Relational Clichès: Constraining Constructive Induction During Relational Learning. In Proceedings of the 8th International Workshop on Machine Learning (ML-91), 203-207. Evanston, Illinois.

  • Silverstein, G. & Pazzani, M. J. (1993). Learning Relational Clichés. In Proceedings of the IJCAI-93 Workshop on Inductive Logic Programming, 71-82.

  • Srinivasan, A., Muggleton, S. H. & Bain, M. E. (1992). Distinguishing Noise from Exceptions in Non-Monotonic Learning. In Proceedings of the International Workshop on Inductive Logic Programming (ILP-92), 97-107. Tokyo, Japan.

  • Theron, H. & Cloete, I. (1996). BEXA: A Covering Algorithm for Learning Propositional Concept Descriptions. Machine Learning 24: 5-40.

    Google Scholar 

  • Utgoff, P. E. (1986). Shift of Bias for Inductive Concept Learning. In Michalski R., Carbonell, J. & Mitchell T. (eds.) Machine Learning: An Artificial Intelligence Approach, Vol. II, 107-148. Morgan Kaufmann: Los Altos, CA.

    Google Scholar 

  • Van Horn, K. S. & Martinez, T. R. (1993). The BBG Rule Induction Algorithm. In Proceedings of the 6th Australian Joint Conference on Artificial Intelligence, 348-355. Melbourne, Australia.

  • Vapnik, V. N. & Chervonenkis, Y. A. (1971). On the Uniform Convergence of Relative Frequencies to Their Probabilities. Theory of Probability and Its Applications 16: 264-280.

    Google Scholar 

  • Vapnik, V. N. & Chervonenkis, Y. A. (1981). Necessary and Sufficient Conditions for the Uniform Convergence of Means to Their Expectations. Theory of Probability and Its Applications 26: 532-553.

    Google Scholar 

  • Venturini, G. (1993). SIA: A Supervised Inductive Algorithm with Genetic Search for Learning Attributes Based Concepts. In Brazdil P (ed.), Proceedings of the 6th European Conference on Machine Learning (ECML-93), Vol. 667 of Lecture Notes in Artificial Intelligence, 280-296. Springer-Verlag: Vienna, Austria.

    Google Scholar 

  • Wallace, C. S. & Boulton, D. M. (1968). An Information Measure for Classification. Computer Journal 11: 185-194.

    Google Scholar 

  • Watanabe, L. & Rendell, L. (1991). Learning Structural Decision Trees from Examples. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), 770-776.

  • Webb, G. I. (1992). Learning Disjunctive Class Descriptions by Least Generalisation. Tech. rep. TR C92/9, Deakin University, School of Computing & Mathematics, Geelong, Australia.

    Google Scholar 

  • Webb, G. I. (1993). Systematic Search for Categorical Attribute-Value Data-Driven Machine Learning. In Rowles, C., Liu, H. & Foo, N. (eds.) Proceedings of the 6th Australian Joint Conference on Artificial Intelligence (AI '93), 342-347. World Scientific: Melbourne.

    Google Scholar 

  • Webb, G. I. (1994). Recent Progress in Learning Decision Lists by Prepending Inferred Rules. In Proceedings of the 2nd Singapore International Conference on Intelligent Systems, B280-B285.

  • Webb, G. I. (1995). OPUS: An Efficient Admissible Algorithm for Unordered Search. Journal of Artificial Intelligence Research 5: 431-465.

    Google Scholar 

  • Webb, G. I. & Agar, J. W. M. (1992). Inducing Diagnostic Rules for Glomerular Disease with the DLG Machine Learning Algorithm. Artificial Intelligence in Medicine 4: 419-430.

    Google Scholar 

  • Webb, G. I. & Brkič, N. (1993). Learning Decision Lists by Prepending Inferred Rules. In Proceedings of the AI '93 Workshop on Machine Learning and Hybrid Systems. Melbourne, Australia.

  • Weiss, S. M. & Indurkhya, N. (1991). Reduced Complexity Rule Induction. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), 678-684.

  • Weiss, S. M. & Indurkhya, N. (1993a). Optimized Rule Induction. IEEE Expert 8(6): 61-69.

    Google Scholar 

  • Weiss, S. M. & Indurkhya, N. (1993b). Rule-Based Regression. In Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), 1072-1078.

  • Weiss, S. M. & Indurkhya, N. (1995). Rule-Based Machine Learning Methods for Functional Prediction. Journal of Artificial Intelligence Research 3: 383-403.

    Google Scholar 

  • Widmer, G. (1993). Combining Knowledge-Based and Instance-Based Learning to Exploit Quantitative Knowledge. Informatica 17: 371-385. Special Issue on Multistrategy Learning.

    Google Scholar 

  • Wiese, M. (1996). A Bidirectional ILP Algorithm. In Proceedings of the MLnet Familiarization Workshop on Data Mining with Inductive Logic Programming (ILP for KDD), 61-72.

  • Wnek, J. & Michalski, R. S. (1994). Hypothesis-Driven Constructive Induction in AQ17-HCI: A Method and Experiments. Machine Learning 14(2): 139-168. Special Issue on Evaluating and Changing Representation.

    Google Scholar 

  • Wolpert, D. H. (1993). On Overfitting Avoidance as Bias. Tech. rep. SFI TR 92-03-5001. The Santa Fe Institute, Santa Fe, NM.

    Google Scholar 

  • Zelle, J. M., Mooney, R. J. & Konvisser, J. B. (1994). Combining Top-Down and Bottom-Up Techniques in Inductive Logic Programming. In Cohen, W. & Hirsh, H. (eds.) Proceedings of the 11th International Conference on Machine Learning (ML-94), 343-351. Morgan Kaufmann: New Brunswick, NJ.

    Google Scholar 

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  1. Johannes Fürnkranz

    Present address: Austrian Research Institute for Artificial Intelligence, Schottengasse 3, A-1010, Wien, Austria

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    Fürnkranz, J. Separate-and-Conquer Rule Learning. Artificial Intelligence Review 13, 3–54 (1999). https://doi.org/10.1023/A:1006524209794

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