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11 ANALYTICAL LEARNING
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Newell, A (1990) Unified theories of cognition Cambridge, MA: Harvard University Press Qin, Y, Mitchell, T, & Simon, H (1992) Using explanation-based generalization to simulate human learning from examples and learning by doing Proceedings of the Florida A1 Research Symposium (pp 235-239) Ram, A, & Leake, D B (Eds) (1995) Goal-driven learning Cambridge, MA: MIT Press Rosenblwm, P, & Laird, J (1986) Mapping explanation-based generalization onto SOARFifih National Conference on Artificial Intelligence (pp 561-567) AAAI Press Russell, S (1989) The use of knowledge in analogy and induction San Francisco: Morgan Kaufmann Shavlik, J W (1990) Acquiring recursive and iterative concepts with explanation-based learning Machine Learning, 5, 39 Silver, B (1983) Learning equation solving methods from worked examples Proceedings of the I983 International Workshop on Machine Learning (pp 99-104) CS Department, University of Illinois at Urbana-Champaign Silver, B (1986) Precondition analysis: Learning control information In R Michalski et al (Eds), Machine Learning: An AI approach (pp 647470) San Mateo, CA Morgan Kaufmann Soloway, E (1977) Knowledge directed learning using multiple levels of description (PhD thesis) University of Massachusetts, Arnherst Tadepalli, P (1990) Tractable learning and planning in games (Technical report ML-TR-31) (PhD dissertation) Rutgers University Computer Science Department Tambe, M, Newell, A, & Rosenbloom, P S (1990) The problem of expensive chunks and its solution by restricting expressiveness Machine Learning, 5(4), 299-348 Waldinger, R (1977) Achieving several goals simultaneously In E Elcock & D Michie Pds), Machine Intelligence 8 London: Ellis Horwood Ltd Winston, P, Binford, T, Katz, B, & Lowry, M (1983) Learning physical descriptions from functional definitions, examples, and precedents Proceedings of the National Conference on Artijcial Intelligence (pp 433-439) san Mateo, CA: Morgan Kaufmann Wisniewski, E J, & Medin, D L (1995) Harpoons and long sticks: The interaction of theory and similarity in rule induction In A Ram & D B Leake (Eds), Goal-driven learning @p 177-210) Cambridge, MA: MIT Press
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Purely inductive learning methods formulate general hypotheses by finding empirical regularities over the training examples Purely analytical methods use prior knowledge to derive general hypotheses deductively,This chapter considers methods that combine inductive and analytical mechanisms to obtain the benefits of both approaches: better generalization accuracy when prior knowledge is available and reliance on observed training data to overcome shortcomings in prior knowledge The resulting combined methods outperform both purely inductive and purely analytical learning methods This chapter considers inductive-analytical learning methods based on both symbolic and artificial neural network representations
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In previous chapters we have seen two paradigms for machine learning: inductive learning and analytical learning Inductive methods, such as decision tree induction and neural network BACKPROPAGATION, general hypotheses that fit the seek observed training data Analytical methods, such as PROLOG-EBG, seek general hypotheses that fit prior knowledge while covering the observed data These two learning paradigms are based on fundamentally different justifications for learned hypotheses and offer complementary advantages and disadvantages Combining them offers the possibility of more powerful learning methods
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Purely analytical learning methods offer the advantage of generalizing more accurately from less data by using prior knowledge to guide learning However, they can be misled when given incorrect or insufficient prior knowledge Purely inductive methods offer the advantage that they require no explicit prior knowledge and learn regularities based solely on the training data However, they can fail when given insufficient training data, and can be misled by the implicit inductive bias they must adopt in order to generalize beyond the observed data Table 121 summarizes these complementary advantages and pitfalls of inductive and analytical learning methods This chapter considers the question of how to combine the two into a single algorithm that captures the best aspects of both The difference between inductive and analytical learning methods can be seen in the nature of the justiJications that can be given for their learned hypotheses Hypotheses output by purely analytical learning methods such as PROLOGEBG carry a logical justification; the output hypothesis follows deductively from the domain theory and training examples Hypotheses output by purely inductive carry learning methods such as BACKPROPAGATION a statistical justification; the output hypothesis follows from statistical arguments that the training sample is sufficiently large that it is probably representative of the underlying distribution of examples This statistical justification for induction is clearly articulated in the PAC-learning results discussed in 7 Given that analytical methods provide logically justified hypotheses and inductive methods provide statistically justified hypotheses, it is easy to see why combining them would be useful: Logical justifications are only as compelling as the assumptions, or prior knowledge, on which they are built They are suspect or powerless if prior knowledge is incorrect or unavailable Statistical justifications are only as compelling as the data and statistical assumptions on which they rest They are suspect or powerless when assumptions about the underlying distributions cannot be trusted or when data is scarce In short, the two approaches work well for different types of problems By combining them we can hope to devise a more general learning approach that covers a more broad range of learning tasks Figure 121 summarizes a spectrum of learning problems that varies by the availability of prior knowledge and training data At one extreme, a large volume
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