Abstract
The distribution-independent model of (supervised) concept learning due to Valiant (1984) is extended to that of semi-supervised learning (ss-learning), in which a collection of disjoint concepts is to be simultaneously learned with only partial information concerning concept membership available to the learning algorithm. It is shown that many learnable concept classes are also ss-learnable. A new technique of learning, using an intermediate oracle, is introduced. Sufficient conditions for a collection of concept classes to be ss-learnable are given.
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Anderberg, M. (1973). Cluster analysis for applications. New York: Academic Press.
Angluin, D. (1987). Learning regular sets from queries and counterexamples. Information and Com-putation, 75, 87-106.
Angluin, D. (1988a). Queries and concept learning. Machine Learning, 2, 319-342.
Angluin, D. (1988b). Learning with hints. Proceedings of the 1988 Workshop on Computational Learning Theory (pp. 167-181). Cambridge, MA: Morgan Kaufmann.
Angluin, D. (1988c). Negative results for equivalence queries. (Technical Report YALEU/DCS/RR-648). New Haven, Connecticut: Yale University, Department of Computer Science.
Angluin, D. (1988d). Equivalence queries and DNF formulas. (Technical Report YALEU/DCS/RR-659). New Haven, Connecticut: Yale University, Department of Computer Science.
Berman, P., & Roos, R. (1987). Learning one-counter languages in polynomial time. Proceedings of the 28th IEEE Symposium on Foundations of Computer Science (pp. 61-67). Los Angeles: IEEE Computer Society Press.
Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. (1986). Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension. Proceedings of the 18th Annual ACM Symposium on Theory of Computation (pp. 273-282). Berkeley, CA: Association for Computing Machinery.
Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. (1987). Learnability and the Vapnik-Chervonenkis dimension. (Technical Report UCSC-CRL-87-20). Santa Cruz, CA: University of California, Santa Cruz.
Carbonell, J. G., Michalski, R. S. & Mitchell, T. M. (1983). An overview of machine learning. In R. S. Michalski, J. G. Carbonell & T. M. Mitchell (Eds. ), Machine learning: An artificial intelligence approach. Palo Alto, CA: Tioga Press.
Duda, R., & Hart, P. (1973). Pattern classification and scene analysis. New York: John Wiley & Sons.
Garey, M., & Johnson, D. (1979). Computers and intractability: A guide to the theory of NP-complete-ness. San Francisco: W. H. Freeman.
Hartigan, J. (1975). Cluster algorithms. New York: John Wiley & Sons.
Haussler, D. (1988). Quantifying inductive bias: AI learning algorithms and Valiant's learning frame-work. Artificial Intelligence, 36, 177-221.
Haussler, D., Kearns, M., Littlestone, N., & Warmuth, M. (1988). Equivalence of models for poly-nomial learnability. Proceedings of the 1988 Workshop on Computational Learning Theory (pp. 42-55). Cambridge, MA: Morgan Kaufmann.
Haussler, D., Littlestone, N., & Warmuth, M. (1988). Predicting 0, 1 functions on randomly drawn points. Proceedings of the 29th Annual Symposium on Foundations of Computer Science (pp. 100-109). White Plains, NY: IEEE Computer Society Press.
Kearns, M., Li, M., Pitt, L., & Valiant, L. G. (1987a). On the learnability of Boolean formulae. Proceedings of the 19th Annual ACM Symposium on Theory of Computing (pp. 285-295). New York: Assoc. Comp. Mach.
Kearns, M., Li, M., Pitt, L., & Valiant, L. G. (1987b). Recent results on Boolean concept learning. Proceedings of the Fourth International Workshop on Machine Learning. Irvine, CA: Morgan Kaufmann.
Littlestone, N. (1988). Learning quickly when irrelevant attributes abound: a new linear threshold algorithm. Machine Learning, 2, 285-319.
Natarajan, B. K. (1987). On learning Boolean functions. Proceedings of the 19th Annual ACM Sym-posium on Theory of Computing (pp. 296-304). New York: Assoc. Comput. Mach.
Pitt, L., & Valiant, L. G. (1988). Computational limitations on learning from examples. Journal of the ACM, 35, 965-984.
Pitt, L., & Warmuth, M. K. (1988). Reductions among prediction problems: on the difficulty of predicting automata. Proceedings of the Third Annual Conference on Structure in Complexity Theory (pp. 60-69). Washington, D. C.: IEEE Computer Society Press.
Rivest, R. (1987). Learning decision-lists. Machine Learning, 2, 229-246.
Romesburg, H. (1984). Cluster analysis for researchers. Belmont, CA: Lifetime Learning.
Valiant, L. G. (1984). A theory of the learnable. CACM, 27, 1134-1142.
Valiant, L. G. (1985). Learning disjunctions of conjunctions. Proceedings of the Ninth International Joint Conference on Artificial Intelligence(pp. 560-566), Los Angeles, CA: Morgan Kaufmann.
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Board, R., Pitt, L. Semi-Supervised Learning. Machine Learning 4, 41–65 (1989). https://doi.org/10.1023/A:1022653227824
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DOI: https://doi.org/10.1023/A:1022653227824