This paper provides a systematic study of inductive inference of indexable concept classes in learning scenarios in which the learner is successful if its final hypothesis describes a finite variant of the target concept-henceforth called learning with anomalies. As usual, we distinguish between learning from only positive data and learning from positive and negative data. We investigate the following learning models: finite identification, conservative inference, set-driven learning, and behaviorally correct learning. In general, we focus our attention on the case that the number of allowed anomalies is finite but not a priori bounded. However, we also present a few sample results that affect the special case of learning with an a priori bounded number of anomalies. We provide characterizations of the corresponding models of learning with anomalies in terms of finite tell-tale sets. The varieties in the degree of recursiveness of the relevant tell-tale sets observed are already sufficient to quantify the differences in the corresponding models of learning with anomalies. In addition, we study variants of incremental learning and derive a complete picture concerning the relation of all models of learning with and without anomalies mentioned above.
CITATION STYLE
Grieser, G., Lange, S., & Zeugmann, T. (2000). Learning recursive concepts with anomalies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1968, pp. 101–115). Springer Verlag. https://doi.org/10.1007/3-540-40992-0_8
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