Abstract
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.
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Grieser, G., Lange, S., Zeugmann, T. (2000). Learning Recursive Concepts with Anomalies. In: Arimura, H., Jain, S., Sharma, A. (eds) Algorithmic Learning Theory. ALT 2000. Lecture Notes in Computer Science(), vol 1968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40992-0_8
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DOI: https://doi.org/10.1007/3-540-40992-0_8
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