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ALT
2010
Springer

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

11 years 6 months ago
Recursive Teaching Dimension, Learning Complexity, and Maximum Classes
This paper is concerned with the combinatorial structure of concept classes that can be learned from a small number of examples. We show that the recently introduced notion of recursive teaching dimension (RTD, reflecting the complexity of teaching a concept class) is a relevant parameter in this context. Comparing the RTD to self-directed learning, we establish new lower bounds on the query complexity for a variety of query learning models and thus connect teaching to query learning. For many general cases, the RTD is upper-bounded by the VC-dimension, e.g., classes of VC-dimension 1, (nested differences of) intersection-closed classes, "standard" boolean function classes, and finite maximum classes. The RTD thus is the first model to connect teaching to the VC-dimension. The combinatorial structure defined by the RTD has a remarkable resemblance to the structure exploited by sample compression schemes and hence connects teaching to sample compression. Sequences of teaching ...
Thorsten Doliwa, Hans-Ulrich Simon, Sandra Zilles
Added 06 Dec 2010
Updated 06 Dec 2010
Type Conference
Year 2010
Where ALT
Authors Thorsten Doliwa, Hans-Ulrich Simon, Sandra Zilles
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