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 ...

• Type: Conference
• Year: 2010
• Where: ALT
• Authors: Thorsten Doliwa, Hans-Ulrich Simon, Sandra Zilles
• Keywords: ALT 2010, Combinatorial Structure, Concept Classes, Machine Learning, Recursive Teaching Dimension